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Chapter 10: Q 35. (page 644)

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

Expert verified

a. y^=-13832+14954x

b. Slope is Slope=14954

c. The residual is-25708miles.

Step by step solution

01

Given Information

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

y^=a+bx

y^is predicted mileage andxis the age.

02

Equation of least square regression line

Constant ais given in row with Age and in column with Coef.

a=-13832

Slope bis given in row with age and in column with Coef.

b=14954

So, lest square equation becomes:

y^=-13832+14954x

y^is predicted mileage and x is age.

03

Slope of above line

From above part y^=-13832+14954x

Coefficient of xis slope.

Hence, slope is 14954miles per year.

04

Residual

The data points is given to be x=10

Hence, y^=-13832+14954x

=-13832+14954(10)

=135708miles

Residual is y-y^

=110000-135708

=-25708miles

So, predict overestimates the mileage by25708miles.

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