In a Comprehensive Road Test for New Car Models, One $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x$

question 109

Essay

In a comprehensive road test for new car models, one variable measured is the time it takes the car to accelerate from 0 to 60 miles per hour. To model acceleration time, a regression analysis is conducted on a random sample of 129 new cars. TIME60: y = Elapsed time (in seconds) from 0 mph to 60 mph MAX: x = Maximum speed attained (miles per hour) The simple linear model $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x$ was fit to the data. Computer printouts for the analysis are given below:
NWEIGHTED LEAST SQUARES LINEAR REGRESSION OF TIME60
$\begin{array}{l|c|c|c|c}\text { PREDICTOR } & & & & \\\text { VARIABLES } & \text { COEFFICIENT } & \text { STD ERROR } & \text { STUDENT'S T } & \text { P } \\\hline \text { CONSTANT } & 18.7171 & 0.63708 & 29.38 & 0.0000 \\\text { MAX } & -0.08365 & 0.00491 & -17.05 & 0.0000\end{array}$

$\begin{array} { l l l l } \text { R-SQUARED } & 0.6960 & \text { RESID. MEAN SQUARE (MSE) } & 1.28695 \\ \text { ADJUSTED R-SQUARED } & 0.6937 & \text { STANDARD DEVIATION } & 1.13444 \end{array}$
$\begin{array}{l|r|c|c|c|c}\text { SOURCE } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \\\hline \text { REGRESSION } & 1 & 374.285 & 374.285 & 290.83 & 0.0000 \\\text { RESIDUAL } & 127 & 163.443 & 1.28695 & & \\\text { TOTAL } & 128 & 537.728 & & &\end{array}$

CASES INCLUDED 129 MISSING CASES 0
Find and interpret the estimate $\hat { \beta } _ { 1 }$ in the printout above.

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