It is believed that the average numbers of hours spent study

It is believed that, the average numbers of hours spent studying per day (HOURS) during undergraduate education should have a positive linear relationship with the starting salary (SALARY, measured in thousands of dollars per month) after graduation. Given below is the Excel output from regressing starting salary on number of hours spent studying per day for a sample of 51 students.   

Note: Some of the numbers in the output are purposely erased.

Regression Statistics

Multiple R

0.8857

R Square

0.7845

Adjusted R Square

0.7801

Standard Error

1.3704

Observations

51

ANOVA

df

SS

MS

F

Significance F

Regression

1

335.0472

335.0473

178.3859

Residual

1.8782

Total

50

427.0798

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

-1.8940

0.4018

-4.7134

2.051E-05

-2.7015

-1.0865

Hours

0.9795

0.0733

13.3561

5.944E-18

0.8321

1.1269

a) What is the error sum of squares (SSE) of the above regression? Show how you obtain your answer.

b) The 90% confidence interval for the average change in SALARY (in thousands of dollars) as a result of spending an extra hour per day studying is

A) wider than [-2.70159, -1.08654].

B) narrower than [-2.70159, -1.08654].

C) wider than [0.8321927, 1.12697].

D) narrower than [0.8321927, 1.12697].

Explain your reasoning.

c) To test the claim that average SALARY depends positively on HOURS against the null hypothesis that average SALARY does not depend linearly on HOURS, what is the p-value of the test statistic? What are the results of the test? Explain your answer.

Regression Statistics
Multiple R	0.8857
R Square	0.7845
Adjusted R Square	0.7801
Standard Error	1.3704
Observations	51
ANOVA
	df	SS	MS	F	Significance F
Regression	1	335.0472	335.0473	178.3859
Residual			1.8782
Total	50	427.0798
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-1.8940	0.4018	-4.7134	2.051E-05	-2.7015	-1.0865
Hours	0.9795	0.0733	13.3561	5.944E-18	0.8321	1.1269

Solution

a) SSE=SSt-SSR=427.0798-335.0472=93.0326.

b)answer is B. This is because as the confidence co-efficient decreases, the z value also decreases.

c) p value is 0. Since this value is < 0.05, we reject the null hypothesis and conclude that there is linear reltion between salary and hours.