741Introductory Econometrics IPage 2 of 3The following table contains the ACT scores' (i.e. standardized test scores for highschool achievement and university admissions in the United States) and the GPA (gradepoint average) for eight university students. Grade point average is based on a four-point scale and has been rounded to one digit after the decimal.Table 1: Students' GPA and ACT scoresStudent GPA ACT12.82123.42433.026272943.553.63.02.72572583.730(a) Estimate the relationship between GPA and ACT using OLS; that is, obtain theintercept and slope estimates in the equationGPABo + B, ACT.Interpret the regression results. Does the intercept have a useful interpretationhere? Explain.(b) Compute the fitted values and residuals for each observation, and verify that theresiduals (approximately) sum to zero.(c) How much of the variation in GPA for these eight students is explained by ACT?Explain.

(a). Estimate the relationship between GPA and ACT: The data represents the values of GPA scores and…

The following table contains the ACT scores' (i.e. standardized test scores for high school achievement and university admissions in the United States) and the GPA (grade point average) for eight university students. Grade point average is based on a four- point scale and has been rounded to one digit after the decimal.

The following table contains the ACT scores' (i.e. standardized test scores for high school achievement and university admissions in the United States) and the GPA (grade point average) for eight university students. Grade point average is based on a four- point scale and has been rounded to one digit after the decimal.

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Question

741
Introductory Econometrics I
Page 2 of 3
The following table contains the ACT scores' (i.e. standardized test scores for high
school achievement and university admissions in the United States) and the GPA (grade
point average) for eight university students. Grade point average is based on a four-
point scale and has been rounded to one digit after the decimal.
Table 1: Students' GPA and ACT scores
Student GPA ACT
1
2.8
21
2
3.4
24
3
3.0
26
27
29
4
3.5
5
3.6
3.0
2.7
25
7
25
8
3.7
30
(a) Estimate the relationship between GPA and ACT using OLS; that is, obtain the
intercept and slope estimates in the equation
GPA
Bo + B, ACT.
Interpret the regression results. Does the intercept have a useful interpretation
here? Explain.
(b) Compute the fitted values and residuals for each observation, and verify that the
residuals (approximately) sum to zero.
(c) How much of the variation in GPA for these eight students is explained by ACT?
Explain.

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