Exercise 7—Multiple Regression (with dummies)

Points: 15

The California syntax consists of four Multiple Regression Analyses, each predicting attitudes toward immigration as measured by the four-item index RawImm4. The first multiple regression uses three demographic items as predictors. In the second multiple regression these same predictors are converted to dummy variables. The third regression adds a number of additional dummied independent variables. The fourth regression adds three political independent variables. In answering the questions be sure to read through the relevant syntax.

Part 1—California results

Cal1. What proportion of the variation in the DV is explained by Multiple Regression Analysis 1 (through line 70) of the California syntax file?

Cal2. What is the equation for this regression analysis?

Cal3. Draw the simple arrow diagram illustrating this model including Beta coefficients, Adjusted R² and N.

Cal4. What is the proper interpretation for the strongest predictor?

Cal5. In the analysis produced by Multiple Regression Analysis 2 (through line 97), what proportion of the variation in the DV is explained?

Cal6. What is the reference category for the age variable in this regression?

Cal7. Do these results suggest older or younger Californians more supportive of immigration?

Cal 8. In Multiple Regression 2, are those with a college education more or less supportive of immigration than those with a high school education? How do you know?

Cal9. In the analysis produced by Multiple Regression Analysis 3 (through line 97) of the California syntax, how well does the multivariate equation fit the data?

Cal10. What is the overall significance of this equation?

Cal11. Which is its strongest predictor?

Cal12. How should the coefficient for white be interpreted?

Cal13. What percent of the variation in the DV is explained by the analysis produced by Multiple Regression 4 of the California syntax?

Cal14. What is the proper interpretation of the Beta coefficient for interest?

Cal15 Should we be concerned over multi-collinearity in Multiple Regression 4? Why?

Part 2—Texas results

The Texas syntax consists of four pairs of Multiple Regression analyses. The first regression of each pair uses ImmIncl as the dependent variable; while the second regression of each pair sets ImmExcl as its dependent variable. In answering the questions again be sure to read through the relevant syntax.

Tex1. What proportion of the variation in ImmIncl is explained by the analysis produced by Multiple Regression 1a of the Texas syntax file?

Tex2. What proportion of the variation in ImmExcl is explained by the analysis produced by Multiple Regression 1b procedure of the Texas syntax file?

Tex3. What is the equation for regression 1a predicting ImmIncl?

Tex4. What is the equation for regression 1b ImmExcl?

Tex5. Which is the strongest predictor of variation in both ImmIncl and ImmExcl?

Tex6. In Multiple Regressions 2a and 2b what are their respective adjusted R² values?

Tex7. Why might these values be lower than the adjusted R² values in Multiple Regression 1a and 1b?

Tex8. In Multiple Regressions 3a and 3b what are their respective values of R²?

Tex9. What are the strongest predictors in Multiple Regressions 3a & 3b?

Tex10. What is the proper interpretation of their respective Beta coefficients?

Tex11. What are the respective Adjusted R² values for Multiple Regression 4a & 4b?

Tex12 Apart from being ideologically liberal, in Multiple Regression 4a, what is the best predictor of ImmIncl?

Tex13. How does that same variable fare in predicting ImmExcl? Be precise.

Tex14. What is the Beta and significance of the best predictor of ImmExcl in Multiple Regression 4b?

Tex15. In the analyses produced by Multiple Regressions 4a & 4b predicting ImmIncl and ImmExcl respectively, what is the proper interpretation of the Beta coefficients for interest?