Midterm 1 Solutions

Midterm 1 – Solutions 1. Question. [True or False; Give brief justification] Classification is a pervasive problem that encompasses many diverse applications. Answer: True. There are many practical problems that are classification problems. 2. Question. [True or False; Give brief justification] Examples of classification include detecting spam email messages based upon the message header and content, categorizing cells as malignant or benign based upon the results of MRI scans, and classifying galaxies based upon their shapes. Answer: True. These are examples that are given in the lecture videos. 3. Question. Give some examples of quantitative data. Answer: the daily temperature, the precipitation in a region, the number of passengers in an international airport, and so on. 4. Question. Give some examples of binary data. Answer: The gender, whether or not someone receive a job offer, whether or not the airplane has taken off, etc. 5. Question. [True or False; Give brief justification] Time series data are often recorded at equal intervals (doesn’t have to be). Answer: True. 6. Question. [True or False; Give brief justification] Examples of time series data are Daily sales, stock prices, child’s height on each birthday. Answer: True. 7. Question. [True or False; Give brief justification] Is following the procedure of SVM? • Given data {xij }, where xij is the jth factor of data point i P • The classifier is the line 0 = a0 + j aj xj P 2 • Maximize gap by minimizing j aj Answer: False. It is incomplete. For example, it needs components (e.g., inequalities) to enforce the classifying condition. 8. Question. Describe how to do scaling to make data between 0 and 1. Answer: Subtract the minimum. Then divide by the range (the maximum minors the minimum. 9. Question. Describe how to do standardization? Answer: Subtract the mean (or sample mean). Divide by the standard deviation (or sample standard deviation). 10. Question. One shouldn’t measure model’s effectiveness on data it was trained on, why? Answer: Because (a) The model fit captures both real and random effects; and (b) Only real effects are duplicated in other data. 11. Question. [True or False; Give brief justification] One can use a Training Set to build the models, use a Validation Set to pick a model, and then use a Test Set to estimate the performance of the chosen model. Answer: True. 12. Question. What does the following comment do in the R language? > ?seq Answer: Display the help menu of the function “seq”. 17. Question. [True or False; Give brief justification] Clustering is a supervised learning problem. Answer: False. It is an unsupervised learning problem. There is no response variable in it. 18. Question. [True or False; Give brief justification] Classification is a unsupervised learning problem. Answer: False. The class is the response variable. 19. Question. [True or False; Give brief justification] In a box-and-whisker plot, the middle horizontal line of the box corresponds to the median of the data. Answer: True. Refer to the construction of the box-and-whisker plot. 20. Question. [True or False; Give brief justification] In a box-and-whisker plot, the upper horizontal line of the box corresponds to the upper quartile of the data. Answer: True. Refer to the definition of the boxplot. 21. Question. [True or False; Give brief justification] Is the following a right description of the CUSUM procedure? Suppose xt is the observed value at time t. Assume that µ is the mean of x, if no change. One computes the following quantity, St = max {0, St−1 + (xt − µ)} . For a prescribed T , if St ≥ T , then a change is declared. Answer: True. 22. Question. [True or False; Give brief justification] In a simple Exponential Smoothing setting, if St is the expected baseline response at time period t and xt is the observed response, we have St = αxt + (1 − α)St−1 , for 0 < α < 1. Answer: True. 23. Question. [True or False; Give brief justification] The triple exponential smoothing is also called the Winter’s Method or the Holt-Winters Method. Answer: True. ISyE 6501, Midterm-1, Tuesday 9/13/2022 5 24. Question. [True or False; Give brief justification] ARIMA(0, 0, q) is the MA (Moving Average) model Answer: True. 25. Question. [True or False; Give brief justification] ARIMA(p, 0, 0) is the AR (Autoregressive) model Answer: True. 26. Question. [True or False; Give brief justification] ARIMA (0, 1, 0) is the Random walk Answer: True. 27. Question. [True or False; Give brief justification] ARIMA (0, 0, 0) is the white noise Answer: True. 28. Question. Justify why the following is true. n  1 P 1 √ maximizey1 ,...,yn e− 2σ2 n σ 2π i=1 (zi −yi )2 → minimizey1 ,...,yn n X i=1 ( zi − y i ) 2 Answer: Take the logarithmic transform, which is a monotone transform. Then remove the constant factor and terms. 29. Question. Give an illustration on how regression can be used as a predictive tool. Answer: Using the least squares estimates of the coefficients in the linear function, input the values of the explanatory variables. The resulting value of the linear function is the predicted value. 30. Question. Does Correlation lead to Causation? Answer: No. It is possible to be correlated, however, there is no causal relationship.