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

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Essay

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= - 25.3 + 1.28 police +0.0188+ 0.0188 polexp +0.0969+ 0.0969 registr
 Predictor  Coef  Stdev  t-ratio p Constant 25.2917.851.420.190 police 1.28310.92751.380.200 polexp 0.0188270.0084602.230.053 registr 0.096860.035362.740.023\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=??Rsq=??%Rsq(adj)=??%s = ? ? \quad \mathrm { R } - s q = ? ? \% \quad \mathrm { R } - s q ( a d j ) = ? ? \%
Analysis of Variance
 SOURCE  DF  SS  MS Fp Regression 33300711002107.140.000 Error 9924103 Total 1233932\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:
 car-thf  police  polexp  registr  car-thf 1.000 police 0.4661.000 polexp 0.9700.3901.000 registr 0.9760.4060.9581.000\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?

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