In a Comprehensive Road Test for New Car Models, One $y$

question 72

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 $0 \mathrm { mph }$ to $60 \mathrm { mph }$
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:
$\begin{array}{l|c|c|c|c}\text { PREDICTOR } & & & & \\\text { VARIABLES } & \text { COEFFICIENT } & \text { STD ERROR } & \text { STUDENT'S T } & \text { P } \\\hline \text { CONSTANT } & 18.7171 & 0.63708 & 29.38 & 0.0000 \\\text { MAX } & -0.08365 & 0.00491 & -17.05 & 0.0000\end{array}$

$\begin{array}{llll}\text { R-SQUARED } & 0.6960 & \text { RESID. MEAN SQUARE (MSE) } & 1.28695 \\\text { ADJUSTED R-SQUARED } & 0.6937 & \text { STANDARD DEVIATION } & 1.13444\end{array}$




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

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Definitions:

Tax Expense

Tax Expense is the total amount of taxes owed by an individual or corporation to the federal, state, and local government, reflecting in the financial statements of the period in which the tax is accrued.

Premium Amortization

The systematic reduction of a premium paid above the par value of a bond, allocated over the bond's life until maturity.

Bond Amortization Schedule

A schedule that details the reduction of a bond's principal amount over time, often including payments of both principal and interest.

Unamortized Premium

The portion of a bond premium that has not yet been amortized or gradually written off over time.