Chapter 13.1, Problem 6PB

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.

Results of regression analysis

1. a. Report the prediction equations relating crime rate to income at urbanization levels of (i) 0 and (ii) 100. Interpret.
2. b. For the simple regression model relating y = crime rate to x = income, MINITAB reports

   $\text{crime = -11}\text{.6 + 2}\text{.61 income}$

   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?

3. 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 urbanization (ii) controlling urbanization. (Note: The reversal in the association between income and education is an example of Simpson’s paradox.)