Answer question based on data below For a male employee with 5 years of experien
ID: 3268502 • Letter: A
Question
Answer question based on data below
For a male employee with 5 years of experience and a starting salary of $30,000, what is the approximate 95% confidence interval for his annual salary?
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
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
Step1. For a confidence level of 1-alpha, use t table to find talpha/2 with df=36 [df for MS(Residual)]. The t36,0.025=2.028.
Step2. Compute the point estimate, beta0hat+beta1hatx1*+beta2hatx2*+beta3hatx3*
Annual Salary=27946.57894+1665.251558(5)+0.266374185(30000)-3285.541043(0)=44264.06228
Step3. The 95% c.i is
(beta0hat+beta1hatx1*+beta2hatx2*+beta3hatx3*)+-2.028(Sy*), where, SY* is the estimate of standard deviation of Y*. Substitute the value of SY* in following formula to obtain the 95% c.i.
44264.06228+-2.028()
=44264.06228+-2.028