Chapter 10.1, Problem 33E

Solution

a)

The equation of least squares regression line.

Given:The dot plot and Minitab output for least squares regression analysis for these data.

  

  

Explanation:The least regression analysis is carried out to explain mileage using age(in years) of cars. Here Age is explanatory variable(x) and mileage is response variable (y). The least square regression equation can be written using the coefficients of age which is slope and y intercept or coefficient of constant as shown below.

  $\hat{y}=-13832+14954x$

  $\hat{y}$ is the predicted mileage

x is the age in years of the cars.

b)

Interpret the slope of the least square line.

Given:

The least square regression line equation is

  $\hat{y}=-13832+14954x$

Explanation:The least regression analysis is carried out to explain mileage using age(in years) of cars. Here Age is explanatory variable(x) and mileage is response variable (y). From the regression line the slope of the least squares regression line slope is the coefficient of explanatory variable or 14954 miles. The slope is interpreted as the amount by which response variable predicted to change for one unit change in explanatory variable. So, for an increment in age of the car the predicted mileage will increase by 14,954 miles.

c)

The residual for 10 year old car which has 110,000 miles on it.

Given:The least square regression line equation is

  $\hat{y}=-13832+14954x$

Calculation:The estimate of mileage for a 10 year old car is calculated as shown below

  $\begin{array}{l}\hat{y}=-13832+14954x\\ \hat{y}=-13832+14954*10=135708\end{array}$

The residual is calculated as shown below

  $\text{Residual}=y-\hat{y}=110,000-135,708=-25,708$

Conclusion:

The residual for the student’s 10 year old car is -25,708.