The Florida data file, shown partly on page 283, has data from the 67 Florida counties on y = crime rate

(number per 1000 residents), x1 = median income (thousands of dollars), and x2 = percentage in urban environment.

(a) Figure 11.12 shows a scatterplot relating y to x1. Predict the sign that the estimated effect of x1 has in the prediction equation ˆy = a + bx1. Explain.

(b) Figure 11.13 shows partial regression plots relating y to each explanatory variable, controlling for the other. Explain how these relate to the signs of b1 and b2 in the prediction equation ˆy = a + b1x1 + b2x2.

(c) Table 11.13 shows some software output for the bivariate and multiple regression models. Report the prediction equation relating y to x1, and interpret the slope.

(d) Report the prediction equation relating y to both x1 and x2. Interpret the coefficient of x1, and compare to (c).

(e) The correlations are ryx1 = 0.43, ryx2 = 0.68, and rx1x2 = 0.73. Use these to explain why the x1 effect seems so different in

(c) and (d).

(f) Report the prediction equations relating crime rate to income at urbanization levels of (i) 0, (ii) 50, (iii) 100. Interpret.