HW6_STAT302

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Jan 9, 2024

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HW6: 150 points Submission by blackboard – April 8, 2022 This HW is very useful for understanding multiple linear regression analysis and modeling Statewide crime rate data for 1996: (200 points): Open in SPSS the statewide crime rate data. Variables are explained in the excel spreadsheet. Question 1 (50) Our interest is to explain/predict “CRIME” (number of incidents per 100,100 people) by means of other variables in the table – METRO, POVERY, COLLEGE, INCOME. This means you have to examine the association between CRIME and each (or a combination of) the rest of the data. a) Use SPSS correlation function to calculate the bivariate correlations among ALL the variables (5 of them, no need to copy them all here). Note: Do not consider state name as variable! What are the three highest (in magnitude) bivariate correlations (between which variables)? 1. Poverty & Income – 0.646 in magnitude 2. Crime & Metro – 0.525 in magnitude 3. Income and College – 0.524 in magnitude b) What is the bivariate correlation value between CRIME and INCOME, and is it statistically significant at alpha = 0.05? a. Yes, since the significance is over 0.05. c) What is the partial correlation value between CRIME and INCOME when controlling for METRO, and is it statistically significant at alpha = 0.05? a. -0.290 b. It is not statistically significant as the significance is less than 0.05. d) How do you explain the difference between the bivariate and the partial correlation values (as well as the sign of those values) between CRIME and INCOME? a. Because the correlation between CRIME and INCOME was not huge to start with, controlling for METRO made the correlation even small as there are more variables to consider. Question 2 (100) Find the multiple regression linear equation (no interaction variables) to predict CRIME (response variable) from the rest of the variables (predictors) by using the backward elimination procedure in SPSS . Start with the linear regression of CRIME as a function of all the predictors (4 of them): a. What is the final (last step) multiple regression equation to predict CRIME? Note: Write the equation, for example: Crime = Intercept + ……. and enter both the variables and their slope coefficients. a. Crime = -706.953 + 49.549*Poverty – 3.738*College + 7.859 *Metro + 0.008 *Income b. For the final step model: What is the F-stat value and how is it calculated from ANOVA.

a. b. F-stat is 12.180. c. For the final step model: What is the P-value of the F-stat and is the linear association of crime rate to the multiple predictors statistically significant at alpha = 0.05? a. The p-value is <0.01, therefore it is statistically significant. d. Copy and paste here the VIFs for each predictor (for the final step model). a. e. Is multi-collinearity a problem and why (for the final step model)? a. No, because all of the variables are similar. f. Compare the final step multiple regression model results with the first step multiple regression model results – R 2 , the Adjusted R 2 and the Standard Error - and comment on the difference in these results.

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