Question

Drive my car

a. What is the equation of the least-squares regression line? Be sure to define any symbols you use.

b. Interpret the slope of the least-squares line.

c. One student reported that her $10$-year-old car had $110,000$ miles on it. Find and

interpret the residual for this data point.

Short answer

a. $\hat{y}=-13832+14954x$

b. Slope is $\text{Slope}=14954$

c. The residual is$-25708$miles.

Step-by-step solution

Given Information

It is given that Least square regression line is given by:

$\hat{y}=a+bx$

$\hat{y}$is predicted mileage and$x$is the age.

Equation of least square regression line

Constant $a$is given in row with Age and in column with Coef.

$a=-13832$

Slope $b$is given in row with age and in column with Coef.

$b=14954$

So, lest square equation becomes:

$\hat{y}=-13832+14954x$

$\hat{y}$is predicted mileage and $x$ is age.

Slope of above line

From above part $\hat{y}=-13832+14954x$

Coefficient of $x$is slope.

Hence, slope is $14954$miles per year.

Residual

The data points is given to be $x=10$

Hence, $\hat{y}=-13832+14954x$

$=-13832+14954\left(10\right)$

$=135708\text{miles}$

Residual is $y-\hat{y}$

$=110000-135708$

$=-25708\text{miles}$

So, predict overestimates the mileage by$25708$miles.