A used car dealer wants to develop a regression equation that determines mileage
ID: 3365712 • Letter: A
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? OIt strengthened the linear relationship. O Can not be determined It weakened the linear relationship.Explanation / Answer
Output of REGRESSION from Data Analysis Tool pack is given below :
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.97558
R Square
0.951756
Adjusted R Square
0.946931
Standard Error
9273.356
Observations
12
ANOVA
df
SS
MS
F
Significance F
Regression
1
1.7E+10
1.7E+10
197.2791
6.57E-08
Residual
10
8.6E+08
85995140
Total
11
1.78E+10
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
-9376.49
7544.574
-1.24281
0.242288
-26186.8
7433.867
-26186.8
7433.867
AGE
11008.13
783.7417
14.04561
6.57E-08
9261.843
12754.41
9261.843
12754.41
a)The slope of the regression equation = 11008.13
b)Correlation coefficient = 0.98
c) After adding additional car information, the output is :
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.636754
R Square
0.405456
Adjusted R Square
0.351407
Standard Error
34785.4
Observations
13
ANOVA
Df
SS
MS
F
Significance F
Regression
1
9.08E+09
9.08E+09
7.501578
0.019269
Residual
11
1.33E+10
1.21E+09
Total
12
2.24E+10
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
30828.18
25373.69
1.214966
0.249815
-25018.9
86675.3
-25018.9
86675.3
AGE
7460.658
2723.96
2.738901
0.019269
1465.261
13456.05
1465.261
13456.05
The slope = 7460.66
d)Correlation coefficient = 0.64
e) Since the correlation coefficient lessens, that means it weakens the linear relationship.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.97558
R Square
0.951756
Adjusted R Square
0.946931
Standard Error
9273.356
Observations
12
ANOVA
df
SS
MS
F
Significance F
Regression
1
1.7E+10
1.7E+10
197.2791
6.57E-08
Residual
10
8.6E+08
85995140
Total
11
1.78E+10
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
-9376.49
7544.574
-1.24281
0.242288
-26186.8
7433.867
-26186.8
7433.867
AGE
11008.13
783.7417
14.04561
6.57E-08
9261.843
12754.41
9261.843
12754.41
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