TV following table contains the ACT scores and the GPA (grade point average) for
ID: 3207568 • Letter: T
Question
TV following table contains the ACT scores and the GPA (grade point average) for eight college student. 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 estimate in the equation GPA = beta_c + beta_1 ACT 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 residual (approximately) sum to zero What is the predicted value of GPA when ACT = 20? How much of the variation in GPA for these eight students is explained by ACT? Explain.Explanation / Answer
The regression output from Excel is:
(a) The line of regression is:
GPA=0.5681+0.1022*ACT
(Residuals verified from Excel output)
(b) GPA=0.5681+0.1022*20=2.6121
(c) 50.6% of variation is explianed.
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 RESIDUAL OUTPUT Observation Predicted GPA Residuals 1 2.714286 0.085714 2 3.020879 0.379121 3 3.225275 -0.22527 4 3.327473 0.172527 5 3.531868 0.068132 6 3.123077 -0.12308 7 3.123077 -0.42308 8 3.634066 0.065934Related Questions
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