Question

using the weights (lb) and highway fuel consumption amounts (mi/gal) of the 48 cars listed in the accompanying data set, one gets this regression equation: ŷ = 58.9 - 0.00749x, where x represents weight. complete parts (a) through (d). click the icon to view the car data. a. what does the symbol ŷ represent? a. ŷ represents the actual value of highway fuel consumption. b. ŷ represents the predicted value of weight. c. ŷ represents the predicted value of highway fuel consumption. d. ŷ represents the actual value of weight.

Explanation:

In a regression equation, \(\hat{y}\) is the predicted value of the response variable. Here, the response variable is highway fuel consumption (since \(x\) is weight, used to predict fuel consumption). Option A is incorrect as \(\hat{y}\) is predicted, not actual. Option B is wrong because \(\hat{y}\) is about fuel consumption, not weight. Option D is incorrect as \(x\) represents weight, and \(\hat{y}\) is not actual weight. So \(\hat{y}\) represents the predicted highway fuel consumption.

Answer:

C. \(\hat{y}\) represents the predicted value of highway fuel consumption.