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 estimated average change in salary (in thousands of dollars) as a result of spending an extra hour per day studying?
b) What is the value of the measured t-test statistic to test whether average SALARY depends linearly on HOURS?
c) What is the p-value of the measured F-test statistic to test whether HOURS affects SALARY?
d) What are the degrees of freedom for testing whether HOURS affects SALARY?
e) What is the error sum of squares (SSE) of the above regression? Show how you obtain your answer.
f) 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.
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.