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

Explanation:

In a regression equation, \(\hat{y}\) denotes the predicted value of the dependent variable. Here, the dependent variable is highway fuel consumption (since \(x\) is weight, the independent variable), and the equation is used to predict highway fuel consumption. So \(\hat{y}\) is the predicted value of highway fuel consumption.

Answer:

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