Questions: Using the weights (Ib) and highway fuel consumption amounts (mi/gal) of the 48 cars listed in the accompanying data set, one gets this regression equation: y-hat = 58.9 - 0.00749 x, where x represents weight. Complete parts (a) through (d). c. What is the predictor variable? A. The predictor variable is highway fuel consumption, which is represented by x. B. The predictor variable is highway fuel consumption, which is represented by y. C. The predictor variable is weight, which is represented by y. D. The predictor variable is weight, 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 2993 lb ? The best predicted value of highway fuel consumption of a car that weighs 2993 lb is mi / gal. (Round to one decimal place as needed.)

Using the weights (Ib) and highway fuel consumption amounts (mi/gal) of the 48 cars listed in the accompanying data set, one gets this regression equation: y-hat = 58.9 - 0.00749 x, where x represents weight. Complete parts (a) through (d). c. What is the predictor variable? A. The predictor variable is highway fuel consumption, which is represented by x. B. The predictor variable is highway fuel consumption, which is represented by y. C. The predictor variable is weight, which is represented by y. D. The predictor variable is weight, 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 2993 lb ? The best predicted value of highway fuel consumption of a car that weighs 2993 lb is mi / gal. (Round to one decimal place as needed.)
Transcript text: Using the weights (Ib) 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). c. What is the predictor variable? A. The predictor variable is highway fuel consumption, which is represented by $x$. B. The predictor variable is highway fuel consumption, which is represented by $y$. C. The predictor variable is weight, which is represented by $y$. D. The predictor variable is weight, 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 $2993 \mathrm{lb} ?$ The best predicted value of highway fuel consumption of a car that weighs 2993 lb is $\square$ $\mathrm{mi} / \mathrm{gal}$. (Round to one decimal place as needed.)
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Solution

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Solution Steps

Solution Approach

For part (c), identify the predictor variable in the regression equation. The predictor variable is the independent variable, which is represented by \( x \) in the equation.

For part (d), use the given regression equation to predict the highway fuel consumption for a car that weighs 2993 lb. Substitute \( x = 2993 \) into the regression equation and solve for \( \hat{y} \).

Step 1: Identify the Predictor Variable

The regression equation is given by: \[ \hat{y} = 58.9 - 0.00749x \] In this equation, \( x \) represents the weight of the car. Therefore, the predictor variable is weight, which is represented by \( x \).

Step 2: Predict Highway Fuel Consumption

To find the best predicted value for a car that weighs 2993 lb, substitute \( x = 2993 \) into the regression equation: \[ \hat{y} = 58.9 - 0.00749 \times 2993 \]

Step 3: Perform the Calculation

Calculate the value of \( \hat{y} \): \[ \hat{y} = 58.9 - 0.00749 \times 2993 \] \[ \hat{y} \approx 58.9 - 22.41757 \] \[ \hat{y} \approx 36.4824 \]

Step 4: Round the Result

Round the result to one decimal place: \[ \hat{y} \approx 36.5 \]

Final Answer

  • The answer to part (c) is D: The predictor variable is weight, which is represented by \( x \).
  • The best predicted value of highway fuel consumption for a car that weighs 2993 lb is: \[ \boxed{36.5 \text{ mi/gal}} \]
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