Question

a sample of 12 cars was taken, and the horsepower to miles per gallon was recorded. the computer output for regression is below.

	intercept	horsepower
standard error	6.276668196	0.070541433
t stat	7.474667	-2.84595
p - value	2.1237e - 05	0.017370344

what is the equation of the regression line?

options:
$hat{y}=0.07 + 6.28x$
$hat{y}=7.47 - 2.86x$
$hat{y}=-0.20 + 46.92x$
$hat{y}=46.92 - 0.20x$

Explanation:

Step1: Identify regression formula structure

The simple linear regression equation is $\hat{y} = b_0 + b_1x$, where $b_0$ is the intercept coefficient, and $b_1$ is the predictor (Horsepower) coefficient.

Step2: Extract coefficients from output

From the table:
Intercept coefficient $b_0 = 46.91600662 \approx 46.92$
Horsepower coefficient $b_1 = -0.200757246 \approx -0.20$

Step3: Substitute into regression formula

Substitute the rounded coefficients into the equation: $\hat{y} = 46.92 - 0.20x$

Answer:

$\hat{y} = 46.92 - 0.20x$