5. Does studying really pay off? To answer that question, a curious student in a

Question

5. Does studying really pay off? To answer that question, a curious student in a statistics class asked 10 students how many hours they studied for the most recent test and the grade they received. The data are recorded here.

GRADE   89   92   32   92   90   30   87   88   34   30

HOURS   25   26   12   32   29   10   21   27   15   18

a. Estimate a linear regression equation using Data Analysis in Excel. (10 pts)

b. Based upon the coefficient of the regression model, what do you conclude? (4 pts)

c. If you study one more hour, on average, what will happen to your grade according to the model? (5 pts)

d. Using a GLOBAL test, is there evidence of a linear relationship between the number of hours spent studying and a student’s grade on the test? Use alpha =0.01. (15pts)

Explanation / Answer

(a)

The regression equation is GRADE = -11.3651 + 3.6170 HOURS

(b) GRADE and HOURS are linearly correlated. The correlation is positive. More the HOURS, higher the GRADE.

(c) GRADE will increase by 3.6170

(d) p- value (0.0004) < 0.01, so 0. There is evidence of a linear relationship between the number of hours spent studying and a student’s grade on the test.

Regression Analysis r² 0.813 n   10 r   0.902 k   1 Std. Error   13.812 Dep. Var. GRADE ANOVA table Source SS   df   MS F p-value Regression 6,626.3060 1   6,626.3060 34.74 .0004 Residual 1,526.0940 8   190.7617 Total 8,152.4000 9   Regression output confidence interval variables coefficients std. error    t (df=8) p-value 95% lower 95% upper std. coeff. Intercept -11.3651 0.000 HOURS 3.6170 0.6137 5.894 .0004 2.2018 5.0322 0.902

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