Question: Concern over the number of car thefts grew into a project to determine the relationship between car thefts by state and these variables:

x1 = Police per 10,000 persons, by state

x2 = Expenditure by local government for police protection, in thousands, by state

x3 = New passenger car registrations, in thousands, by state.

Data from 13 states were collected. The regression results are:

The regression equation is

car-thf = - 25.3 + 1.28police + 0.0188polexp + 0.0969registr

Predictor Coef StDev t-ratio p

Constant -25.29 17.85 -1.42 0.190

police 1.2831 0.9275 ? ?

polexp 0.018827 0.008460 ? ?

registr 0.09686 0.03536 ? ?

s =? ? R-sq = ??% R-sq(adj) =? ?%

Analysis of Variance

SOURCE DF SS MS F p

Regression 3 33007 11002 107.14 ?

Error 9 924 103

Total 12 33932

Correlation between the variables:

car-thf police polexp registr

car-thf 1.000

police 0.466 1.000

polexp 0.970 0.390 1.000

registr 0.976 0.406 0.958 1.000

Compute the following:

a) Standard error of estimate

b) How much of the variation in thefts is explained by the model

c) Adjusted R-Squared

d) t-values associated with your coefficient estimates and their p-values

e) Do the partial regression coefficients have the algebraic sign you might expect? What, if any, multicollinearity do you detect?

Perform a test for each partial regression coefficient using a 0.05 significance level. Please state your null/alternative hypothesis both verbally and symbolically in each case. What conclusions can you draw? Do these data provide enough evidence to conclude at the 5% significance level that the model is useful in predicting the car thefts? Why or why not? Please state your null/alternative hypothesis both verbally and symbolically.