Motorcycle Fatalities
a Traffic Consultant Has Analyzed the Factors That

question 56

Essay

Motorcycle Fatalities
A traffic consultant has analyzed the factors that affect the number of motorcycle fatalities.She has come to the conclusion that two important variables are the number of motorcycle and the number of cars.She proposed the model $$\tilde { y } = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } ^ { 2 } + \beta _ { 4 } x _ { 2 } ^ { 2 } + \beta _ { 5 } x _ { 1 } x _ { 2 } + \varepsilon$$ (the second-order model with interaction),where y = number of annual fatalities per county,x₁ = number of motorcycles registered in the county (in 10,000),and x₂ = number of cars registered in the county (in 1000).The computer output (based on a random sample of 35 counties)is shown below:
THE REGRESSION EQUATION IS $$y = 69.7 + 11.3 x _ { 1 } + 7.61 x _ { 2 } - 1.15 x _ { 1 } ^ { 2 } - 0.51 x _ { 2 } ^ { 2 } - 0.13 x _ { 1 } x _ { 2 }$$ $\begin{array}{ccc}\text { Predictor}&\text { Coef } & \text { StDev } & T \\\hline\text { Constant}& 69.7 & 41.3 & 1.688 \\x_{1} &11.3 & 5.1 & 2.216 \\ x_{2}&7.61 & 2.55 & 2.984 \\x_1^2&-1.15 & .64 & -1.797 \\& & \\x_2^2&-.51 & .20 & -2.55 \\& & \\& & \\ x_{1} x_{2}&-.13 & .10 & -1.30\end{array}$ $$S= 15.2 \quad \mathrm { R } - \mathrm { Sq } = 47.2 \%$$ ANALYSIS OF VARIANCE
$$\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \boldsymbol { df } & \mathbf { S S } & \boldsymbol { M S } & \boldsymbol { F } \\\hline \text { Repressian } & 5 & 5959 & 1191.800 & 5.181 \\\text { Error } & 29 & 6671 & 230.034 & \\\hline \text { Total } & 34 & 12630 & & \\\hline\end{array}$$
-{Motorcycle Fatalities Narrative} Test at the 1% significance level to determine if the $x _ { 1 } ^ { 2 }$ term should be retained in the model.

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Definitions:

Cumulative Gross Earnings

The total gross income earned by an individual or entity before any deductions over a given period.

State Tax Rate

The percentage at which individuals or businesses within a state are taxed by the state government.

FICA

The Federal Insurance Contributions Act; a U.S. law that requires a deduction from paychecks to fund Social Security and Medicare benefits.

OASDI

The Old-Age, Survivors, and Disability Insurance program, part of the U.S. Social Security system, providing benefits to eligible retirees, their families, and the disabled.