Using the weights ( $\mathrm{lb}$ ) and highway fuel consumption amounts (mi/gal) of the 48 cars listed in the accompanying data set, one gets this regression equation: $\hat{y}=58.9-0.00749 x$, where $x$ represents weight. Complete parts (a) through (d).
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A. The slope is 58.9 and the $y$-intercept is 0.007499 .
B. The slope is -0.00749 and the $y$-intercept is 58.9 .
C. The slope is 58.9 and the $y$-intercept is -0.00749 .
D. The slope is 0.00749 and the $y$-intercept is 58.9 .
c. What is the predictor variable?
A. The predictor variable is weight, which is represented by $x$.
B. The predictor variable is weight, which is represented by $y$.
C. The predictor variable is highway fuel consumption, which is represented by $y$.
D. The predictor variable is highway fuel consumption, which is represented by $x$.
d. Assuming that there is a significant linear correlation between weight and highway fuel consumption, what is the best predicted value for a car that weighs $3000 \mathrm{lb}$ ?
The best predicted value of highway fuel consumption of a car that weighs $3000 \mathrm{lb}$ is $\square \mathrm{mi} / \mathrm{gal}$.
(Round to one decimal place as needed.)
Answer
Therefore, the best predicted value of highway fuel consumption of a car that weighs 3000 lb is \(\boxed{36.43} \, \mathrm{mi/gal}\).
Step 1 ：The regression equation is given as \(\hat{y}=58.9-0.00749 x\), where \(x\) represents weight.
Step 2 ：From the equation, we can see that the slope is -0.00749 and the \(y\)-intercept is 58.9.
Step 3 ：The predictor variable in this case is weight, which is represented by \(x\).
Step 4 ：To find the best predicted value for a car that weighs 3000 lb, we substitute \(x=3000\) into the regression equation.
Step 5 ：So, \(\hat{y}=58.9-0.00749 \times 3000\).
Step 6 ：After calculating, we find that \(\hat{y}=36.43\).
Step 7 ：Therefore, the best predicted value of highway fuel consumption of a car that weighs 3000 lb is \(\boxed{36.43} \, \mathrm{mi/gal}\).
