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Chapter 10: Q. 33 (page 626)

Thirty randomly selected seniors at Council High School were asked to report the age (in years) and mileage of their main vehicles. Here is a scatterplot of the data:

(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 in the context of this problem. (c) One student reported that her 10-year-old car had110000 miles on it. Find the residual for this data value. Show your work

Short Answer

Expert verified

(a) The equation of the least-squares regression line is y^=-13832+14954x

(b) The slope of the least-squares line in the context of this problem is 14954miles per year

(c) The residual for this data value is25708miles.

Step by step solution

01

Part (a) Step 1: Given information

02

Part (a) Step 2: Explanation

The least-squares regression line's general equation is:

y^=a+bx

with ythe predicted mileage and x the age

The constant ais given in the column "Coef" and in the row "Constant":

a=-13832

The slope bis given in the row with "Age" and in the column with "Coef"

b=14954

The least-square equation then becomes

y^=-13832+14954x.

03

Part (b) Step 1: Given information

04

Part (b) Step 2: Explanation

From part (a)

y^=-13832+14954x

y=predicted mileage

x=age

The slope is the coefficient of x

Slope =14954.

05

Part (c) Step 1: Given information

06

Part (c) Step 2: Explanation

From part (a)

y^=-13832+14954x

Replace xwith 10

y=-13832+14954(10)=135708miles

The discrepancy between the actual and predicted values is the residual:

Residual=y-y^=110000-135708=-25708miles.

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