The following table contains the ACT scores and the GPA (grade point average) fo

Question

The following table contains the ACT scores and the GPA (grade point average) for eight college students. Grade point average is based on a four-point scale and has been rounded to one digit after the decimal. Estimate the relationship between GPA and ACT using OLS; that is, obtain the intercept and slope estimates in the equation GPA^= beta^_ + beta^_iACT. Comment on the direction of the relationship. Does the intercept have a useful interpretation here? Explain. How much higher is the GPA predicted to be if the ACT score is increased by five points? Compute the fitted values and residuals for each observation, and verify that the residuals (approximately) sum to zero.

Explanation / Answer

A) The regression equation is

y=a+bx

from Excel

The fitted model is

y=0.57 +0.10 (Act)

Slope=0.10

if we increase 1 point in GPA then there is 0.10 increase in ACT

Suppose x=5 points

y=0.57+0.1*5 =1.07

b) Residuals = Actual- fitted values

SUMMARY OUTPUT Regression Statistics Multiple R 0.759884 R Square 0.577424 Adjusted R Square 0.506994 Standard Error 0.269173 Observations 8 ANOVA df SS MS F Significance F Regression 1 0.594025 0.594025 8.198622 0.028677 Residual 6 0.434725 0.072454 Total 7 1.02875 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 0.568132 0.928421 0.611933 0.563036 -1.70363 2.839897 -1.70363 2.839897 ACT 0.102198 0.035692 2.863324 0.028677 0.014863 0.189533 0.014863 0.189533

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