PROBLEM 2 A researcher is interested in an underlying model of crime per 1000 people (tc) across towns in Connecticut. He is modeling the crime rate as a function of police expenditures per capita (pe measured as dollars per person), the unemployment rate (ue = 1 represents a 1% unemployment rate), and the average wage (wage measured in thousands of dollars). 1) Formulate the population model of interest and discuss the expected sign (priors) for each of the coefficients. 2) Is is likely that E(upe, ue, wage) = 0? Argue carefully. The results of the sample regression are presented in Listing 1. 3) Interpret each of the coefficients carefully. Are the results consistent with your priors? Explain. 4) Suppose that Greenwich Connecticut has an actual crime rate of tc = 12.63, pe = $214.19, ue = 1.7%, and wage = $97.25. Given these charac- teristics, is Greenwhich performing better or worse than predicted by your model? 5) What change in the unemployment rate would lead to a decrease of 9 crimes per 1000 people? Listing 1: Determinants of average salary. Call : lm ( formula la vgsal bs) Residuals : Min 1Q -1.35039 -0.14368 Median 0.00689 3Q 0.14759 Max 0.74891 Coefficients: Estimate Std. Error t value Pr(>It D. (Intercept) 10.64757 0.0 186.02 It D. (Intercept) 10.64757 0.0 186.02