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

question 88

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 $= - 25.3 + 1.28$ 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:
$\begin{array} { l c c c c } & \text { car-thf } & \text { police } & \text { polexp } & \text { registr } \\ \text { car-thf } & 1.000 & & & \\ \text { police } & 0.466 & 1.000 & & \\ \text { polexp } & 0.970 & 0.390 & 1.000 & \\ \text { registr } & 0.976 & 0.406 & 0.958 & 1.000 \end{array}$
-What,if any,multicollinearity do you detect?

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Definitions:

Substitute

An alternative option or something that replaces another.

Cash

Physical form of currency, such as coins and banknotes, used to conduct transactions or stored as a financial asset.

Transferable

Pertaining to assets or rights that can be legally transferred from one party to another.

Uncollectible

Refers to debts or receivables that are deemed impossible to collect on or recover due to the debtor's inability to pay.