Question

g the weights (lb) and highway fuel consumption amounts (mi/gal) of the 48 cars listed in the accompanying set, one gets this regression equation: ŷ = 58.9 - 0.00749x, where x represents weight. complete parts (a) ugh (d).
click the icon to view the car data.

a. the predictor variable is highway fuel consumption, which is represented by y.
b. the predictor variable is highway fuel consumption, which is represented by x.
c. the predictor variable is weight, which is represented by x.
d. the predictor variable is weight, which is represented by y.
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 \boxed{} mi/gal.
(round to one decimal place as needed.)

Explanation:

Step1: Identify the regression equation

The given regression equation is \(\hat{y} = 58.9 - 0.00749x\), where \(x\) represents weight and \(\hat{y}\) represents the predicted highway fuel consumption.

Step2: Substitute \(x = 2993\) into the equation

We substitute \(x = 2993\) into the equation \(\hat{y} = 58.9 - 0.00749x\).
First, calculate \(0.00749\times2993\):
\(0.00749\times2993 = 0.00749\times(3000 - 7)=0.00749\times3000 - 0.00749\times7 = 22.47 - 0.05243 = 22.41757\)

Then, calculate \(\hat{y}\):
\(\hat{y}=58.9 - 22.41757 = 36.48243\)

Step3: Round to one decimal place

Rounding \(36.48243\) to one decimal place gives \(36.5\).

Answer:

\(36.5\)