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Mathematics, 08.03.2021 19:40, sickboi
The following table contains ACT scores and GPA (grade point average) scores for 8 college students. (The ACT is an SAT-type test, popular at Midwestern schools.
Instead of ranging from 200 – 800, the ACT ranges from 20 – 30.) Grade point average is based on a 4-point scale and has been rounded to one digit after the decimal.
Student GPA ACT
1 2.8 21
2 3.4 24
3 3.0 26
4 3.5 27
5 3.6 29
6 3.0 25
7 2.7 25
8 3.7 30
i) Estimate the relationship between GPA and ACT using OLS; that is, obtain the intercept and the slope estimates for the model
GPAi = α + β(ACTi) + μi
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 increases by 5 points?
ii) Compute the fitted values and the residuals for each observation and verify that the residuals sum to zero.
iii) What is the predicted value of GPA when ACT = 20?
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Answers: 3
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