States
Concern Over the Number of Car Thefts Grew into a Project

States
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 MINITAB regression results are:
The regression equation is car-thf $= - 25.3 + 1.28$ police $+ 0.0188$ polexp $+ 0.0969$ registr
$\begin{array} { l l l c l } \text { Predictor } & \text { Coef } & \text { Stdev } & \text { t-ratio } & p \\ \text { Constant } & - 25.29 & 17.85 & - 1.42 & 0.190 \\ \text { police } & 1.2831 & 0.9275 & 1.38 & 0.200 \\ \text { polexp } & 0.018827 & 0.008460 & 2.23 & 0.053 \\ \text { registr } & 0.09686 & 0.03536 & 2.74 & 0.023 \end{array}$
$$s = ? ? \quad \mathrm { R } - s q = ? ? \% \quad \mathrm { R } - s q ( a d j ) = ? ? \%$$
Analysis of Variance
$\begin{array} { l l l l c l } \text { SOURCE } & \text { DF } & \text { SS } & \text { MS } & F & p \\ \text { Regression } & 3 & 33007 & 11002 & 107.14 & 0.000 \\ \text { Error } & 9 & 924 & 103 & & \\ \text { Total } & 12 & 33932 & & & \end{array}$
Correlation between the variables:
$\begin{array} { l c c c c } & \text { car-thf } & \text { police } & \text { polexp } & \text { registr } \\ \text { car-thf } & 1.000 & & & \\ \text { police } & 0.466 & 1.000 & & \\ \text { polexp } & 0.970 & 0.390 & 1.000 & \\ \text { registr } & 0.976 & 0.406 & 0.958 & 1.000 \end{array}$
-Do the partial regression coefficients have the algebraic sign you might expect?