Question

1. You have data on three variables for college graduates: years of work experience,

student GPA and monthly salary after graduation in $. You collect data from 6 students.

Student	Years of Work Experience	GPA	Monthly Salary ($)
1	3	2.6	3300
2	0	3.4	3600
3	4	3.6	4000
4	1	3.2	3500
5	2	3.5	3900
6	5	2.9	3600

Following are the regression results for the data using Excel. In this problem, you will be interpreting the regression results.

Please answer the following questions based on this table

5) Which variables have a statistically significant relationship with the dependent variable at the 1% level?(Use three decimals on p value)

6) What is the 95% confidence interval estimate for the coefficient of GPA?

7) What is the 90% confidence interval estimate for the coefficient of Years of work experience?

Answer 1

The regression output is as follows

Question (5)

The dependent variable here is Monthly Salary ($) and the independent variables are Years of Work Experience and GPA

If the p-value of independent variable is less than significance level 0.01, then we can say that that the independent variable is statistically significant

Here the p-value of Work of years experience indpendent variable is 0.018714 which is less than significance level of 0.01, hence the independent variable Years of Work Experience has a statistically significant relationship with Monthly Salary ($)

Here the p-value of GPA indpendent variable is 0.002456 which is less than significance level of 0.01, hence the independent variable GPA has a statistically significant relationship with Monthly Salary ($)

Question (6)

The 95% confidence interval estimate for the coefficient of GPA

95% CI for GPA = 683.1346 t-value * 71.7393

Here 683.1346 is the coefficient of GPA and 71.7393 is the standard error of GPA

degrees of freedom (df) = n -2

= 6 - 2

= 4

So the t-value at 95% confidence level and degrees of freedom 4 from the below attached table = 2.776

You can find the confidence level at the bottom of the image

So 95% CI for GPA = 683.1346 2.776 * 71.7393

= 683.1346 199.1483

So 95% CI for GPA = (483.9863, 882.2929)

Question (7)

The 90% confidence interval estimate for the coefficient of Years of Work Experience

90% CI for Years of Work Experiecne = 68.6542 t-value * 14.7521

Here 68.6542 is the coefficient of Years of Work experience and 14.7521 is the standard error of Years of Work Experience

degrees of freedom (df) = n -2

= 6 - 2

= 4

So the t-value at 90% confidence level and degrees of freedom 4 from the below attached table = 2.132

You can find the confidence level at the bottom of the image

So 90% CI for Years of Work Expericne = 68.6542 2.132 * 14.7521

= 68.6542 31.4515

So 90% CI for Years of Work Experience = (37.2027, 100.106)