Trendlines and Regression Analysis Questions with Answers

Business Analytics Trendlines and Regression Analysis 1. A regression model that involves a single independent variable is called________. A) single regression B) unit regression C) simple regression D) individual regression Answer: C 2. Regression models of ________ data focus on predicting the future. A) missing B) time-series C) panel D) cross-sectional Answer: B Identify the components of simple linear regression models and discuss their applications The following table exhibits the age of antique furniture and the corresponding prices. Use the table to answer the following question(s). (Hint: Use scatter diagram and the Excel Trendline tool where necessary). 3. What is the relationship between the age of the furniture and their values? A) Nonlinear B) Linear C) Curvilinear D) No relationship Answer: B 4. Which of the following is true of linear functions used in predictive analytical models? A) It is used when the rate of change in a variable decreases or increases quickly and then levels out. B) It is used when there is a steady decrease or increase over a range of a variable. C) It is used when there is increase at a specific rate. D) It is used when there is a rise or fall at a constantly increasing rate. Answer: B 5. Which of the following mathematical functions, used in predictive analytical models, is represented by the formula y=a x3 +b x 2 +dx + e ? A) exponential functions B) power functions C) logarithmic functions D) polynomial functions Answer: D 6. In _________ functions, represented by y=a b x, y rises or falls at constantly increasing rates. A) logarithmic B) power C) exponential D) polynomial Answer: C 7. In Excel's Trendline tool, the value of the _______ gives the measure of fit of the line to the data. A) linear function B) R-squared C) moving average D) set intercept Answer: B 8. Which of the following is true of the R-squared (R2 ) value in Excel's Trendline function? A) A value of 1.0 for R2 indicates maximum deviation of the data from the line. B) If the value of R2 is above 1.0, the line will be at a perfect fit for the data. C) The value of R2 will always be between -1 and 1. D) As the value of R2 gets higher, the line will be a better fit for the data. Answer: D 9. Which of the following equations correctly expresses the relationship between the two variables? A) Value = (-181.16) + 13.493 × Number of years B) Number of years = Value / 12.537 C) Value = (459.34 / Number of years) × 4.536 D) Number of years = (17.538 × Value) / (-157.49) Answer: A The following table exhibits the age of antique furniture and the corresponding prices. Use the table to answer questions 1, and 2. (Hint: Use scatter chart and the Excel Trendline .tool where necessary) ?What is the relationship between the age of the furniture and their values (10 A) Linear B) Nonlinear C) Collinear D) No relationship Answer: A 11) What is the expected value for a 90 year-old piece of furniture? A) $1002.45 B) $997.98 C) $934.56 D) $1033.21 Answer: D 12) In a linear relationship, which of the following accounts for the many possible values of the dependent variable that vary around the mean? A) the coefficient of the dependent variable X B) the value of the intercept ß0 C) the random error term ε D) the standard error SYX Answer: C 13) Which of the following is true about the observed errors associated with estimating the value of the dependent variable using the regression line? A) They are the horizontal distances between slopes and y-intercepts. B) The errors are also referred to as critical values. C) They are always maximized by the regression lines. D) The errors can be negative or positive. Answer: D 14) For an independent variable Y, the error associated with the i th observation is: A) ei = Yi - Ŷi B) Yi = (ei)2 - Ŷi C) (Ŷi)2 ei = Yi D) ei = (Yi + Ŷi)2 Answer: A Use the data given below to answer the following question(s). Following is an extract from the database of a construction company. The table shows the height of walls in feet and the cost of raising them. The estimated simple linear regression equation is given as Ŷ = b0 + b1X. (Hint: Use Excel functions). 15. What is the value of the coefficient b0? A) -2.25321 B) 0.010697 C) 254.8371 D) 86.81704 Answer: C 16. What is the value of the coefficient b1? A) 86.81704 B) 254.8371 C) 0.010697 D) -2.14625 Answer: A 17. What is the estimated cost of raising a 10-inch wall? A) 1505.786 B) 1103.578 C) 968.6109 D) 1123.008 Answer: D 18. Which of the following statements is true when using the Excel Regression tool? A) The range for the independent variable values must be specified in the box for the Input Y Range. B) Checking the option Constant is Zero forces the intercept to zero. C) The Regression tool can be found in the Tools tab under Insert group. D) Adding an intercept term reduces the analysis' fit to the data. Answer: B 19. Which of the following generates a scatter chart in Excel with the values predicted by the regression model included? A) Trendline B) Residual Plots C) R Square D) Line Fit Plots Answer: D 20. The R2 value: A) is the variability of the observed Y-values from the predicted values. B) indicates that as the independent variable increases, the intercept term does too. C) gives the proportion of variation in the dependent variable that is explained by the independent variable. D) transforms the cumulative probability scale (vertical axis) so that the graph of the cumulative normal distribution is a straight line. Answer: C 21. For a simple linear regression model, significance of regression is: A) a measure of how well the regression line fits the data. B) a hypothesis test of whether the true regression coefficient ß1 is zero. C) a statistic that modifies the value of R2 by incorporating the sample size and the number of explanatory variables in the model. D) the variability of the observed Y-values from the predicted values. Answer: B 22. Which of the following Excel functions is applied to test for significance of regression? A) COVAR B) ANOVA C) SINH D) TREND Answer: B 23. While testing hypotheses for regression coefficients, the t-test for the slope is expressed as: Answer: A 24. _________ provide information about the unknown values of the true regression coefficients, accounting for sampling error. A) Standard errors B) Confidence intervals C) Adjusted R Squares D) P-values Answer: B 25. Standard residuals: A) help detect outliers that may bias the results of a regression analysis. B) cause differences in the regression equation by changing the slope and intercept. C) point out the ranges for the population intercept and slope at a 95% confidence level. D) provide information for testing hypothesis associated with the intercept and slope. Answer: A 26. A(n) __________ is an extreme value that is different from the rest of the data. A) critical value B) standard error C) expected value D) outlier Answer: D 27. While checking for linearity by examining the residual plot, the residuals must: A) exhibit a linear trend. B) form a parabolic shape. C) be randomly scattered. D) be below the x-axis. Answer: C 28. Which of the following is true when testing for normality of errors? A) Normality is verified by inspecting for a bell-shaped distribution. B) It is easier to evaluate normality with small sample sizes. C) A scatter diagram of the whole data is always used to verify normality. D) Errors are normally distributed when the scatter diagram shows a straight-line distribution. Answer: A 29. _________ means that the variation about the regression line is constant for all values of the independent variable. A) Autocorrelation B) Normality of errors C) Homoscedasticity D) Linearity. Answer: C 30. Which of the following helps in evaluation of autocorrelation? A) Breusch-Pagan test B) Durbin-Watson statistic C) Hosmer-Lemeshow test D) Cochran-Mantel-Haenszel statistics Answer: B 31) In multiple regression, R Square is referred to as the: A) multiple correlation coefficient. B) coefficient of autocorrelation. C) coefficient of multiple determination. D) multiple significance coefficient. Answer: C 32. Which of the following is true about multiple linear regression? A) It is a linear regression model with more than one dependent variable. B) The regression coefficients are called fractional regression coefficients. C) It uses least squares to estimate the intercept and slope coefficients. D) The ANOVA tests for the significance of each variable separately. Answer: C 33. When using the t-statistic in multiple regression to determine if a variable should be removed: A) R2 will increase if the variable is removed. B) if |t| > 1, the standard error will decrease. C) a large number of independent variables is convenient. D) if |t| < 1, the standard error will increase. Answer: A 34. When two or more independent variables in the same regression model can predict each other better than the dependent variable, the condition is referred to as____________ . A) autocorrelation B) heteroscedasticity C) multicollinearity D) homoscedasticity. Answer: C 35. Which of the following is true about multicollinearity? A) The effect of a dependent variable on another becomes difficult to isolate. B) Regression coefficients become clearer and are easier to interpret. C) P-values reduce significantly leading to rejection of null hypothesis. D) It is best measured using the statistic variance inflation factor (VIF). Answer: D 36. Categorical variables that have been coded are called __________. A) limited dependent variables B) dummy variables C) instrumental variables D) observable variables. Answer: B 37. Interaction is: A) the principle of having a model with maximum explanatory variables. B) the process of coding categorical variables. C) a measure to determine the correlation between dependent variables. D) the dependence between two independent variables. Answer: 38. How many additional dummy variables are required if a categorical variable has 4 levels? A) 2 B) 3 C) 1 D) 4 Answer: B 39. When a scatter chart of data shows a nonlinear relationship, the nonlinear model can be expressed as: A) Y = β0 + β1X + β2X2 + ε B) Y = β0 + β1X + (β2X)2 + ε C) Y = β0 + β1X + β2X D) Y = β0 + β1X2 + β2X2 + ε Answer: A 40. In a curvilinear regression model, the ________ represents the curvilinear effect. A) intercept B) error term C) slope D) R Square Answer: C 41) In predictive analysis models, a second-order polynomial has only one hill or valley. Answer: True 42) Excel's Trendline feature cannot be used in modeling trends which include time variables. Answer: False 43) The best-fitting line maximizes the residuals. Answer: False 44) Creating a scatter chart with an added trendline is visually superior to the scatter chart generated by line fit plots. Answer: True 45) The standard error may be assumed to be large if the data are clustered close to the regression line. Answer: False 46) An increase in adjusted R2 indicates that the regression model has improved. Answer: True 47) A good regression model has the fewest number of explanatory variables providing an adequate interpretation of the dependent variable. Answer: True