A Traffic Consultant Has Analysed the Factors That Affect the Number

question 66

Essay

A traffic consultant has analysed the factors that affect the number of traffic fatalities. She has come to the conclusion that two important variables are the number of cars and the number of tractor-trailer trucks. She proposed the second-order model with interaction: $y =$ $\beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } ^ { 2 } + \beta _ { 4 } x _ { 2 } ^ { 2 } + \beta _ { 5 } x _ { 1 } x _ { 2 } + \varepsilon$ .
Where:
y = number of annual fatalities per shire. $x _ { 1 }$ = number of cars registered in the shire (in units of 10 000). $x _ { 2 }$ = number of trucks registered in the shire (in units of 1000).
The computer output (based on a random sample of 35 shires) is shown below.
THE REGRESSION EQUATION IS $y =$ $69.7 + 11.3 x _ { 1 } + 7.61 x _ { 2 } - 1.15 x _ { 1 } ^ { 2 } - 0.51 x _ { 2 } ^ { 2 } - 0.13 x _ { 1 } x _ { 2 }$ . $$\begin{array} { | c | r r c | } \hline \text { Predictor } & \text { Coef } & \text { SiDev } & T \\\hline \text { Constant } & 69.7 & 41.3 & 1.688 \\x _ { 1 } & 11.3 & 5.1 & 2.216 \\x _ { 2 } & 7.61 & 2.55 & 2.984 \\x _ { 1 } ^ { 2 } & - 1.15 & 0.64 & - 1.797 \\x _ { 2 } ^ { 2 } & - 0.51 & 0.20 & - 2.55 \\x _ { 1 } x _ { 2 } & - 0.13 & 0.10 & - 1.30 \\\hline\end{array}$$ S = 15.2 R-Sq = 47.2%.
ANALYSIS OF VARIANCE $$\begin{array} { | l | c c c c | } \hline \begin{array} { l } \text { Source of } \\\text { Variation }\end{array} & d f & \text { SS } & M S & F \\\hline \text { Regression } & 5 & 5959 & 1191.800 & 5.181 \\\text { Error } & 29 & 6671 & 230.034 & \\\hline \text { Total } & 34 & 12630 & & \\\hline\end{array}$$ What does the coefficient of $x _ { 2 } ^ { 2 }$ tell you about the model?

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Definitions:

Lower Tariffs

Reducing taxes or duties to be paid on imported goods, usually to encourage international trade.

Firm's Production

The total output of goods and services produced by a company within a specific period.

Gray Market

The trade of legal goods through unauthorized distribution channels, distinct from black market goods which are illegal.

Offshore Locations

Sites or jurisdictions outside a country's borders where businesses can operate under favorable legal, tax, or regulatory conditions.