Question

The variables in our dataser include the college grade point average (colGPA), high school GPA (hSGPA) and achievement test seore (MCt) for a wampin of 141 wibdimts fram a large university, both college and hight school GPAs are on a four-point seale We estimate the following, modet by OLS: colGPA=β₁ +β₂ /sGPA+β₃ ACT+u and obtain the following parameter estimates β₁ = 0.5⋅ β₂ = 0.6. β₃ = 0.01.

Predict difference of college GPA s of two students (oolcPAB - colGpani where the student B han a 0.2 points higher GPA in high school and 3 points lower ACT score compared to student A. The answer should be given up to 2 decimal spaces, e.g. 0.35,0.23,0.20,1.23, etc.

Answer 1

The predicted difference in college GPA between student B, who has a 0.2 points higher high school GPA and a 3 points lower ACT score than student A, is 0.09 points.

Step-by-step explanation:

The question requires the calculation of the predicted difference in college GPA between two students (student B and student A) based on the provided model and parameter estimates. According to the given regression equation colGPA = β1 + β2*hSGPA + β3*ACT + u, and the parameter estimates β1 = 0.5, β2 = 0.6, and β3 = 0.01. Assuming student B has a 0.2 points higher high school GPA (hSGPA) and a 3 points lower ACT score than student A, the predicted difference in their college GPAs is calculated as:

• Difference in hSGPA component = β2 * (hSGPA_B - hSGPA_A) = 0.6 * (hSGPA_A + 0.2 - hSGPA_A) = 0.6 * 0.2 = 0.12
• Difference in ACT component = β3 * (ACT_B - ACT_A) = 0.01 * (ACT_A - 3 - ACT_A) = -0.01 * 3 = -0.03
• Total predicted difference colGPA_B - colGPA_A = Difference in hSGPA component + Difference in ACT component = 0.12 - 0.03 = 0.09

So the predicted difference in college GPA between student B and student A is 0.09.

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