First-Year College GPA Researchers at the College Board wanted to build a model that describes one’s first-year college GPA. The researchers obtained the following model: y = 0.06x1 + 0.07x2 + 0.18x3 + 0.29x4
where y represents the z-score for first-year college grade point average (GPA)
x1 represents the z-score on the math portion of the SAT
x2 represents the z-score on the critical reading portion of the SAT
x3 represents the z-score on the writing portion of the SAT
x4 represents the z-score of the student’s high school grade point average (GPA)
Source: Kobrin, J., Sinharay, S., Haberman, S.J., & Chajewski, M. An Investigation of the Fit of Linear Regression Models to Data from an SAT Validity Study. College Board Research Report 2011–13.
(a) Suppose a student has a z-score of 1.52 on the math portion of the SAT. Explain what this result represents.
(b) What is the impact of a z-score of -1 for the student’s high school GPA?
(c) Interpret the slope coefficient for high school GPA
(d) The coefficient of determination for this model is 0.24. Interpret this value.
(e) The correlation coefficient between x2 and x3 is 0.71. What might this suggest?
(f) Predict the z-score for first-year college GPA if x1 = -0.54, x2 = 1.32, x3 = 0.98, and x4 = 0.36. Would we expect a student with these credentials to have an above or below average first-year college GPA?
Step 1 of 5) First-Year College GPA Researchers at the College Board wanted to build a model that describes one’s first-year college GPA. The researchers obtained the following model: y = 0.06x1 + 0.07x2 + 0.18x3 + 0.29x4 where y represents the z-score for first-year college grade point average (GPA) x1 represents the z-score on the math portion of the SAT x2 represents the z-score on the critical reading portion of the SAT x3 represents the z-score on the writing portion of the SAT x4 represents the z-score of the student’s high school grade point average (GPA) Source: Kobrin, J., Sinharay, S., Haberman, S.J., & Chajewski, M. An Investigation of the Fit of Linear Regression Models to Data from an SAT Validity Study. College Board Research Report 2011–13. (a) Suppose a student has a z-score of 1.52 on the math portion of the SAT. Explain what this result represents. (b) What is the impact of a z-score of -1 for the student’s high school GPA (c) Interpret the slope coefficient for high school GPA (d) The coefficient of determination for this model is 0.24. Interpret this value. (e) The correlation coefficient between x2 and x3 is 0.71. What might this suggest (f) Predict the z-score for first-year college GPA if x1 = -0.54, x2 = 1.32, x3 = 0.98, and x4 = 0.36. Would we expect a student with these credentials to have an above or below average first-year college GPA