A government 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 of residents older than 65. A portion of the data is shown; the entire data set can be obtained from the text website, labeled Crime.
a. Estimate Crime = β0 + β1 Poverty + β2 Income + β3Under 18 + β4Over 65 + ε. Discuss the individual and joint significance of the explanatory variables at the 5% significance level.
b. At the 5% level, conduct a partial F test to determine if the influence of Under 18 is different from that of Over 65.
c. Which explanatory variables are likely to be collinear? Find their sample correlation coefficients to confirm.