It is believed that, the average numbers of hours spent studying per day (HOURS)

Question

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 partial Excel output from regressing starting salary on the 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

i State the linear regression equation.

ii Interpret the meaning of the intercept and slope coefficients.

iii Interpret the meaning of the coefficient of determination.

iv Explain the meaning of the error sum of squares (SSE).

v Compute the SSE of the above regression.

Explanation / Answer

i.

The linear regression equation is

salary = -1.8940 + 0.9795*hours

ii):

The slope is : 0.9795

It shows that for unit increase in independent variable (hours), dependent variable is increased by 0.9795 units.

The intercept is: -1.8940

It shows the number of hours of studying is zero, then starting salary is -1.8940.

iii)

The coefficient of determination (r-sqaure) is 0.7845.

That is 78.45% of variation in dependent variable is exalained by independent variable.

iv)

The error sum of sqaure shows the unexplained variation by the model.

v)

From the output we have

SSR = 335.0472

SST = 427.0798

So the SSE is

SSE= SST-SSR = 427.0798 - 335.0472 = 92.0326

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