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Engineers Want to Know What Factors Are Associated with Gas $R$

question 22

Essay

Engineers want to know what factors are associated with gas mileage. The regression
below predicts the average miles per gallon (MPG) for 82 cars using their engine
horsepower (HP) and weight (WT, in 100's of pounds). Dependent variable is MPG
$R$ squared $= 82.4 \% \quad$ R squared (adjusted) $= 81.9 \%$ $s = 4.255$ with $82 - 3 = 79$ degrees of freedom
$Engineers want to know what factors are associated with gas mileage. The regression below predicts the average miles per gallon (MPG) for 82 cars using their engine horsepower (HP) and weight (WT, in 100's of pounds). Dependent variable is MPG R squared = 82.4 \% \quad R squared (adjusted) = 81.9 \% s = 4.255 with 82 - 3 = 79 degrees of freedom \begin{array}{llllr} \text { Variable } & \text { Coeffïcient } & \text { SE(Coeff) } & \text { t-ratio } & \text { p-value } \\ \text { Constant } & 66.855 & 2.079 & 32.2 & <0.0001 \\ \text { HP } & -0.0209708 & 0.015 & -1.4 & 0.1661 \\ \text { WT } & -0.990369 & 0.1047 & -9.45 & <0.0001 \end{array} a. Write down the regression equation. b. Write down the hypotheses for the test of the coefficient of horsepower. Conduct the test and explain your conclusion in the context of this problem. c. Write down the hypotheses for the test of the coefficient of weight. Conduct the test and explain your conclusion in the context of this problem. d. Explain the meaning of the coefficient of weight in the context of this problem. e. Explain the meaning of the intercept of this regression in the context of this problem. f. Compute the predicted gas mileage of a 3500 pound car with a 150 horsepower engine. The plots are MPG vs. HP, MPG vs. WT, residuals vs. predicted values, and a normal probability plot of residuals. g. Check the conditions of this regression and comment on whether they are satisfied.$

$\begin{array}{llllr}\text { Variable } & \text { Coeffïcient } & \text { SE(Coeff) } & \text { t-ratio } & \text { p-value } \\\text { Constant } & 66.855 & 2.079 & 32.2 & <0.0001 \\\text { HP } & -0.0209708 & 0.015 & -1.4 & 0.1661 \\\text { WT } & -0.990369 & 0.1047 & -9.45 & <0.0001\end{array}$

a. Write down the regression equation.
b. Write down the hypotheses for the test of the coefficient of horsepower. Conduct the test
and explain your conclusion in the context of this problem.
c. Write down the hypotheses for the test of the coefficient of weight. Conduct the test and
explain your conclusion in the context of this problem.
d. Explain the meaning of the coefficient of weight in the context of this problem.
e. Explain the meaning of the intercept of this regression in the context of this problem.
f. Compute the predicted gas mileage of a 3500 pound car with a 150 horsepower engine.
The plots are MPG vs. HP, MPG vs. WT, residuals vs. predicted values, and a normal
probability plot of residuals. $Engineers want to know what factors are associated with gas mileage. The regression below predicts the average miles per gallon (MPG) for 82 cars using their engine horsepower (HP) and weight (WT, in 100's of pounds). Dependent variable is MPG R squared = 82.4 \% \quad R squared (adjusted) = 81.9 \% s = 4.255 with 82 - 3 = 79 degrees of freedom \begin{array}{llllr} \text { Variable } & \text { Coeffïcient } & \text { SE(Coeff) } & \text { t-ratio } & \text { p-value } \\ \text { Constant } & 66.855 & 2.079 & 32.2 & <0.0001 \\ \text { HP } & -0.0209708 & 0.015 & -1.4 & 0.1661 \\ \text { WT } & -0.990369 & 0.1047 & -9.45 & <0.0001 \end{array} a. Write down the regression equation. b. Write down the hypotheses for the test of the coefficient of horsepower. Conduct the test and explain your conclusion in the context of this problem. c. Write down the hypotheses for the test of the coefficient of weight. Conduct the test and explain your conclusion in the context of this problem. d. Explain the meaning of the coefficient of weight in the context of this problem. e. Explain the meaning of the intercept of this regression in the context of this problem. f. Compute the predicted gas mileage of a 3500 pound car with a 150 horsepower engine. The plots are MPG vs. HP, MPG vs. WT, residuals vs. predicted values, and a normal probability plot of residuals. g. Check the conditions of this regression and comment on whether they are satisfied.$
g. Check the conditions of this regression and comment on whether they are satisfied.

Definitions:

Public Good

A product or service that is provided without profit to all members of a society, either by the government or a private individual or organization.

Public Good

A good that is non-excludable and non-rivalrous, meaning its consumption by one individual does not reduce its availability to others and people cannot be effectively excluded from using it.

Public Good

A good that is non-excludable and non-rivalrous, meaning it can be used simultaneously by more than one person without reducing its availability to others.

Flat Road Tax

A fixed-rate tax imposed on vehicle owners, irrespective of the vehicle's value, emissions, or usage levels.

Engineers Want to Know What Factors Are Associated with Gas RRR

Definitions:

Engineers Want to Know What Factors Are Associated with Gas $R$