Data was collected from 40 employees to develop a regression model to predict th
ID: 3268492 • Letter: D
Question
Data was collected from 40 employees to develop a regression model to predict the employee’s annual salary using their years with the company (Years), their starting salary (Starting), and their Gender (Male = 0, Female = 1). The results from Excel regression analysis are shown below:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.718714957
R Square
0.516551189
Standard Error
10615.63461
Observations
40
ANOVA
df
SS
MS
F
Significance F
Regression
3
4334682510
1444894170
12.82165585
7.48476E-06
Residual
36
4056901131
112691698.1
Total
39
8391583641
Coefficients
Standard Error
t Stat
P-value
Intercept
27946.57894
4832.438706
5.783121245
1.35464E-06
Years
1665.251558
425.0829092
3.917474737
0.000383313
Starting
0.266374185
0.12610443
2.112330112
0.041661598
Gender
-3285.541043
5617.145392
-0.584912943
0.56225464
In testing the null hypothesis that the regression equation is not significant at the 0.05 level, what is the appropriate conclusion?
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.718714957
R Square
0.516551189
Standard Error
10615.63461
Observations
40
ANOVA
df
SS
MS
F
Significance F
Regression
3
4334682510
1444894170
12.82165585
7.48476E-06
Residual
36
4056901131
112691698.1
Total
39
8391583641
Coefficients
Standard Error
t Stat
P-value
Intercept
27946.57894
4832.438706
5.783121245
1.35464E-06
Years
1665.251558
425.0829092
3.917474737
0.000383313
Starting
0.266374185
0.12610443
2.112330112
0.041661598
Gender
-3285.541043
5617.145392
-0.584912943
0.56225464
Explanation / Answer
Here the test-statistic for testing the null hypothesis that the regression equation is not significant again the alternative
that it is significant is given by, F = MSReg / MSTotal = 1444894170 / 112691698.1 = 12.82165585.
The p-value of the test = P(F > 12.82165585) , where F ~ F-distribution with (3,36) d.f.
= 7.48476E-06
Since , p-value = 7.48476E-06 < level of signficance = 0.05, we reject our null hypothesis. Hence, we conclude that the regression equation is significant. (Ans).
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