13.6 Crime rate and income Refer to the previous exercise.

MINITAB reports the following results for the multiple regression of y = crime rate on x1 = median income

(in thousands of dollars) and x2 = urbanization.

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Results of regression analysis Term Constant income urbanization Coef 40.0 SE Coef T-Value P-Value 16.4 2.44 0.017 -0.791 0.805 -0.98 0.330 5.78 0.000 0.642 0.111 a. Report the prediction equations relating crime rate to in- come at urbanization levels of (i) 0 and (ii) 100. Interpret. b. For the simple regression model relating y = crime rate to x = income, MINITAB reports crime = -11.6 +2.61 income Interpret the effect of income, according to the sign of its slope. How does this effect differ from the effect of income in the multiple regression equation? c. Use the estimated slope for income in the simple and multiple regression model to explain the difference in the interpretation of the slope when (i) ignoring urban- ization (ii) controlling urbanization. (Note: The reversal in the association between income and education is an example of Simpson's paradox.)