Multiple Regression Analysis: Normality of Residuals and Prediction Power - Prof. Naoru Ko, Assignments of Public Policy

Download Multiple Regression Analysis: Normality of Residuals and Prediction Power - Prof. Naoru Ko and more Assignments Public Policy in PDF only on Docsity! PROBLEM SET 4 (Due on Thursday, May 1st) Use the dataset salary.sav to answer following questions. Select clerical workers (JOBCAT = 1) in the dataset. Consider a multiple regression with the following dependent and independent variables: Dependent variable: Current Salary Independent variables: Beginning Salary Job Seniority Age of Employee Work Experience 1. Residual Analysis: q1. You are interested in checking if the residuals are distributed normally. To check this, obtain a normal probability plot of residuals (Normal Q-Q plot) using the residuals obtained from the following multiple regression. Use standardized residuals for both plots. Include the plot in your answer. Discuss if the residuals appear to be normally distributed or not. There are some deviation on the top and the bottom. This indicates that for small and large current salary values, the residuals may not be normally distributed. -4 -2 0 2 4 Observed Value -3 -2 -1 0 1 2 3 Ex pe ct ed N or m al Normal Q-Q Plot of Standardized Residual q2. Interpret the results of the Kolmogorov-Smironov and Shapiro-Wilk tests in the table obtained from q1. Specify the null hypothesis and state if it is rejected or not. Include the table to your answer. Tests of Normality .077 227 .002 .952 227 .000Standardized Residual Statistic df Sig. Statistic df Sig. Kolmogorov-Smirnova Shapiro-Wilk Lilliefors Significance Correctiona. The test of normality with the null hypothesis that the residuals come from normal distributed is rejected. Thus, the test indicates that the residuals are NOT normally distributed. 2. Prediction: q3. You are interested in checking the prediction power of your regression model. To see this, construct a scatter plot with Unstandardized Predicted Current Salary on Y-axis and Observed current Salary and X-axis. Does the prediction seem more or less accurate? Include the plot in your answer. The prediction seems to be fairly reasonable except a couple of outliers. 5000 10000 15000 20000 25000 30000 CURRENT SALARY 5000.00000 10000.00000 15000.00000 20000.00000 25000.00000 U ns ta nd ar di ze d Pr ed ic te d Va lu e R Sq Linear = 0.693