F IL E A governm ent researcher examines the factors that influence a city's crime rate. For 41 cities, she collects the crime rate (crimes per 100,000 residents), the poverty rate

(in %), the median income (in $ 1,000s), the percent of residents younger than 18, and the percent o f residents older than 65. A portion o f the data is shown; the entire data set can be obtained from the te xt website, labeled Crime.

Crime Poverty Income Under 18 Over 65 710.6 3.8 58.422 18.3 23.4 1317.7 16.7 48.729 19.0 10.3 139.7 3.9 59.445 19.7 16

a. Estimate Crime = β 0 + β 1 Poverty + β 2 Income +

β 3Under 18 + β 4Over 65 + ε . Discuss the individual and jo in t significance o f the explanatory variables at the 5%

significance level.

b. At the 5% level, conduct a partial F test to determ ine if the influence o f Under 18 is different from that of Over 65.

c. W hich explanatory variables are likely to be collinear?

Find their sample correlation coefficients to confirm.