A used car dealer wants to develop a regression equation that determines mileage

Question

A used car dealer wants to develop a regression equation that determines mileage as a function of the age of a car in years. He collects the data shown below for the 12 cars he has on his lot.

Assignment 10q4 data

a) What is the slope of the regression equation? Give your answer to two decimal places.  

b) What is the value of the correlation coefficient? Give your answer to two decimal places.  

c) A 4 year old car is delivered to his lot with 160000 miles. Manually enter these values in the data table above and rerun the regression analysis. What is the value of the slope? Give your answer to two decimal places.  

d) Including the additional car, what is the value of the correlation coefficient? Give your answer to two decimal places.  

e) Did the additional car strengthen or weaken the linear relationship between age and mileage?

A. It strengthened the linear relationship

B. Can not be determined

C. It weakened the linear relationship.

Data: https://www.webassign.net/userimages/10q4r1.csv?db=v4net&id=289120

Age Mileage

7 52654

4 49300

13 113671

7 63001

7 69850

7 68048

12 106979

8 82719

7 80894

10 109258

14 149804

8 98915

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Mileage
Independent Variable: Age
Mileage = 7725.1569 + 9157.6069 Age
Sample size: 12
R (correlation coefficient) = 0.91999294
R-sq = 0.846387
Estimate of error standard deviation: 12129.694

Parameter estimates:

Analysis of variance table for regression model:

Hence,

a) Slope = 9157.61

b) Correlation coefficient = 0.92

After reruning the software with additional data values, we will have:

c) Slope = 4891.41

d) Correlation coefficient = 0.19

e) It weakened the linear relationship.

Option C is correct.

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 7725.1569 11250.871 0 10 0.68662747 0.5079 Slope 9157.6069 1233.7055 0 10 7.422847 <0.0001

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