Solutions Statistics

Solution) It is believed that the average number of hours spent studying per day (HOURS) during undergraduate

Question: It is believed that the average number of hours spent studying per day (HOURS) during undergraduate education should have a positive linear relationship with 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.

*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
Regression	1	335.0472	335.0473	178.3859
Residual	49	92.0326	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) State the regression equation.

(b) Interpret the meaning of b₀ and b₁ in this problem.

(c) What is the predicted value of starting salary when the average number of hours spent studying per day is 5?

(d) At the 0.05 level of significance, is there evidence of a positive linear relationship between the average number of hours spent studying per day and the starting salary?

(e) Construct a 95% confidence interval estimate of the population slope β₁. Interpret the confidence interval estimate.

(f) How useful do you think this regression model is for predicting the starting salaries?

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