ISOM835_Lab 7_LR II_solution

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1 Lab 7: Linear Regression – Advanced Topics – Solution ISOM 835 Predictive Analytics Sawyer Business School Dr. Kate Li ISOM This lab consists of two portions: 1. SAS Enterprise Guide Demonstration: Linear Regression – Advanced Topics (20 pts) 2. Questions 1-4 (80 pts) While you work through each lab, please take notes of things that you don’t understand and/or are not sure about. I will give you time to ask questions during the following class. Complete the following questions by yourself Question 1 (22 pts): Examining Residuals a. (4 pts) Import BodyFat2.csv and run a regression of PctBodyFat2 on Weight , Abdomen , Forearm , and Wrist and create diagnostic plots. Provide screenshots of the regression result.

2 b. (4 pts) Do the residual plots indicate any problems with the constant variance assumption? It does not appear that the data violate the assumption of constant variance.

3 c. (4 pts) Is there any indication of nonlinear relationship between the response variable and the predictors by the evidence in the residual plots? The residual plots do not suggest any obvious nonlinear relationship. d. (4 pts) Does the Quantile-Quantile plot indicate any problems with the normality assumption? The normality assumption seems to be met, although some points at the two ends deviate from the reference line more noticeably.

4 e. (6 pts) Generate the plots of (1) studendized residuals, (2) Cook’s D, (3) DFFITS, and (4) DFBETAS, and make sure that observation number of potential influential points are printed on the plots. Provide the plots and comment on which observations are identified as potential influential observations based on the suggested cutoff values of the statistics. Steps: 1) Modify the previous task. 2) With Plots selected at the left, select Custom list of plots and then check the boxes for Studentized residuals by predicted values plot , Plot Cook’s D statistic , DFFITS plots , and DFBETAS plots . Uncheck the box next to Diagnostic Plots . 3) With Predictions selected at the left: a. Check the box for Original sample under Data to predict . b. Check Predictions and Diagnostic statistics under Save output data . c. Check the box for Residuals under Additional statistics . 4) Click Save . Do not replace the results from the previous run. 5) Right-click the previous task and select Add as a Code Template . 6) Double-click the node for the code in order to edit it and find the PROC REG section of the code. 7) Make the following changes: PLOTS(ONLY LABEL)=RSTUDENTBYPREDICTED PLOTS(ONLY LABEL)=COOKSD PLOTS(ONLY LABEL)=DFFITS PLOTS(ONLY LABEL)=DFBETAS

5 ! Add the option (LABEL) within the parentheses after the words PLOTS. 8) Click Save and then select Save As to name and locate the file. 9) Click Run above the code window. Studendized residual plot: There are only a modest number of observations farther than two standard error units from the mean of 0. Cook’s D plot: There are 10 labeled outliers, but observation 39 is clearly the most extreme.

6 DFFITS plot: The same observations are shown to be influential by the DFFITS statistic. DFBETAS plot: DFBETAS are extreme for observation 39 on the parameters for Weight and Forearm circumference.

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