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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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 14PPS
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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.
Transcribed Image Text: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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