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: \\(\hat{y} = 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 \\(\hat{y}\\) represent?
\\(\bigcirc\\) a. \\(\hat{y}\\) represents the predicted value of highway fuel consumption.
\\(\bigcirc\\) b. \\(\hat{y}\\) represents the predicted value of weight.
\\(\bigcirc\\) c. \\(\hat{y}\\) represents the actual value of highway fuel consumption.
\\(\bigcirc\\) d. \\(\hat{y}\\) represents the actual value of weight.

Explanation:

In a regression equation, \(\hat{y}\) denotes the predicted value of the response variable. Here, the regression equation is for highway fuel consumption (with \(x\) as weight, the explanatory variable). So \(\hat{y}\) predicts highway fuel consumption, not weight (eliminating B, D) and it's a predicted, not actual, value (eliminating C).

Answer:

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