SCENARIO 17-5
You Worked as an Intern at We Always

question 74

Short Answer

SCENARIO 17-5
You worked as an intern at We Always Win Car Insurance Company last summer. You notice that
individual car insurance premiums depend very much on the age of the individual, the number of
traffic tickets received by the individual, and the population density of the city in which the individual
lives. You performed a regression analysis in EXCEL and obtained the following information: $\begin{array}{l}\begin{array}{lr}\hline {\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.63 \\\text { R Square } & 0.40 \\\text { Adjusted R Square } & 0.23 \\\text { Standard Error } & 50.00 \\\text { Observations } & 15.00 \\\hline\end{array}\\\\\text { ANOVA }\\\begin{array}{lrcccr}\hline & d f &{\text { SS }} & \text { MS } & \text { F }&{\text { Significance } F} \\\hline \text { Regression } & 3 & & 5994.24 & 2.40 & 0.12 \\\text { Residual } & 11 & 27496.82 & & & \\\text { Total } & & 45479.54 & & & \\\hline\end{array}\\\\\begin{array}{lrrrrrr}\hline & \text { Coefficients } & \begin{array}{c}\text { Standard } \\\text { Error }\end{array} & \text { t Stat } & \text { P-value } & \text { Lower 99.0\% } & \text { Upper 99.0\% } \\\hline \text { Intercept } & 123.80 & 48.71 & 2.54 & 0.03 & -27.47 & 275.07 \\\text { AGE } & -0.82 & 0.87 & -0.95 & 0.36 & -3.51 & 1.87 \\\text { TICKETS } & 21.25 & 10.66 & 1.99 & 0.07 & -11.86 & 54.37 \\\text { DENSITY } & -3.14 & 6.46 & -0.49 & 0.64 & -23.19 & 16.91 \\\hline\end{array}\end{array}$
AGE -0.82 0.87 -0.95 0.36 -3.51 1.87
TICKETS 21.25 10.66 1.99 0.07 -11.86 54.37
DENSITY -3.14 6.46 -0.49 0.64 -23.19 16.91
-Referring to Scenario 17-5, to test the significance of the multiple regression model, the value
of the test statistic is ______.

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Definitions:

Variation

The measure of dispersion within a dataset, indicating how much individual data points differ from the average value.

First-order Model

A simple linear model that describes a relationship between two variables with a direct correlation, without considering complex interactions.

Air Temperatures

Measurements of the atmosphere's heat content at different places and times, essential for weather forecasting and climate study.

Distance From Coast

The linear measurement between a specific point and the nearest point on the coast, often used in geographical and environmental studies.