Reading 1 Multiple Regression - Answers

Question #1 of 144 Question ID: 1586011 An analyst is estimating whether company sales is related to three economic variables. The regression exhibits conditional heteroskedasticity, serial correlation, and multicollinearity. The analyst uses White and Newey-West corrected standard errors. Which of the following is most accurate? A) B) C) The regression will still exhibit heteroskedasticity and multicollinearity, but the serial correlation problem will be solved. The regression will still exhibit multicollinearity, but the heteroskedasticity and serial correlation problems will be solved. The regression will still exhibit serial correlation and multicollinearity, but the heteroskedasticity problem will be solved. Explanation The correction mentioned solves for heteroskedasticity and serial correlation. (Module 1.3, LOS 1.i) Question #2 of 144 Question ID: 1471868 Consider the following estimated regression equation, with the standard errors of the slope coefficients as noted: Salesi = 10.0 + 1.25 R&Di + 1.0 ADVi – 2.0 COMPi + 8.0 CAPi where the standard error for the estimated coefficient on R&D is 0.45, the standard error for the estimated coefficient on ADV is 2.2 , the standard error for the estimated coefficient on COMP is 0.63, and the standard error for the estimated coefficient on CAP is 2.5. The equation was estimated over 40 companies. Using a 5% level of significance, which of the estimated coefficients are significantly different from zero? A) ADV and CAP only. B) R&D, ADV, COMP, and CAP. C) R&D, COMP, and CAP only. Explanation The critical t-values for 40-4-1 = 35 degrees of freedom and a 5% level of significance are ± 2.03. The calculated t-values are: t for R&D = 1.25 / 0.45 = 2.777 t for ADV = 1.0/ 2.2 = 0.455 t for COMP = -2.0 / 0.63 = -3.175 t for CAP = 8.0 / 2.5 = 3.2 Therefore, R&D, COMP, and CAP are statistically significant. (Module 1.1, LOS 1.b) Question #3 of 144 Question ID: 1479906 Which of the following is least likely a method used to detect heteroskedasticity? A) Scatter plot. B) Breusch-Pagan test. C) Breusch-Godfrey test. Explanation The Breusch-Godfrey test is used to detect serial correlation. The Breusch-Pagan test is a formal test used to detect heteroskedasticity while a scatter plot can give visual clues about presence of heteroscedasticity. (Module 1.3, LOS 1.h) Question #4 of 144 Question ID: 1479913 One of the main assumptions of a multiple regression model is that the variance of the residuals is constant across all observations in the sample. A violation of the assumption is most likely to be described as: A) unstable remnant deviation. B) positive serial correlation. C) heteroskedasticity. Explanation Heteroskedasticity is present when the variance of the residuals is not the same across all observations in the sample, and there are sub-samples that are more spread out than the rest of the sample. (Module 1.3, LOS 1.h) Question #5 of 144 Question ID: 1479918 During the course of a multiple regression analysis, an analyst has observed several items that she believes may render incorrect conclusions. For example, the coefficient standard errors are too small, although the estimated coefficients are accurate. She believes that these small standard error terms will result in the computed t-statistics being too big, resulting in too many Type I errors. The analyst has most likely observed which of the following assumption violations in her regression analysis? A) Positive serial correlation. B) Homoskedasticity. C) Multicollinearity. Explanation Positive serial correlation is the condition where a positive regression error in one time period increases the likelihood of having a positive regression error in the next time period. The residual terms are correlated with one another, leading to coefficient error terms that are too small. (Module 1.3, LOS 1.i) Question #6 - 11 of 144 Question ID: 1471914 Using the regression model developed, the closest prediction of sales for December 20x6 is: A) $44,000. B) $36,000. C) $55,000. Explanation 1.76 + 0.23 * (150) − 0.08 * (7.5) = 35.66. (Module 1.1, LOS 1.b) Question #7 - 11 of 144 Question ID: 1471915 Will Stumper conclude that the housing starts coefficient is statistically different from zero and how will he interpret it at the 5% significance level: A) not different from zero; sales will rise by $0 for every 100 house starts. B) different from zero; sales will rise by $100 for every 23 house starts. C) different from zero; sales will rise by $23 for every 100 house starts. Explanation A p-value (0.017) below significance (0.05) indicates a variable which is statistically different from zero. The coefficient of 0.23 indicates that sales will rise by $23 for every 100 house starts. (Module 1.1, LOS 1.b) Question #8 - 11 of 144 Question ID: 1585998 Is the regression coefficient of changes in mortgage interest rates different from zero at the 5 percent level of significance? A) no, because coefficient is negative. B) yes, because p-value < 0.05. C) yes, because -0.08 < 0.05. Explanation A coefficient is statistically significantly different from zero if its p-value is less than the level of significance. (Module 1.1, LOS 1.b) Question #9 - 11 of 144 Question ID: 1471917 In this multiple regression, the F-statistic indicates the: A) degree of correlation between the independent variables. B) deviation of the estimated values from the actual values of the dependent variable. C) the joint significance of the independent variables. Explanation The F-statistic indicates the joint significance of the independent variables. The deviation of the estimated values from the actual values of the dependent variable is the standard error of estimate. The degree of correlation between the independent variables is the coefficient of correlation. (Module 1.1, LOS 1.b) Question #10 - 11 of 144 Question ID: 1471918 The regression statistics above indicate that for the period under study, the independent variables (housing starts, mortgage interest rate) together explained approximately what percentage of the variation in the dependent variable (sales)? A) 9.80. B) 67.00. C) 77.00. Explanation The question is asking for the coefficient of determination. (Module 1.1, LOS 1.b) Question #11 - 11 of 144 Question ID: 1585999 In this multiple regression, if Stumper discovers that the residuals exhibit positive serial correlation, the most likely effect is: A) standard errors are not affected but coefficient estimate is inconsistent. B) standard errors are too low but coefficient estimate is consistent. C) standard errors are too high but coefficient estimate is consistent. Explanation Positive serial correlation in residuals does not affect the consistency of coefficients (i.e., the coefficients are still consistent) but the estimated standard errors are too low leading to artificially high t-statistics. (Module 1.1, LOS 1.b) Question #12 of 144 Question ID: 1586006 Consider the following estimated regression equation: AUTOt = 10.0 + 1.25 PIt + 1.0 TEENt – 2.0 INSt The equation was estimated over 40 companies. The predicted value of AUTO if PI is 4, TEEN is 0.30, and INS = 0.6 is closest to: A) 14.90. B) 14.10. C) 17.50. Explanation Predicted AUTO = 10 + 1.25 (4) + 1.0 (0.30) – 2.0 (0.6) = 10 + 5 + 0.3 – 1.2 = 14.10 (Module 1.2, LOS 1.f) Question #13 - 16 of 144 Question ID: 1501597 Salve runs a regression using the squared residuals from the model using the original dependent variables. The coefficient of determination of this model is 6%. Which of the following is the most appropriate conclusion at a 5% level of significance? A) B) C) Because the test statistic of 7.20 is higher than the critical value of 3.84, we reject the null hypothesis of no conditional heteroskedasticity in residuals. Because the test statistic of 7.20 is lower than the critical value of 7.81, we fail to reject the null hypothesis of no conditional heteroskedasticity in residuals. Because the test statistic of 3.60 is lower than the critical value of 3.84, we reject the null hypothesis of no conditional heteroskedasticity in residuals. Explanation The chi-square test statistic = n × R2 = 120 × 0.06 = 7.20. The one-tailed critical value for a chi-square distribution with k = 3 degrees of freedom and α of 5% is 7.81. Therefore, we should not reject the null hypothesis and conclude that we don't have a problem with conditional heteroskedasticity. (Module 1.3, LOS 1.h) Question #14 - 16 of 144 Question ID: 1501598 Which of the following misspecifications is most likely to cause serial correlation in residuals? A) Data improperly pooled. B) Improper variable scaling. C) Improper variable form. Explanation Out of the four forms of model misspecifications, serial correlation in residuals may be caused by omission of important variables (not an answer choice) and by improper data pooling. (Module 1.3, LOS 1.g) Question #15 - 16 of 144 Question ID: 1501599 Should Salve be concerned about residual serial correlation? A) Yes, for one lag only. B) Yes, for two lags only. C) No. Explanation The BG test statistic has an F-distribution with p and n – p – k – 1 degrees of freedom, where p = the number of lags tested. Given n = 120 and k = 3, critical F-values (5% level of significance) are 3.92 (p = 1) and 3.08 (p = 2). BG stats in Indian Equities—Fama-French Model are lower than the critical F-values; therefore, serial correlation does not seem to be a problem for both lags. (Module 1.3, LOS 1.i) Question #16 - 16 of 144 Question ID: 1501600 Should Salve be concerned about residual multicollinearity? A) Yes, and Salve should exclude either variable SMB or HML from the model. B) Yes, and Salve should exclude variable Rm-Rf from the model. C) No. Explanation Multicollinearity is detected using the variance inflation factor (VIF). VIF values greater than 5 (i.e., R2 > 80%) warrant further investigation, while values above 10 (i.e., R2 > 90%) indicate severe multicollinearity. None of the variables have VIF > 5. (Module 1.3, LOS 1.j) Question #17 of 144 Question ID: 1479903 When constructing a regression model to predict portfolio returns, an analyst runs a regression for the past five year period. After examining the results, she determines that an increase in interest rates two years ago had a significant impact on portfolio results for the time of the increase until the present. By performing a regression over two separate time periods, the analyst would be attempting to prevent which type of misspecification? A) Incorrectly pooling data. B) Inappropriate variable scaling. C) Inappropriate variable form. Explanation The relationship between returns and the dependent variables can change over time, so it is critical that the data be pooled correctly. Running the regression for multiple sub-periods (in this case two) rather than one time period can produce more accurate results. (Module 1.3, LOS 1.g) Question #18 - 20 of 144 Question ID: 1471907 Concerning the assumptions of multiple regression, Grimbles is: A) correct to agree with Voiku’s list of assumptions. B) incorrect to agree with Voiku’s list of assumptions because one of the assumptions is stated incorrectly. C) incorrect to agree with Voiku’s list of assumptions because two of the assumptions are stated incorrectly. Explanation Assumption 2 is stated incorrectly. Some correlation between independent variables is unavoidable; and high correlation results in multicollinearity. However, an exact linear relationship between linear combinations of two or more independent variables should not exist. Assumption 4 is also stated incorrectly. The assumption is that the residuals are serially uncorrelated (i.e., they are not serially correlated). (Module 1.1, LOS 1.b) Question #19 - 20 of 144 Question ID: 1471909 The most appropriate decision with regard to the F-statistic for testing the null hypothesis that all of the independent variables are simultaneously equal to zero at the 5 percent significance level is to: A) B) C) reject the null hypothesis because the F-statistic is larger than the critical F-value of 2.66. reject the null hypothesis because the F-statistic is larger than the critical F-value of 3.19. fail to reject the null hypothesis because the F-statistic is smaller than the critical Fvalue of 2.66. Explanation RSS = 368.7 – 140.3 = 228.4, F-statistic = (228.4 / 3) / (140.3 / 176) = 95.51. The critical value for a one-tailed 5% F-test with 3 and 176 degrees of freedom is 2.66. Because the F-statistic is greater than the critical F-value, the null hypothesis that all of the independent variables are simultaneously equal to zero should be rejected. (Module 1.1, LOS 1.b) Question #20 - 20 of 144 The multiple regression, as specified, most likely suffers from: Question ID: 1585996 A) heteroskedasticity. B) multicollinearity. C) serial correlation of the error terms. Explanation The regression is highly significant (based on the F-stat in Part 3), but the individual coefficients are not (all p-values > 0.05). This is a result of a regression with significant multicollinearity problems. (Module 1.1, LOS 1.b) Question #21 of 144 Question ID: 1586002 Which of the following statements regarding the R2 is least accurate? A) The R2 of a regression will be greater than or equal to the adjusted-R2 for the same regression. B) R2 is the coefficient of determination of the regression. C) The R2 is the ratio of the unexplained variation to the explained variation of the dependent variable. Explanation The R2 is the ratio of the explained variation to the total variation. (Module 1.2, LOS 1.d) Question #22 - 26 of 144 Question ID: 1472050 Using the regression model developed, the closest prediction of sales for December 20X6 is: A) $36,000. B) $55,000. C) $44,000. Explanation 1.76 + 0.23 × (150) – 0.08 × (7.5) = 35.66. (Module 1.2, LOS 1.f) Question #23 - 26 of 144 Question ID: 1489312 Will Jack conclude that the housing starts coefficient is statistically different from zero and how will he interpret it at the 5% significance level? A) Different from zero; sales will rise by $100 for every 23 house starts. B) Not different from zero; sales will rise by $0 for every 100 house starts. C) Different from zero; sales will rise by $23 for every 100 house starts. Explanation A p-value (0.017) below significance (0.05) indicates a variable that is statistically different from zero. The coefficient of 0.23 indicates that sales will rise by $23 for every 100 house starts. Remember the rule p-value < significance, then reject null. (Module 1.1, LOS 1.b) Question #24 - 26 of 144 Question ID: 1479916 In this multiple regression, the F-statistic indicates the: A) the joint significance of the independent variables. B) degree of correlation between the independent variables. C) deviation of the estimated values from the actual values of the dependent variable. Explanation The F-statistic is for the general linear F-test to test the null hypothesis that slope coefficients on all variables are equal to zero. (Module 1.2, LOS 1.e) Question #25 - 26 of 144 Question ID: 1472054 The regression statistics indicate that for the period under study, the independent variables (housing starts, mortgage interest rate) together explain approximately what percentage of the variation in the dependent variable (sales)? A) 67.00. B) 9.80. C) 77.00. Explanation The question is asking for the coefficient of determination. (Module 1.2, LOS 1.d) Question #26 - 26 of 144 Question ID: 1484386 For this question only, assume that the regression of squared residuals on the independent variables has R2 = 11%. At a 5% level of significance, which of the following conclusions is most accurate? A) B) C) Because the critical value is 3.84, we reject the null hypothesis of no conditional heteroskedasticity. With a test statistic of 13.53, we can conclude the presence of conditional heteroskedasticity. With a test statistic of 0.22, we cannot reject the null hypothesis of no conditional heteroskedasticity. Explanation Chi-square = n × R2 = 123 × 0.11 = 13.53. Critical Chi-square (degree of freedom = k = 2) = 5.99. Because the test statistic exceeds the critical value, we reject the null hypothesis (of no conditional heteroskedasticity). (Module 1.3, LOS 1.h) Question #27 - 31 of 144 Question ID: 1636800 Which model would be a better choice for making a forecast? A) Model TWO because it has a higher adjusted R2. B) Model TWO because serial correlation is not a problem. C) Model ONE because it has a higher R2. Explanation Model TWO has a higher adjusted R2 and thus would produce the more reliable estimates. As is always the case when a variable is removed, R2 for Model TWO is lower. The increase in adjusted R2 indicates that the removed variable, Q3, has very little explanatory power, and removing it should improve the accuracy of the estimates. (Module 1.2, LOS 1.d) Question #28 - 31 of 144 Question ID: 1479951 Using Model ONE, what is the sales forecast for the second quarter of the next year? A) $51.09 million. B) $46.31 million. C) $56.02 million. Explanation The estimate for the second quarter of the following year would be (in millions): 31.4083 + (−2.4631) + (24 + 2) × 0.851786 = 51.091666. (Module 1.2, LOS 1.f) Question #29 - 31 of 144 Which model misspecification is most likely to cause multicollinearity? A) Inappropriate variable form. Question ID: 1479952 B) Ommission of important variable(s). C) Inappropriate variable scaling. Explanation Inappropriate variable scaling may lead to multicollinearity or heteroskedasticity in residuals. Omission of important variable may lead to biased and inconsistent regression parameters and also heteroskedasticity/serial correlation in residuals. Inappropriate variable form can lead to heteroskedasticity in residuals. (Module 1.3, LOS 1.g) Question #30 - 31 of 144 Question ID: 1479953 If it is determined that conditional heteroskedasticity is present in model one, which of the following inferences are most accurate? A) Regression coefficients will be unbiased but standard errors will be biased. B) Both the regression coefficients and the standard errors will be biased. C) Regression coefficients will be biased but standard errors will be unbiased. Explanation Presence of conditional heteroskedasticity will not affect the consistency of regression coefficients but will bias the standard errors leading to incorrect application of t-tests for statistical significance of regression parameters. (Module 1.3, LOS 1.h) Question #31 - 31 of 144 Question ID: 1479955 If Mercado determines that Model TWO is the appropriate specification, then he is essentially saying that for each year, value of sales from quarter three to four is expected to: A) grow by more than $1,000,000. B) remain approximately the same. C) grow, but by less than $1,000,000. Explanation The specification of Model TWO essentially assumes there is no difference attributed to the change of the season from the third to fourth quarter. However, the time trend is significant. The trend effect for moving from one season to the next is the coefficient on TREND times $1,000,000 which is $852,182 for Equation TWO. (Module 1.1, LOS 1.b) Question #32 - 34 of 144 Question ID: 1710719 What is the correct interpretation of the coefficient of closed in the first regression? A) If a model is closed to new investors, the expected excess fund return is 1.65%. B) A closed fund is likely to generate a return of 1.65%. C) A closed fund is estimated to have an extra return of 1.65% relative to funds that are not closed. Explanation The interpretation of the coefficient is the extra return relative to the alternative outcome. (Module 1.4, LOS 1.l) Question #33 - 34 of 144 Question ID: 1710720 To check for only the outliers in the sample, Lee should most appropriately use: A) Studentized residuals. B) leverage. C) Breusch-Pagan statistic. Explanation Outliers are extreme observations of the dependent variable. Studentized residuals are used to identify outliers. Leverage is used to identify high-leverage observations (in the independent variable),The Breusch-Pagan test statistic is used to identify conditional heteroskedasticity in residuals. (Module 1.4, LOS 1.k) Question #34 - 34 of 144 Question ID: 1710721 Which of the following is least accurate statement about logit models? A) Logistic regression (logit) models use log odds as the dependent variable. B) A logit model assumes that residuals have a normal distribution. C) The coefficients of the logit model are estimated using the maximum likelihood estimation methodology. Explanation A logit model assumes that residuals have a logistic distribution, which is similar to a normal distribution but with fatter tails. The other statements are correct. (Module 1.4, LOS 1.m) Question #35 - 38 of 144 Regarding Sophie's statement on multiple regression: A) only Statement 1 is correct. B) only Statement 2 is correct. C) both statements are correct. Explanation Question ID: 1501587 Multiple regression models can be used to identify relations between variables, forecast the dependent variable, and test existing theories. Statement 1 is inaccurate in because it mentions forecast independent (and not dependent) variables. (Module 1.1, LOS 1.a) Question #36 - 38 of 144 Question ID: 1501588 Based on the credit spread model, if an issuer gets included in the CDX index and assuming everything else the same, which of the following statements most accurately describes the model's forecast? A) The credit spread on the firm’s issue would decrease by 10 bps. B) The credit spread on the firm’s issue will increase by 32 bps. C) The credit spread on the firm’s issue will decrease by 32 bps. Explanation The coefficient on the index dummy variable is –0.32, and if the variable takes a value of 1 (inclusion in the index), the credit spread would decrease by 0.32%, or 32 bps. (Module 1.1, LOS 1.b) Question #37 - 38 of 144 Question ID: 1501589 Which of the following is least likely an assumption of multiple linear regression? A) The dependent variable is not serially correlated. B) There is no linear relationship between the independent variables. C) The error term is normally distributed. Explanation The assumption calls for the residual (or errors) to be not serially correlated. The dependent variable can have serial correlation. Other assumptions are accurate. (Module 1.1, LOS 1.c) Question #38 - 38 of 144 Question ID: 1501590 Which assumption of multiple regression is most likely evaluated using a QQ plot? A) Serial correlation of residuals. B) Conditional heteroskedasticity. C) Error term is normally distributed. Explanation A normal QQ plot of the residuals can visually indicate violation of the assumption that the residuals are normally distributed. (Module 1.1, LOS 1.c) Question #39 of 144 Question ID: 1479867 Jason Fye, CFA, wants to check for seasonality in monthly stock returns (i.e., the January effect) after controlling for market cap and systematic risk. The type of model that Fye would most appropriately select is: A) Neither multiple regression nor logistic regression. B) Multiple regression model. C) logistic regression model. Explanation Fye wants to test a theory of January effect on stock returns (dependent variable) using a dummy (January = 1, other months = 0), market cap, and beta (independent variables). A multiple regression model would be most appropriate. Because the dependent variable (stock returns) is not a qualitative variable, a logistic regression would not apply. (Module 1.1, LOS 1.a) Question #40 of 144 Question ID: 1630876 One choice a researcher can use to test for nonstationarity is to use a: A) Breusch-Pagan test, which uses a modified t-statistic. B) Dickey-Fuller test, which uses a modified t-statistic. C) Dickey-Fuller test, which uses a modified χ2 statistic. Explanation The Dickey-Fuller test estimates the equation (xt – xt-1) = b0 + (b1 - 1) * xt-1 + et and tests if H0: (b1 – 1) = 0. Using a modified t-test, if it is found that (b1– 1) is not significantly different from zero, then it is concluded that b1 must be equal to 1.0 and the series has a unit root. (Module 1.3, LOS 1.h) Question #41 - 45 of 144 Question ID: 1471970 According to the model and the data for the Chicago metropolitan area, the forecast of generator sales is: A) $65 million above the average. B) $35.2 million above the average. C) $55 million above average. Explanation The model uses a multiple regression equation to predict sales by multiplying the estimated coefficient by the observed value to get: [5 + (2 × 0.10) + (3 × 5) + (10 × 3) + (5 × (−3))] × $1,000,000 = $35.2 million. (Module 1.2, LOS 1.e) Question #42 - 45 of 144 Question ID: 1479876 Williams proceeds to test the hypothesis that none of the independent variables has significant explanatory power. Using the joint F-test for the significance of all slope coefficients, at a 5% level of significance: A) all of the independent variables have explanatory power. B) none of the independent variables has explanatory power. C) at least one of the independent variables has explanatory power. Explanation From the ANOVA table, the calculated F-statistic is (mean square regression / mean square error) = (83.80 / 28.88) = 2.9017. From the F distribution table (4 df numerator, 21 df denominator) the critical F value is 2.84. Because 2.9017 is greater than 2.84, Williams rejects the null hypothesis and concludes that at least one of the independent variables has explanatory power. (Module 1.2, LOS 1.e) Question #43 - 45 of 144 Question ID: 1479877 With respect to testing the validity of the model's results, Williams may wish to perform: A) both a Breusch-Godfrey test and a Breusch-Pagan test. B) a Breusch-Pagan test, but not Breusch-Godfrey. C) a Breusch-Godfrey test, but not a Breusch-Pagan test. Explanation Since the model utilized is not an autoregressive time series, a test for serial correlation is appropriate so the Breusch-Godfrey test would be used. The Breusch-Pagan test for heteroskedasticity would also be a good idea. (Module 1.2, LOS 1.e) Question #44 - 45 of 144 Question ID: 1471974 When Williams ran the model, the computer said the R2 is 0.233. She examines the other output and concludes that this is the: A) neither the unadjusted nor adjusted R2 value, nor the coefficient of correlation. B) unadjusted R2 value. C) adjusted R2 value. Explanation This can be answered by recognizing that the unadjusted R-square is (335.2 / 941.6) = 0.356. Thus, the reported value must be the adjusted R2. To verify this we see that the adjusted Rsquared is: 1− ((26 − 1) / (26 − 4 − 1)) × (1 − 0.356) = 0.233. Note that whenever there is more than one independent variable, the adjusted R2 will always be less than R2. (Module 1.2, LOS 1.e) Question #45 - 45 of 144 Question ID: 1471975 In preparing and using this model, Williams has least likely relied on which of the following assumptions? A) The residuals are homoscedastic. B) The disturbance or error term is normally distributed. C) There is a linear relationship between the independent variables. Explanation Multiple regression models assume that there is no linear relationship between two or more of the independent variables. The other answer choices are both assumptions of multiple regression. (Module 1.2, LOS 1.e) Question #46 of 144 Question ID: 1479901 A multiple regression model has included independent variables that are not linearly related to the dependent variable. The model is most likely misspecified due to: A) incorrect data pooling. B) incorrect variable form. C) incorrect variable scaling. Explanation Incorrect variable form misspecification occurs if the relationship between dependent and independent variables is nonlinear. (Module 1.3, LOS 1.g) Question #47 of 144 Question ID: 1471870 Consider the following regression equation: Salesi = 10.0 + 1.25 R&Di + 1.0 ADVi – 2.0 COMPi + 8.0 CAPi where Sales is dollar sales in millions, R&D is research and development expenditures in millions, ADV is dollar amount spent on advertising in millions, COMP is the number of competitors in the industry, and CAP is the capital expenditures for the period in millions of dollars. Which of the following is NOT a correct interpretation of this regression information? A) B) C) If R&D and advertising expenditures are $1 million each, there are 5 competitors, and capital expenditures are $2 million, expected Sales are $8.25 million. If a company spends $1 million more on capital expenditures (holding everything else constant), Sales are expected to increase by $8.0 million. One more competitor will mean $2 million less in Sales (holding everything else constant). Explanation Predicted sales = $10 + 1.25 + 1 – 10 + 16 = $18.25 million. (Module 1.1, LOS 1.b) Question #48 of 144 Question ID: 1479883 One possible problem that could jeopardize the validity of the employment growth rate model is multicollinearity. Which of the following would most likely suggest the existence of multicollinearity? A) The variance of the observations has increased over time. B) The Durbin–Watson statistic is significant. C) The F-statistic suggests that the overall regression is significant, however the regression coefficients are not individually significant. Explanation One symptom of multicollinearity is that the regression coefficients may not be individually statistically significant even when according to the F-statistic the overall regression is significant. The problem of multicollinearity involves the existence of high correlation between two or more independent variables. Clearly, as service employment rises, construction employment must rise to facilitate the growth in these sectors. Alternatively, as manufacturing employment rises, the service sector must grow to serve the broader manufacturing sector. The variance of observations suggests the possible existence of heteroskedasticity. If the Durbin–Watson statistic may be used to test for serial correlation at a single lag. (Module 1.2, LOS 1.f) Question #49 of 144 Question ID: 1586005 Consider the following estimated regression equation: Salesi = 10.0 + 1.25 R&Di + 1.0 ADVi − 2.0 COMPi + 8.0 CAPi Sales are in millions of dollars. An analyst is given the following predictions on the independent variables: R&D = 5, ADV = 4, COMP = 10, and CAP = 40. The predicted level of sales is closest to: A) $310.25 million. B) $300.25 million. C) $320.25 million. Explanation Predicted sales = $10 + 1.25 (5) + 1.0 (4) −2.0 (10) + 8 (40) = 10 + 6.25 + 4 − 20 + 320 = $320.25 (Module 1.2, LOS 1.f) Question #50 of 144 Question ID: 1479902 When pooling the samples over multiple economic environments in a multiple regression model, which of the following errors is most likely to occur? A) Model misspecification. B) Heteroskedasticity. C) Multicollinearity. Explanation When data are improperly pooled over multiple economic environments in a multiple regression analysis, the model would be misspecified. (Module 1.3, LOS 1.g) Question #51 of 144 Question ID: 1472067 An analyst runs a regression of portfolio returns on three independent variables. These independent variables are price-to-sales (P/S), price-to-cash flow (P/CF), and price-to-book (P/B). The analyst discovers that the p-values for each independent variable are relatively high. However, the F-test has a very small p-value. The analyst is puzzled and tries to figure out how the F-test can be statistically significant when the individual independent variables are not significant. What violation of regression analysis has occurred? A) multicollinearity. B) conditional heteroskedasticity. C) serial correlation. Explanation An indication of multicollinearity is when the independent variables individually are not statistically significant but the F-test suggests that the variables as a whole do an excellent job of explaining the variation in the dependent variable. (Module 1.3, LOS 1.j) Question #52 of 144 Question ID: 1472012 Which of the following statements regarding heteroskedasticity is least accurate? A) Heteroskedasticity may occur in cross-sectional or time-series analyses. B) Heteroskedasticity results in an estimated variance that is too small and, therefore, affects statistical inference. C) The assumption of linear regression is that the residuals are heteroskedastic. Explanation The assumption of regression is that the residuals are homoskedastic (i.e., the residuals are drawn from the same distribution). (Module 1.3, LOS 1.h) Question #53 of 144 Question ID: 1586003 May Jones estimated a regression that produced the following analysis of variance (ANOVA) table: Source Sum of squares Degrees of freedom Mean square Regression 20 1 20 Error 80 40 2 Total 100 41 The values of R2 and the F-statistic for joint test of significance of all the slope coefficients are: A) R2 = 0.25 and F = 0.909. B) R2 = 0.20 and F = 10. C) R2 = 0.25 and F = 10. Explanation R2 = RSS / SST = 20 / 100 = 0.20 The F-statistic is equal to the ratio of the mean squared regression to the mean squared error. F = 20 / 2 = 10 (Module 1.2, LOS 1.e) Question #54 - 56 of 144 Question ID: 1479936 The predicted price of a house that has 2,000 square feet of space and 4 bedrooms is closest to: A) $114,000. B) $256,000. C) $185,000. Explanation 66,500 + 74.30(2,000) + 10,306(4) = $256,324 (Module 1.2, LOS 1.f) Question #55 - 56 of 144 Question ID: 1479937 The conclusion from the hypothesis test of H0: b1 = b2 = 0, is that the null hypothesis should: A) not be rejected as the calculated F of 40.73 is greater than the critical value of 3.29. B) be rejected as the calculated F of 40.73 is greater than the critical value of 3.33. C) be rejected as the calculated F of 40.73 is greater than the critical value of 3.29. Explanation We can reject the null hypothesis that coefficients of both independent variables equal 0. The F value for comparison is F2,29 = 3.33. The degrees of freedom in the numerator is 2; equal to the number of independent variables. Degrees of freedom for the denominator is 32 − (2+1) = 29. The critical value of the F-test needed to reject the null hypothesis is thus 3.33. The actual value of the F-test statistic is 40.73, so the null hypothesis should be rejected, as the calculated F of 40.73 is greater than the critical value of 3.33. (Module 1.2, LOS 1.e) Question #56 - 56 of 144 Question ID: 1479938 Which of the following is most likely to present a problem in using this regression for forecasting? A) Heteroskedasticity. B) Multicollinearity. C) Autocorrelation. Explanation Multicollinearity is present in a regression model when some linear combination of the independent variables are highly correlated. We are told that the two independent variables in this question are highly correlated. We also recognize that unconditional heteroskedasticity is present – but this would not pose any major problems in using this model for forecasting. No information is given about autocorrelation in residuals, but this is generally a concern with time series data (in this case, the model uses cross-sectional data). (Module 1.3, LOS 1.j) Question #57 of 144 Question ID: 1471872 Henry Hilton, CFA, is undertaking an analysis of the bicycle industry. He hypothesizes that bicycle sales (SALES) are a function of three factors: the population under 20 (POP), the level of disposable income (INCOME), and the number of dollars spent on advertising (ADV). All data are measured in millions of units. Hilton gathers data for the last 20 years and estimates the following equation (standard errors in parentheses): SALES = α + 0.004 POP + 1.031 INCOME + 2.002 ADV (0.005) (0.337) (2.312) The critical t-statistic for a 95% confidence level is 2.120. Which of the independent variables is statistically different from zero at the 95% confidence level? A) INCOME and ADV. B) ADV only. C) INCOME only. Explanation The calculated test statistic is coefficient/standard error. Hence, the t-stats are 0.8 for POP, 3.059 for INCOME, and 0.866 for ADV. Since the t-stat for INCOME is the only one greater than the critical t-value of 2.120, only INCOME is significantly different from zero. (Module 1.1, LOS 1.b) Question #58 of 144 Question ID: 1489310 Jacob Warner, CFA, is evaluating a regression analysis recently published in a trade journal that hypothesizes that the annual performance of the S&P 500 stock index can be explained by movements in the Federal Funds rate and the U.S. Producer Price Index (PPI). Which of the following statements regarding his analysis is most accurate? A) B) C) If the p-value of a variable is less than the significance level, the null hypothesis can be rejected. If the t-value of a variable is less than the significance level, the null hypothesis should be rejected. If the p-value of a variable is less than the significance level, the null hypothesis cannot be rejected. Explanation The p-value is the smallest level of significance for which the null hypothesis can be rejected. Therefore, for any given variable, if the p-value of a variable is less than the significance level, the null hypothesis can be rejected and the variable is considered to be statistically significant. (Module 1.1, LOS 1.b) Question #59 of 144 Question ID: 1472026 Which of the following statements regarding serial correlation that might be encountered in regression analysis is least accurate? A) Serial correlation occurs least often with time series data. B) Serial correlation does not affect consistency of regression coefficients. C) Positive serial correlation and heteroskedasticity can both lead to Type I errors. Explanation Serial correlation, which is sometimes referred to as autocorrelation, occurs when the residual terms are correlated with one another, and is most frequently encountered with time series data. Positive serial correlation can lead to standard errors that are too small, which will cause computed t-statistics to be larger than they should be, which will lead to too many Type I errors (i.e. the rejection of the null hypothesis when it is actually true). Serial correlation however does not affect the consistency of the regression coefficients. (Module 1.3, LOS 1.h) Question #60 of 144 Question ID: 1479923 Assume that in a particular multiple regression model, it is determined that the error terms are uncorrelated with each other. Which of the following statements is most accurate? A) B) C) Serial correlation may be present in this multiple regression model, and can be confirmed only through a Durbin-Watson test. This model is in accordance with the basic assumptions of multiple regression analysis because the errors are not serially correlated. Unconditional heteroskedasticity present in this model should not pose a problem, but can be corrected by using robust standard errors. Explanation One of the basic assumptions of multiple regression analysis is that the error terms are not correlated with each other. In other words, the error terms are not serially correlated. Multicollinearity and heteroskedasticity are problems in multiple regression that are not related to the correlation of the error terms. (Module 1.3, LOS 1.i) Question #61 of 144 Question ID: 1471980 An analyst runs a regression of monthly value-stock returns on five independent variables over 48 months. The total sum of squares is 430, and the sum of squared errors is 170. Test the null hypothesis at the 2.5% and 5% significance level that all five of the independent variables are equal to zero. A) Rejected at 5% significance only. B) Rejected at 2.5% significance and 5% significance. C) Not rejected at 2.5% or 5.0% significance. Explanation The F-statistic is equal to the ratio of the mean squared regression (MSR) to the mean squared error (MSE). RSS = SST – SSE = 430 – 170 = 260 MSR = 260 / 5 = 52 MSE = 170 / (48 – 5 – 1) = 4.05 F = 52 / 4.05 = 12.84 The critical F-value for 5 and 42 degrees of freedom at a 5% significance level is approximately 2.44. The critical F-value for 5 and 42 degrees of freedom at a 2.5% significance level is approximately 2.89. Therefore, we can reject the null hypothesis at either level of significance and conclude that at least one of the five independent variables explains a significant portion of the variation of the dependent variable. (Module 1.2, LOS 1.e) Question #62 of 144 Question ID: 1479874 Wilson estimated a regression that produced the following analysis of variance (ANOVA) table: Source Sum of squares Degrees of freedom Mean square Regression 100 1 100.0 Error 300 40 7.5 Total 400 41 The values of R2 and the F-statistic to test the null hypothesis that slope coefficients on all variables are equal to zero are: A) R2 = 0.20 and F = 13.333. B) R2 = 0.25 and F = 0.930. C) R2 = 0.25 and F = 13.333. Explanation R2 = RSS / SST = 100 / 400 = 0.25 The F-statistic is equal to the ratio of the mean squared regression to the mean squared error. F = 100 / 7.5 = 13.333 (Module 1.2, LOS 1.e) Question #63 - 65 of 144 Question ID: 1508634 Which of the following tests is least likely to be used to detect autocorrelation? A) Durbin-Watson. B) Breusch-Godfrey. C) Breusch-Pagan. Explanation Durbin-Watson and Breusch-Godfrey test statistic are used to detect autocorrelation. The Breusch-Pagan test is used to detect heteroskedasticity. (Module 1.3, LOS 1.i) Question #64 - 65 of 144 Question ID: 1472023 One of the most popular ways to correct heteroskedasticity is to: A) improve the specification of the model. B) adjust the standard errors. C) use robust standard errors. Explanation Using generalized least squares and calculating robust standard errors are possible remedies for heteroskedasticity. Improving specifications remedies serial correlation. The standard error cannot be adjusted, only the coefficient of the standard errors. (Module 1.3, LOS 1.h) Question #65 - 65 of 144 Question ID: 1479933 If a regression equation shows that no individual t-tests are significant, but the F-statistic is significant, the regression probably exhibits: A) serial correlation. B) multicollinearity. C) heteroskedasticity. Explanation Common indicators of multicollinearity include: high correlation (>0.7) between independent variables, no individual t-tests are significant but the F-statistic is, and signs on the coefficients that are opposite of what is expected. (Module 1.3, LOS 1.j) Question #66 of 144 Question ID: 1472073 A fund has changed managers twice during the past 10 years. An analyst wishes to measure whether either of the changes in managers has had an impact on performance. R is the return on the fund, and M is the return on a market index. Which of the following regression equations can appropriately measure the desired impacts? A) The desired impact cannot be measured. B) R = a + bM + c1D1 + c2D2 + ε, where D1 = 1 if the return is from the first manager, and D2 = 1 if the return is from the third manager. R = a + bM + c1D1 + c2D2 + c3D3 + ε, where D1 = 1 if the return is from the first C) manager, and D2 = 1 if the return is from the second manager, and D3 = 1 is the return is from the third manager. Explanation The effect needs to be measured by two distinct dummy variables. The use of three variables will cause collinearity, and the use of one dummy variable will not appropriately specify the manager impact. (Module 1.4, LOS 1.l) Question #67 of 144 Question ID: 1471869 Consider the following regression equation: Salesi = 20.5 + 1.5 R&Di + 2.5 ADVi – 3.0 COMPi where Sales is dollar sales in millions, R&D is research and development expenditures in millions, ADV is dollar amount spent on advertising in millions, and COMP is the number of competitors in the industry. Which of the following is NOT a correct interpretation of this regression information? A) B) If R&D and advertising expenditures are $1 million each and there are 5 competitors, expected sales are $9.5 million. One more competitor will mean $3 million less in sales (holding everything else constant). C) If a company spends $1 more on R&D (holding everything else constant), sales are expected to increase by $1.5 million. Explanation If a company spends $1 million more on R&D (holding everything else constant), sales are expected to increase by $1.5 million. Always be aware of the units of measure for the different variables. (Module 1.1, LOS 1.b) Question #68 of 144 Question ID: 1479922 Which of the following is a potential remedy for multicollinearity? A) Add dummy variables to the regression. B) Take first differences of the dependent variable. C) Omit one or more of the collinear variables. Explanation The first differencing is not a remedy for the collinearity, nor is the inclusion of dummy variables. The best potential remedy is to attempt to eliminate highly correlated variables. (Module 1.3, LOS 1.i) Question #69 of 144 Question ID: 1586007 Which of the following conditions will least likely affect the statistical inference about regression parameters by itself? A) Multicollinearity. B) Unconditional heteroskedasticity. C) Model misspecification. Explanation Unconditional heteroskedasticity does not impact the statistical inference concerning the parameters. Misspecified models have inconsistent and biased regression parameters. Multicollinearity results in unreliable estimates of regression parameters. (Module 1.3, LOS 1.h) Question #70 - 73 of 144 Question ID: 1685256 What is most likely represented by the Y intercept of the regression? A) The drift of a random walk. B) The return on a particular trading day. C) The intercept is not a driver of returns, only the independent variables. Explanation The omitted variable is represented by the intercept. So, if we have four variables to represent Monday through Thursday, the intercept would represent returns on Friday. Remember when we want to distinguish between "n" classes we always use one less dummy variable the number of classes (n – 1). (Module 1.2, LOS 1.e) Question #71 - 73 of 144 Question ID: 1479957 What can be said of the overall explanatory power of the model at the 5% significance? A) There is no value to calendar trading. B) There is value to calendar trading. The coefficient of determination for the above regression is significantly higher C) than the standard error of the estimate, and therefore there is value to calendar trading. Explanation This question calls for a computation of the F-stat for all independent variables jointly. F = (0.0039 / 4) / (0.9534 / (780 – 4 – 1) = 0.79. The critical F is somewhere between 2.37 and 2.45 so we fail to reject the null that the coefficient are equal to zero. (Module 1.2, LOS 1.e) Question #72 - 73 of 144 Question ID: 1472059 The test mentioned by Jessica is known as the: A) Breusch-Pagan, which is a one-tailed test. B) Breusch-Pagan, which is a two-tailed test. C) Durbin-Watson, which is a two-tailed test. Explanation The Breusch-Pagan is used to detect conditional heteroskedasticity and it is a one-tailed test. This is because we are only concerned about large values in the residuals coefficient of determination. (Module 1.3, LOS 1.h) Question #73 - 73 of 144 Question ID: 1479958 Are Jessica and her son Jonathan correct in terms of the method used to correct for heteroskedasticity and the likely effects? A) Neither is correct. B) Both are correct. C) One is correct. Explanation Jessica is correct. White-corrected standard errors are also known as robust standard errors. Jonathan is correct because for financial data, generally, White-corrected errors are higher than the biased errors leading to lower computed t-statistics and, therefore, less frequent rejection of the null hypothesis (remember incorrectly rejecting a true null is Type I error). (Module 1.3, LOS 1.h) Question #74 - 77 of 144 The adjusted R2 of Model 2 is closest to: Question ID: 1501592 A) 0.39. B) 0.37. C) 0.36. Explanation Given n = 120 months, k = 4 (for Model 2), and R2 = 0.39: R 2 a 120−1 = 1 − [( 120−4−1 ) × (1 − 0.39)] = 0.37 (Module 1.2, LOS 1.d) Question #75 - 77 of 144 Question ID: 1501593 The model better suited for prediction is: A) Model 1 because it has a lower Bayesian information criterion. B) Model 2 because it has a higher Akaike information criterion. C) Model 2 because it has a lower Akaike information criterion. Explanation The Akaike information criterion (AIC) is used if the goal is to have a better forecast, while the Bayesian information criterion (BIC) is used if the goal is a better goodness of fit. Lower values of both criteria indicate a better model. Both criteria are lower for Model 2. (Module 1.2, LOS 1.d) Question #76 - 77 of 144 Question ID: 1639814 The F-statistic for testing H0: coefficient of LIQ = 0 versus Ha: coefficient of LIQ ≠ 0 is closest to: A) 13.53. B) 5.45. C) 2.11. Explanation (SSER −SSEU )/q F = (SSEU )/(n−k−1) where n = 120, k = 4, and q = 1: (38−34)/1 (34)/(120−4−1) = 13.53 (Module 1.2, LOS 1.d) Question #77 - 77 of 144 Question ID: 1501595 What is the predicted return for a stock using Model 1 when SMB = 3.30, HML = 1.25 and Rm-Rf = 5? A) 6.80%. B) 7.88%. C) 9.58%. Explanation Model 1: Return = 1.22 + 0.23 × SMB + 0.34 × HML + 0.88 Rm-Rf = 1.22 + 0.23 × 3.30 + 0.34 × 1.25 + 0.88 × 5 = 6.80%. (Module 1.2, LOS 1.d) Question #78 - 80 of 144 How many dummy variables should Rathod use? Question ID: 1651804 A) Five. B) Six. C) Four. Explanation There are 5 trading days in a week, but we should use (n − 1) or 4 dummies in order to ensure no violations of regression analysis occur. (Module 1.4, LOS 1.l) Question #79 - 80 of 144 Question ID: 1651805 What is most likely represented by the intercept of the regression? A) The return on a particular trading day. B) The intercept is not a driver of returns, only the independent variables. C) The drift of a random walk. Explanation The omitted variable is represented by the intercept. So, if we have four variables to represent Monday through Thursday, the intercept would represent returns on Friday. (Module 1.4, LOS 1.l) Question #80 - 80 of 144 Question ID: 1651806 Are Jessica and her son Jonathan, correct in terms of the method used to correct for heteroskedasticity and the likely effects? A) Both are correct. B) Neither is correct. C) One is correct. Explanation Jessica is correct. White-corrected standard errors are also known as robust standard errors. Jonathan is correct because White-corrected errors are higher than the biased errors leading to lower computed t-statistics and therefore less frequent rejection of the Null Hypothesis (remember incorrectly rejecting a true Null is Type I error). (Module 1.3, LOS 1.h) Question #81 of 144 Question ID: 1471947 An analyst regresses the return of a S&P 500 index fund against the S&P 500, and also regresses the return of an active manager against the S&P 500. The analyst uses the last five years of data in both regressions. Without making any other assumptions, which of the following is most accurate? The index fund: A) regression should have higher sum of squares regression as a ratio to the total sum of squares. B) should have a lower coefficient of determination. C) should have a higher coefficient on the independent variable. Explanation The index fund regression should provide a higher R2 than the active manager regression. R2 is the sum of squares regression divided by the total sum of squares. (Module 1.2, LOS 1.d) Question #82 of 144 Question ID: 1479949 Suppose the analyst wants to add a dummy variable for whether a person has a business college degree and an engineering degree. What is the CORRECT representation if a person has both degrees? Business Engineering Degree Dummy Degree Dummy Variable A) 0 Variable 1 B) 0 0 C) 1 1 Explanation Assigning a zero to both categories is appropriate for someone with neither degree. Assigning one to the business category and zero to the engineering category is appropriate for someone with only a business degree. Assigning zero to the business category and one to the engineering category is appropriate for someone with only an engineering degree. Assigning a one to both categories is correct because it reflects the possession of both degrees. (Module 1.4, LOS 1.l) Question #83 of 144 Question ID: 1471946 Which of the following statements regarding the R2 is least accurate? A) The adjusted-R2 not appropriate to use in simple regression. B) It is possible for the adjusted-R2 to decline as more variables are added to the multiple regression. C) The adjusted-R2 is greater than the R2 in multiple regression. Explanation The adjusted-R2 will always be less than R2in multiple regression. (Module 1.2, LOS 1.d) Question #84 - 87 of 144 In regard to their conversation about the regression equation: A) Brent’s statement is correct; Johnson’s statement is correct. B) Brent’s statement is correct; Johnson’s statement is incorrect. C) Brent’s statement is incorrect; Johnson’s statement is correct. Question ID: 1471900 Explanation Expected sales is the dependent variable in the equation, while expenditures for marketing and salespeople are the independent variables. Therefore, a $1 million increase in marketing expenditures will increase the dependent variable (expected sales) by $1.6 million. Brent's statement is incorrect. Johnson's statement is correct. 12.6 is the intercept in the equation, which means that if all independent variables are equal to zero, expected sales will be $12.6 million. (Module 1.1, LOS 1.b) Question #85 - 87 of 144 Question ID: 1586001 Regarding Brent's Statements 1 and 2: A) Only Statement 1 is correct. B) Only Statement 2 is correct. C) Both statements are correct. Explanation Statement 1 is correct. Comparing the formulae for computation of AIC and BIC, because ln(n) is greater than 2 for even small sample sizes, the BIC metric imposes a higher penalty for overfitting. Statement 2 is correct. Both AIC and BIC evaluate the quality of model fit among competing models for the same dependent variable. Lower values indicate a better model under either criteria. AIC is used if the goal is to have a better forecast, while BIC is used if the goal is a better goodness of fit. (Module 1.2, LOS 1.d) Question #86 - 87 of 144 Question ID: 1471904 Assuming that next year's marketing expenditures are $3,500,000 and there are five salespeople, predicted sales for Mega Flowers should will be: A) $11,600,000. B) $24,000,000. C) $24,200,000. Explanation Using the information provided, expected sales equals 12.6 + (1.6 x 3.5) + (1.2 x 5) = $24.2 million. Remember to check the details - i.e. this equation is denominated in millions of dollars. (Module 1.1, LOS 1.b) Question #87 - 87 of 144 Question ID: 1471905 Brent would like to further investigate whether at least one of the independent variables can explain a significant portion of the variation of the dependent variable. Which of the following methods would be best for Brent to use? A) The F-statistic. B) The multiple coefficient of determination. C) An ANOVA table. Explanation To determine whether at least one of the coefficients is statistically significant, the calculated F-statistic is compared with the critical F-value at the appropriate level of significance. (Module 1.1, LOS 1.b) Question #88 of 144 Question ID: 1479921 Alex Wade, CFA, is analyzing the result of a regression analysis comparing the performance of gold stocks versus a broad equity market index. Wade believes that first lag serial correlation may be present and, in order to prove his theory, should use which of the following methods to detect its presence? A) The Breusch-Pagan test. B) The Durbin-Watson statistic. C) The Hansen method. Explanation The Durbin-Watson statistic is the most commonly used method for the detection of serial correlationat the first lag, although residual plots can also be utilized. For testing of serial correlation beyond the first lag, we can instead use the Breusch-Godfrey test (but is not one of the answer choices). (Module 1.3, LOS 1.i) Question #89 - 91 of 144 Question ID: 1479910 If GDP rises 2.2% and the price of fuels falls $0.15, Baltz's model will predict Company sales to be (in $ millions) closest to: A) $82.00. B) $128.00. C) $206.00. Explanation Sales will be closest to $78 + ($30.22 × 2.2) + [(−412.39) × (−$0.15)] = $206.34 million. (Module 1.2, LOS 1.f) Question #90 - 91 of 144 Question ID: 1479911 Baltz proceeds to test the hypothesis that none of the independent variables has significant explanatory power. He concludes that, at a 5% level of significance: A) B) C) all of the independent variables have explanatory power, because the calculated Fstatistic exceeds its critical value. none of the independent variables has explanatory power, because the calculated F-statistic does not exceed its critical value. at least one of the independent variables has explanatory power, because the calculated F-statistic exceeds its critical value. Explanation MSE = SSE / [n − (k + 1)] = 132.12 ÷ 27 = 4.89. From the ANOVA table, the calculated F-statistic is (mean square regression / mean square error) = 145.65 / 4.89 = 29.7853. From the Fdistribution table (2 df numerator, 27 df denominator) the F-critical value may be interpolated to be 3.36. Because 29.7853 is greater than 3.36, Baltz rejects the null hypothesis and concludes that at least one of the independent variables has explanatory power. (Module 1.2, LOS 1.e) Question #91 - 91 of 144 Question ID: 1479912 Presence of conditional heteroskedasticity is least likely to affect the: A) computed F-statistic. B) coefficient estimates. C) computed t-statistic. Explanation Conditional heteroskedasticity results in consistent coefficient estimates, but it biases standard errors, affecting the computed t-statistic and F-statistic. (Module 1.3, LOS 1.h) Question #92 of 144 Question ID: 1471882 When interpreting the results of a multiple regression analysis, which of the following terms represents the value of the dependent variable when the independent variables are all equal to zero? A) Slope coefficient. B) p-value. C) Intercept term. Explanation The intercept term is the value of the dependent variable when the independent variables are set to zero. (Module 1.1, LOS 1.b) Question #93 of 144 Question ID: 1479908 An analyst is trying to determine whether fund return performance is persistent. The analyst divides funds into three groups based on whether their return performance was in the top third (group 1), middle third (group 2), or bottom third (group 3) during the previous year. The manager then creates the following equation: R = a + b1D1 + b2D2 + b3D3 + ε, where R is return premium on the fund (the return minus the return on the S&P 500 benchmark) and Di is equal to 1 if the fund is in group i. Assuming no other information, this equation will suffer from: A) serial correlation. B) heteroskedasticity. C) multicollinearity. Explanation When we use dummy variables, we have to use one less than the states of the world. In this case, there are three states (groups) possible. We should have used only two dummy variables. Multicollinearity is a problem in this case. Specifically, a linear combination of independent variables is perfectly correlated. X1 + X2 + X3 = 1. There are too many dummy variables specified, so the equation will suffer from multicollinearity. (Module 1.3, LOS 1.h) Question #94 of 144 Question ID: 1471867 Consider the following estimated regression equation, with calculated t-statistics of the estimates as indicated: AUTOt = 10.0 + 1.25 PIt + 1.0 TEENt – 2.0 INSt with a PI calculated t-statistic of 0.45, a TEEN calculated t-statistic of 2.2, and an INS calculated t-statistic of 0.63. The equation was estimated over 40 companies. Using a 5% level of significance, which of the independent variables significantly different from zero? A) TEEN only. B) PI and INS only. C) PI only. Explanation The critical t-values for 40-3-1 = 36 degrees of freedom and a 5% level of significance are ± 2.028. Therefore, only TEEN is statistically significant. (Module 1.1, LOS 1.b) Question #95 of 144 Question ID: 1472077 Consider the following model of earnings (EPS) regressed against dummy variables for the quarters: EPSt = α + β1Q1t + β2Q2t + β3Q3t where: EPSt is a quarterly observation of earnings per share Q1t takes on a value of 1 if period t is the second quarter, 0 otherwise Q2t takes on a value of 1 if period t is the third quarter, 0 otherwise Q3t takes on a value of 1 if period t is the fourth quarter, 0 otherwise Which of the following statements regarding this model is most accurate? The: A) significance of the coefficients cannot be interpreted in the case of dummy variables. B) EPS for the first quarter is represented by the residual. C) coefficient on each dummy tells us about the difference in earnings per share between the respective quarter and the one left out (first quarter in this case). Explanation The coefficients on the dummy variables indicate the difference in EPS for a given quarter, relative to the first quarter. (Module 1.4, LOS 1.l) Question #96 - 99 of 144 Question ID: 1471895 The percentage of the total variation in quarterly stock returns explained by the independent variables is closest to: A) 32%. B) 47%. C) 42%. Explanation The R2 is the percentage of variation in the dependent variable explained by the independent variables. The R2 is equal to the SSRegression/SSTotal, where the SSTotal is equal to SSRegression + SSError. R2 = 126.00/ (126.00+267.00) = 32%. (Module 1.1, LOS 1.b) Question #97 - 99 of 144 Using a 5% level of significance, there is: A) evidence of first-lag serial correlation in residuals. B) evidence of second-lag serial correlation in residuals. C) no evidence of serial correlation in the residuals. Question ID: 1586009 Explanation n=160, k=3. For lag 1, p = 1. (n-k-p-1 = 155). Critical F-stat (1, 155) = 3.90. BG Stat for lag 1 is given as 3.15. We fail to reject the null of no serial correlation in residuals. For lag 2, critical F (2,154) = 3.05. BG stat for lag 2 is given as 3.22 and exceeds the critical value and hence we reject the null of no serial correlation at the 2nd lag. (Module 1.3, LOS 1.i) Question #98 - 99 of 144 Question ID: 1471897 What is the predicted quarterly stock return, given the following forecasts? Employment growth = 2.0% GDP growth = 1.0% Private investment growth = -1.0% A) 4.4%. B) 4.7%. C) 5.0%. Explanation Predicted quarterly stock return is 9.50% + (−4.50)(2.0%) + (4.20)(1.0%) + (−0.30)(−1.0%) = 5.0%. (Module 1.1, LOS 1.b) Question #99 - 99 of 144 Question ID: 1586010 Assuming a restricted model with all three variables removed and a 5% level of significance, the most appropriate conclusion is: A) B) With an F-statistic of 2.66, we fail to reject the null hypothesis of all slope coefficients equal to zero. With an F-statistic of 24.54, we reject the null hypothesis that all the slope coefficients are equal to zero. C) With an F-statistic of 0.472, we fail to reject the null hypothesis of all coefficients equal to zero. Explanation We are testing that all slope coefficients are equal to 0. F = [RSS/K] / [SSE/(n-k-1)] = (126/3) / (267/156) = 42/1.711 = 24.54 Critical F(3,156) = 2.66 F-stat > critical F > reject null that all slope coefficients are equal to zero. (Module 1.2, LOS 1.e) Question #100 of 144 Question ID: 1479914 Which of the following questions is least likely answered by using a qualitative dependent variable? A) B) C) Based on the following company-specific financial ratios, will company ABC enter bankruptcy? Based on the following subsidiary and competition variables, will company XYZ divest itself of a subsidiary? Based on the following executive-specific and company-specific variables, how many shares will be acquired through the exercise of executive stock options? Explanation The number of shares can be a broad range of values and is, therefore, not considered a qualitative dependent variable. (Module 1.3, LOS 1.h) Question #101 - 106 of 144 Question ID: 1479925 The percent of the variation in the fund's return that is explained by the regression is: A) 66.76%. B) 81.71%. C) 61.78%. Explanation The R2 tells us how much of the change in the dependent variable is explained by the changes in the independent variables in the regression: 0.667632. (Module 1.2, LOS 1.d) Question #102 - 106 of 144 Question ID: 1479926 Suppose the Breusch-Godfrey statistic is 3.22. At a 5% level of significance, which of the following is the most accurate conclusion regarding the presence of serial correlation (at two lags) in the residuals? A) B) C) No, because the BG statistic is less than the critical test statistic of 3.49, we don't have evidence of serial correlation. No, because the BG statistic is less than the critical test statistic of 3.55, we don't have evidence of serial correlation. Yes, because the BG statistic exceeds the critical test statistic of 3.16, there is evidence of serial correlation. Explanation Number of lags tested = p = 2. The appropriate test statistic for BG test is F-stat with (p = 2) and (n – p – k – 1 = 18) degrees of freedom. From the table, critical value = 3.55. (Module 1.3, LOS 1.i) Question #103 - 106 of 144 Question ID: 1616908 Gloucester subsequently revises the model to exclude the small cap index and finds that the revised model has a RSS of 106.332. Which of the following statements is most accurate? At a 5% level of significance, the test statistic: A) of 1.40 indicates that we cannot reject the hypothesis that the coefficient of smallcap index is not significantly different from 0. B) C) of 13.39 indicates that we cannot reject the hypothesis that the coefficient of smallcap index is significantly different from 0. of 4.35 indicates that we cannot reject the hypothesis that the coefficient of smallcap index is significantly different from 0. Explanation SSER = SST – RSSR = 164.9963 – 106.3320 = 58.6643 F = [(SSER – SSEU) / q] / [SSEU / (n – k – 1)] = [(58.6643 – 54.8395) / 1] / (54.8395 / 20) = 3.8248 / 2.742 = 1.40 Critical F(1, 20) = 4.35 (from Exhibit 1) Since the test statistic is not greater than the critical value, we cannot reject the null hypothesis that b2 = 0. (Module 1.2, LOS 1.e) Question #104 - 106 of 144 Question ID: 1586013 The best test for unconditional heteroskedasticity is: A) the Breusch-Pagan test only. B) the Breusch-Godfrey test only. C) neither the Durbin-Watson test nor the Breusch-Pagan test. Explanation Breusch-Godfrey and Durbin-Watson tests are for serial correlation. The Breusch-Pagan test is for conditional heteroskedasticity; it tests to see if the size of the independent variables influences the size of the residuals. Although tests for unconditional heteroskedasticity exist, they are not part of the CFA curriculum, and unconditional heteroskedasticity is generally considered less serious than conditional heteroskedasticity. (Module 1.3, LOS 1.i) Question #105 - 106 of 144 Question ID: 1479929 In the month of January, if both the small and large capitalization index have a zero return, we would expect the fund to have a return equal to: A) 2.799. B) 2.322. C) 2.561. Explanation The forecast of the return of the fund would be the intercept plus the coefficient on the January effect: 2.322 = -0.238214 + 2.560552. (Module 1.2, LOS 1.f) Question #106 - 106 of 144 Question ID: 1479930 Assuming (for this question only) that the F-test was significant but that the t-tests of the independent variables were insignificant, this would most likely suggest: A) multicollinearity. B) serial correlation. C) conditional heteroskedasticity. Explanation When the F-test and the t-tests conflict, multicollinearity is indicated. (Module 1.3, LOS 1.j) Question #107 of 144 Question ID: 1479878 Consider the following analysis of variance table: Source Sum of Squares Df Mean Square Regression 20 1 20 Error 80 20 4 Total 100 21 The F-statistic for a test of joint significance of all the slope coefficients is closest to: A) 0.2. B) 0.05. C) 5. Explanation The F-statistic is equal to the ratio of the mean squared regression to the mean squared error. F = MSR / MSE = 20 / 4 = 5. (Module 1.2, LOS 1.e) Question #108 - 111 of 144 Question ID: 1471887 If the number of analysts on NGR Corp. were to double to 4, the change in the forecast of NGR would be closest to? A) −0.035. B) −0.055. C) −0.019. Explanation Initially, the estimate is 0.1303 = 0.043 + ln(2)(−0.027) + ln(47000000)(0.006) Then, the estimate is 0.1116 = 0.043 + ln(4)(−0.027) + ln(47000000)(0.006) 0.1116 − 0.1303 = −0.0187, or −0.019 (Module 1.1, LOS 1.b) Question #109 - 111 of 144 Question ID: 1585993 Based on a R2 calculated from the information in Table 2, the analyst should conclude that the number of analysts and ln(market value) of the firm explain: A) 18.4% of the variation in returns. B) 84.4% of the variation in returns. C) 15.6% of the variation in returns. Explanation R2 is the percentage of the variation in the dependent variable (in this case, variation of returns) explained by the set of independent variables. R2 is calculated as follows: R2 = (SSR / SST) = (0.103 / 0.662) = 15.6%. (Module 1.1, LOS 1.b) Question #110 - 111 of 144 Question ID: 1507766 What is the F-statistic for the hypothesis that all slope coefficients are not statistically significantly different from 0? And, what can be concluded from its value at a 1% level of significance? A) F = 17.00, reject a hypothesis that both of the slope coefficients are equal to zero. B) F = 1.97, fail to reject a hypothesis that both of the slope coefficients are equal to zero. C) F = 5.80, reject a hypothesis that both of the slope coefficients are equal to zero. Explanation The F-statistic is calculated as follows: F = MSR / MSE = 0.051 / 0.003 = 17.00; and 17.00 > 4.61, which is the critical F-value for the given degrees of freedom and a 1% level of significance. However, when F-values are in excess of 10 for a large sample like this, a table is not needed to know that the value is significant. (Module 1.1, LOS 1.b) Question #111 - 111 of 144 Question ID: 1585994 Upon further analysis, Turner concludes that multicollinearity is a problem. What might have prompted this further analysis and what is intuition behind the conclusion? At least one of the t-statistics was not significant, the F-statistic was significant, and A) a positive relationship between the number of analysts and the size of the firm would be expected. B) At least one of the t-statistics was not significant, the F-statistic was significant, and an intercept not significantly different from zero would be expected. At least one of the t-statistics was not significant, the F-statistic was not significant, C) and a positive relationship between the number of analysts and the size of the firm would be expected. Explanation Multicollinearity occurs when there is a high correlation among independent variables and may exist if there is a significant F-statistic for the fit of the regression model, but at least one insignificant independent variable when we expect all of them to be significant. In this case the coefficient on ln(market value) was not significant at the 1% level, but the F-statistic was significant. It would make sense that the size of the firm, i.e., the market value, and the number of analysts would be positively correlated. (Module 1.1, LOS 1.b) Question #112 of 144 Question ID: 1471871 Henry Hilton, CFA, is undertaking an analysis of the bicycle industry. He hypothesizes that bicycle sales (SALES) are a function of three factors: the population under 20 (POP), the level of disposable income (INCOME), and the number of dollars spent on advertising (ADV). All data are measured in millions of units. Hilton gathers data for the last 20 years. Which of the follow regression equations correctly represents Hilton's hypothesis? A) SALES = α x β1 POP x β2 INCOME x β3 ADV x ε. B) SALES = α + β1 POP + β2 INCOME + β3 ADV + ε. C) INCOME = α + β1 POP + β2 SALES + β3 ADV + ε. Explanation SALES is the dependent variable. POP, INCOME, and ADV should be the independent variables (on the right hand side) of the equation (in any order). Regression equations are additive. (Module 1.1, LOS 1.b) Question #113 of 144 Question ID: 1479934 A regression with three independent variables have VIF values of 3, 4, and 2 for the first, second, and third independent variables, respectively. Which of the following conclusions is most appropriate? A) Total VIF of 9 indicates a serious multicollinearity problem. B) Only variable two has a problem with multicollinearity. C) Multicollinearity does not seem to be a problem with the model. Explanation Multicollinearity occurs when an independent variable is highly correlated with a linear combination of the remaining independent variables. VIF values exceeding 5 need to be investigated while values exceeding 10 indicate strong evidence of multicollinearity. (Module 1.3, LOS 1.j) Question #114 - 117 of 144 Question ID: 1479893 Which of the following is least likely to be an assumption regarding linear regression? A) The variance of the residuals is constant. B) The independent variable is correlated with the residuals. C) A linear relationship exists between the dependent and independent variables. Explanation Although the linear regression model is fairly insensitive to minor deviations from any of these assumptions, the independent variable is typically uncorrelated with the residuals. (Module 1.1, LOS 1.c) Question #115 - 117 of 144 Question ID: 1471957 Based upon the information presented in the ANOVA table, what is the coefficient of determination? A) B) C) 0.839, indicating that company returns explain about 83.9% of the variability of industry returns. 0.084, indicating that the variability of industry returns explains about 8.4% of the variability of company returns. 0.916, indicating that the variability of industry returns explains about 91.6% of the variability of company returns. Explanation The coefficient of determination (R2) is the percentage of the total variation in the dependent variable explained by the independent variable. The R2 = (RSS / SS) Total = (3,257 / 3,555) = 0.916. This means that the variation of independent variable (the airline industry) explains 91.6% of the variations in the dependent variable (Pinnacle stock). (Module 1.2, LOS 1.d) Question #116 - 117 of 144 Question ID: 1479894 Based upon her analysis, Carter has derived the following regression equation: Ŷ = 1.75 + 3.25X1. The predicted value of the Y variable equals 50.50, if the: A) predicted value of the dependent variable equals 15. B) predicted value of the independent variable equals 15. C) coefficient of the determination equals 15. Explanation Note that the easiest way to answer this question is to plug numbers into the equation. The predicted value for Y = 1.75 + 3.25(15) = 50.50. The variable X1 represents the independent variable. (Module 1.2, LOS 1.f) Question #117 - 117 of 144 Question ID: 1479895 Carter realizes that although regression analysis is a useful tool when analyzing investments, there are certain limitations. Carter made a list of points describing limitations that Smith Brothers equity traders should be aware of when applying her research to their investment decisions. Point 1: Regression residuals may be homoskedastic. Point 2: Data from regression relationships tends to exhibit parameter instability. Point 3: Regression residuals may exhibit autocorrelation. Point 4: The variance of the error term may change with one or more independent variables. When reviewing Carter's list, one of the Smith Brothers' equity traders points out that not all of the points describe regression analysis limitations. Which of Carter's points most accurately describes the limitations to regression analysis? A) Points 2, 3, and 4. B) Points 1, 3, and 4. C) Points 1, 2, and 3. Explanation One of the basic assumptions of regression analysis is that the variance of the error terms is constant, or homoskedastic. Any violation of this assumption is called heteroskedasticity. Therefore, Point 1 is incorrect, but Point 4 is correct because it describes conditional heteroskedasticity, which results in unreliable estimates of standard errors. Points 2 and 3 also describe limitations of regression analysis. (Module 1.1, LOS 1.c) Question #118 of 144 Question ID: 1472074 The management of a large restaurant chain believes that revenue growth is dependent upon the month of the year. Using a standard 12 month calendar, how many dummy variables must be used in a regression model that will test whether revenue growth differs by month? A) 11. B) 13. C) 12. Explanation The appropriate number of dummy variables is one less than the number of categories because the intercept captures the effect of the other effect. With 12 categories (months) the appropriate number of dummy variables is 11 = 12 – 1. If the number of dummy variables equals the number of categories, it is possible to state any one of the independent dummy variables in terms of the others. This is a violation of the assumption of the multiple linear regression model that none of the independent variables are linearly related. (Module 1.4, LOS 1.l) Question #119 of 144 Question ID: 1472011 Consider the following graph of residuals and the regression line from a time-series regression: These residuals exhibit the regression problem of: A) heteroskedasticity. B) autocorrelation. C) homoskedasticity. Explanation The residuals appear to be from two different distributions over time. In the earlier periods, the model fits rather well compared to the later periods. (Module 1.3, LOS 1.h) Question #120 - 122 of 144 Question ID: 1508632 Using the regression model represented in Exhibit 1, what is the predicted number of housing starts for 20X7? A) 1,394,420. B) 1,751,000. C) 1,394. Explanation Housing starts = 0.42 − (1 × 0.07) + (0.03 × 46.7) = 1.751 million (Module 1.2, LOS 1.f) Question #121 - 122 of 144 Question ID: 1685254 Which of the following statements best describes the explanatory power of the estimated regression? A) The independent variables explain 61.58% of the variation in housing starts. B) C) The residual standard error of only 0.3 indicates that the regression equation is a good fit for the sample data. The large F-statistic indicates that both independent variables help explain changes in housing starts. Explanation The coefficient of determination is the statistic used to identify explanatory power. This can be calculated from the ANOVA table as 3.896/6.327 × 100 = 61.58%. The residual standard error of 0.3 indicates that the standard deviation of the residuals is 0.3 million housing starts. Without knowledge of the data for the dependent variable it is not possible to assess whether this is a small or a large error. The F-statistic does not enable us to conclude on both independent variables. It only allows us the reject the hypothesis that all regression coefficients are zero and accept the hypothesis that at least one isn't. (Module 1.2, LOS 1.e) Question #122 - 122 of 144 Question ID: 1543892 Which of the following is the least appropriate statement in relation to R-square and adjusted R-square: A) B) C) Adjusted R-square is a value between 0 and 1 and can be interpreted as a percentage. Adjusted R-square decreases when the added independent variable adds little value to the regression model. R-square typically increases when new independent variables are added to the regression regardless of their explanatory power. Explanation Adjusted R-square can be negative for a large number of independent variables that have no explanatory power. The other two statements are correct. (Module 1.2, LOS 1.d) Question #123 - 125 of 144 Question ID: 1479880 Using the regression model represented in Exhibit 1, what is the predicted number of housing starts for 20X7? A) 1,394. B) 1,394,420. C) 1,751,000. Explanation Housing starts = 0.42 – (1 × 0.07) + (0.03 × 46.7) = 1.751 million (Module 1.2, LOS 1.e) Question #124 - 125 of 144 Question ID: 1472031 Which of the following statements best describes the explanatory power of the estimated regression? A) B) The large F-statistic indicates that both independent variables help explain changes in housing starts. The residual standard error of only 0.3 indicates that the regression equation is a good fit for the sample data. C) The independent variables explain 61.58% of the variation in housing starts. Explanation The coefficient of determination is the statistic used to identify explanatory power. This can be calculated from the ANOVA table as 3.896 / 6.327 × 100 = 61.58%. The residual standard error of 0.3 indicates that the standard deviation of the residuals is 0.3 million housing starts. Without knowledge of the data for the dependent variable, it is not possible to assess whether this is a small or a large error. The F-statistic does not enable us to conclude on both independent variables. It only allows us the reject the hypothesis that all regression coefficients are zero and accept the hypothesis that at least one isn't. (Module 1.2, LOS 1.d) Question #125 - 125 of 144 Question ID: 1479882 Which of the following is the least appropriate statement in relation to R-square and adjusted R-square? A) B) C) Adjusted R-square decreases when the added independent variable adds little value to the regression model. R-square typically increases when new independent variables are added to the regression. Adjusted R-square can be higher than the coefficient of determination for a model with a good fit. Explanation Adjusted R-squared cannot exceed R-squared (or coefficient of determination) for a multiple regression. . (Module 1.2, LOS 1.d) Question #126 of 144 Question ID: 1471873 Henry Hilton, CFA, is undertaking an analysis of the bicycle industry. He hypothesizes that bicycle sales (SALES) are a function of three factors: the population under 20 (POP), the level of disposable income (INCOME), and the number of dollars spent on advertising (ADV). All data are measured in millions of units. Hilton gathers data for the last 20 years and estimates the following equation (standard errors in parentheses): SALES = 0.000 (0.113) + 0.004 POP + 1.031 INCOME + 2.002 ADV (0.005) (0.337) (2.312) For next year, Hilton estimates the following parameters: (1) the population under 20 will be 120 million, (2) disposable income will be $300,000,000, and (3) advertising expenditures will be $100,000,000. Based on these estimates and the regression equation, what are predicted sales for the industry for next year? A) $557,143,000. B) $509,980,000. C) $656,991,000. Explanation Predicted sales for next year are: SALES = α + 0.004 (120) + 1.031 (300) + 2.002 (100) = 509,980,000. (Module 1.1, LOS 1.b) Question #127 of 144 Question ID: 1479919 Which of the following is least likely a method of detecting serial correlations? A) A scatter plot of the residuals over time. B) The Breusch-Pagan test. C) The Breusch-Godfrey test. Explanation The Breusch-Pagan test is a test of the heteroskedasticity and not of serial correlation. (Module 1.3, LOS 1.i) Question #128 of 144 Question ID: 1479959 A high-yield bond analyst is trying to develop an equation using financial ratios to estimate the probability of a company defaulting on its bonds. A technique that can be used to develop this equation is: A) logistic regression model. B) dummy variable regression. C) multiple linear regression adjusting for heteroskedasticity. Explanation The only one of the possible answers that estimates a probability of a discrete outcome is logit or logistic modeling. (Module 1.4, LOS 1.m) Question #129 - 131 of 144 Question ID: 1479889 What is the expected salary (in $1,000) of a woman with 16 years of education and 10 years of experience? A) 59.18. B) 65.48. C) 54.98. Explanation 34.98 + 1.2(16) + 0.5(10) = 59.18 (Module 1.2, LOS 1.f) Question #130 - 131 of 144 Question ID: 1479890 If the return on the industry index is 4%, the stock's expected return would be: A) 7.6%. B) 9.7%. C) 11.2%. Explanation Y = b0 + bX1 Y = 2.1 + 1.9(4) = 9.7% (Module 1.2, LOS 1.f) Question #131 - 131 of 144 Question ID: 1479891 The percentage of the variation in the stock return explained by the variation in the industry index return is closest to: A) 84.9%. B) 63.2%. C) 72.1%. Explanation The coefficient of determination, R2, is the square the correlation coefficient. 0.8492, = 0.721. (Module 1.2, LOS 1.d) Question #132 of 144 Question ID: 1471928 Which of the following statements least accurately describes one of the fundamental multiple regression assumptions? A) The independent variables are not random. B) The error term is normally distributed. C) The variance of the error terms is not constant (i.e., the errors are heteroskedastic). Explanation The variance of the error term IS assumed to be constant, resulting in errors that are homoskedastic. (Module 1.1, LOS 1.c) Question #133 of 144 Question ID: 1472007 An analyst is trying to estimate the beta for a fund. The analyst estimates a regression equation in which the fund returns are the dependent variable and the Wilshire 5000 is the independent variable, using monthly data over the past five years. The analyst finds that the correlation between the square of the residuals of the regression and the Wilshire 5000 is 0.2. Which of the following is most accurate, assuming a 0.05 level of significance? There is: A) B) C) no evidence that there is conditional heteroskedasticity or serial correlation in the regression equation. evidence of serial correlation but not conditional heteroskedasticity in the regression equation. evidence of conditional heteroskedasticity but not serial correlation in the regression equation. Explanation The test for conditional heteroskedasticity involves regressing the square of the residuals on the independent variables of the regression and creating a test statistic that is n × R2, where n is the number of observations and R2 is from the squared-residual regression. The test statistic is distributed with a chi-squared distribution with the number of degrees of freedom equal to the number of independent variables. For a single variable, the R2 will be equal to the square of the correlation; so in this case, the test statistic is 60 × 0.22 = 2.4, which is less than the chi-squared value (with one degree of freedom) of 3.84 for a p-value of 0.05. There is no indication about serial correlation. (Module 1.3, LOS 1.h) Question #134 of 144 Question ID: 1471927 One of the underlying assumptions of a multiple regression is that the variance of the residuals is constant for various levels of the independent variables. This quality is referred to as: A) a linear relationship. B) homoskedasticity. C) a normal distribution. Explanation Homoskedasticity refers to the basic assumption of a multiple regression model that the variance of the error terms is constant. (Module 1.1, LOS 1.c) Question #135 of 144 Question ID: 1472075 Jill Wentraub is an analyst with the retail industry. She is modeling a company's sales over time and has noticed a quarterly seasonal pattern. If she includes dummy variables to represent the seasonality component of the sales she must use: A) one dummy variables. B) four dummy variables. C) three dummy variables. Explanation Three. Always use one less dummy variable than the number of possibilities. For a seasonality that varies by quarters in the year, three dummy variables are needed. (Module 1.4, LOS 1.l) Question #136 of 144 Question ID: 1471881 Which of the following statements most accurately interprets the following regression results at the given significance level? A) B) C) Variable p-value Intercept 0.0201 X1 0.0284 X2 0.0310 X3 0.0143 The variable X2 is statistically significantly different from zero at the 3% significance level. The variables X1 and X2 are statistically significantly different from zero at the 2% significance level. The variable X3 is statistically significantly different from zero at the 2% significance level. Explanation The p-value is the smallest level of significance for which the null hypothesis can be rejected. An independent variable is significant if the p-value is less than the stated significance level. In this example, X3 is the variable that has a p-value less than the stated significance level. (Module 1.1, LOS 1.b) Question #137 - 140 of 144 Question ID: 1479940 Sutter has detected the presence of conditional heteroskedasticity in Smith's report. This is evidence that: A) the error terms are correlated with each other. B) the variance of the error term is correlated with the values of the independent variables. C) two or more of the independent variables are highly correlated with each other. Explanation Conditional heteroskedasticity exists when the variance of the error term is correlated with the values of the independent variables. Multicollinearity, on the other hand, occurs when two or more of the independent variables are highly correlated with each other. Serial correlation exists when the error terms are correlated with each other. (Module 1.3, LOS 1.j) Question #138 - 140 of 144 Question ID: 1479941 Suppose there is evidence that the variance of the error term is correlated with the values of the independent variables. The most likely effect on the statistical inferences Smith can make from the regressions results using financial data is to commit a: A) B) C) Type I error by incorrectly failing to reject the null hypothesis that the regression parameters are equal to zero. Type II error by incorrectly failing to reject the null hypothesis that the regression parameters are equal to zero. Type I error by incorrectly rejecting the null hypotheses that the regression parameters are equal to zero. Explanation One problem with conditional heteroskedasticity while working with financial data, is that the standard errors of the parameter estimates will be too small and the t-statistics too large. This will lead Smith to incorrectly reject the null hypothesis that the parameters are equal to zero. In other words, Smith will incorrectly conclude that the parameters are statistically significant when in fact they are not. This is an example of a Type I error: incorrectly rejecting the null hypothesis when it should not be rejected. (Module 1.3, LOS 1.h) Question #139 - 140 of 144 Question ID: 1479942 Which of the following is most likely to indicate that two or more of the independent variables, or linear combinations of independent variables, may be highly correlated with each other? Unless otherwise noted, significant and insignificant mean significantly different from zero and not significantly different from zero, respectively. A) B) C) The R2 is low, the F-statistic is insignificant and the Durbin-Watson statistic is significant. The R2 is high, the F-statistic is significant and the t-statistics on the individual slope coefficients are insignificant. The R2 is high, the F-statistic is significant and the t-statistics on the individual slope coefficients are significant. Explanation Multicollinearity occurs when two or more of the independent variables, or linear combinations of independent variables, may be highly correlated with each other. In a classic effect of multicollinearity, the R2 is high and the F-statistic is significant, but the t-statistics on the individual slope coefficients are insignificant. (Module 1.3, LOS 1.j) Question #140 - 140 of 144 Question ID: 1479943 Using the Durbin-Watson test statistic, Smith rejects the null hypothesis suggested by the test. This is evidence that: A) two or more of the independent variables are highly correlated with each other. B) the error term is normally distributed. C) the error terms are correlated with each other. Explanation Serial correlation (also called autocorrelation) exists when the error terms are correlated with each other. Multicollinearity, on the other hand, occurs when two or more of the independent variables are highly correlated with each other. One assumption of multiple regression is that the error term is normally distributed. (Module 1.3, LOS 1.i) Question #141 of 144 Question ID: 1472009 Which of the following statements regarding heteroskedasticity is least accurate? A) B) Conditional heteroskedasticity can be detected using the Breusch-Pagan chisquare statistic. When not related to independent variables, heteroskedasticity does not pose any major problems with the regression. C) Heteroskedasticity only occurs in cross-sectional regressions. Explanation If there are shifting regimes in a time-series (e.g., change in regulation, economic environment), it is possible to have heteroskedasticity in a time-series. Unconditional heteroskedasticity occurs when the heteroskedasticity is not related to the level of the independent variables. Unconditional heteroskedasticity causes no major problems with the regression. Breusch-Pagan statistic has a chi-square distribution and can be used to detect conditional heteroskedasticity. (Module 1.3, LOS 1.h) Question #142 of 144 Question ID: 1472066 When two or more of the independent variables in a multiple regression are correlated with each other, the condition is called: A) multicollinearity. B) conditional heteroskedasticity. C) serial correlation. Explanation Multicollinearity refers to the condition when two or more of the independent variables, or linear combinations of the independent variables, in a multiple regression are highly correlated with each other. This condition distorts the standard error of estimate and the coefficient standard errors, leading to problems when conducting t-tests for statistical significance of parameters. (Module 1.3, LOS 1.j) Question #143 of 144 Question ID: 1479904 Which of the following is least likely to result in misspecification of a regression model? A) Omission of an important independent variable. B) Inappropriate variable form. C) Transforming a variable. Explanation The four types of model specification errors are: omission of an important independent variable, inappropriate variable form, inappropriate variable scaling and data improperly pooled. Transforming an independent variable is usually done to rectify inappropriate variable scaling. (Module 1.3, LOS 1.g) Question #144 of 144 Question ID: 1471891 Which of the following statements regarding the results of a regression analysis is least accurate? The: slope coefficient in a multiple regression is the change in the dependent variable A) for a one-unit change in the independent variable, holding all other variables constant. B) slope coefficient in a multiple regression is the value of the dependent variable for a given value of the independent variable. C) slope coefficients in the multiple regression are referred to as partial betas. Explanation The slope coefficient is the change in the dependent variable for a one-unit change in the independent variable. (Module 1.1, LOS 1.b)