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. \\(\vdots\\) \\(\bigcirc\\) c. \\(\hat{y}\\) represents the actual value of highway fuel consumption. \\(\bigcirc\\) d. \\(\hat{y}\\) represents the actual value of weight. b. what are the specific values of the slope and y-intercept of the regression line? \\(\bigcirc\\) a. the slope is \\(-0.00749\\) and the y-intercept is 58.9. \\(\bigcirc\\) b. the slope is 0.00749 and the y-intercept is 58.9. \\(\bigcirc\\) c. the slope is 58.9 and the y-intercept is \\(-0.00749\\). \\(\bigcirc\\) d. the slope is 58.9 and the y-intercept is 0.007499.

Explanation:

Step1: Recall Regression Equation Form

The general form of a linear regression equation is $\hat{y} = b_0 + b_1x$, where $b_0$ is the y - intercept and $b_1$ is the slope.

Step2: Identify Values from Given Equation

The given regression equation is $\hat{y}=58.9 - 0.00749x$. Comparing with $\hat{y}=b_0 + b_1x$, we can see that $b_0 = 58.9$ (y - intercept) and $b_1=- 0.00749$ (slope).

Answer:

A. The slope is $-0.00749$ and the y - intercept is $58.9$.