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.
Estimate Crime = 0 + 1Poverty + 2Income + 3Under 18 + 4Over 65 + . Discuss the individual and joint significance of the explanatory variables at the 5% significance level.
At the 5% level, conduct a partial F test to determine if the influence of Under 18 is different from that of Over 65.
Which explanatory variables are likely to be collinear? Find their sample correlation coefficients to confirm.
Name two other possible variables you might add to the regression analysis. What are your expectations for the signs of the coefficients?