Question

Larte unhwally both college and hegh school CPNA are on a four. polnt scale. We estimate the following model by ols: codCR = β₁+β₂ h=βA+β₃

ACR+i and obeain the following parameter entimatec rho₁ = 1.2. β₂ = 0.6:, β₃ = 0.01.
Predict differeoce of college GPA s of two stiodents (coicPAB - colGPMA) where the Hudent is tuks a 05 poitits higher Geh in hieh school apd 3 points lower ACT score compared to student A.

Answer 1

The predicted difference in college GPAs for two students with a 0.5 point difference in high school GPA and a 3 point difference in ACT scores is 0.27 points.

Step-by-step explanation:

The student has asked how to predict the difference in college GPAs (colGPA) of two students given that one student has a 0.5-point higher high school GPA and a 3-point lower ACT score compared to the other student. The regression model given is colGPA = β1 + β2*HSGPA + β3*ACT, with parameter estimates β1 = 1.2 (intercept), β2 = 0.6 (coefficient for high school GPA), and β3 = 0.01 (coefficient for ACT score). The predicted difference in colGPA (ΔcolGPA) for the two students can be calculated using the parameter estimates and the differences in their HSGPA and ACT scores.

To predict the difference in college GPAs, we use the differences in HSGPA and ACT scores multiplied by their respective regression coefficients:

ΔcolGPA = (β2 * ΔHSGPA) + (β3 * ΔACT)

ΔcolGPA = (0.6 * 0.5) + (0.01 * -3)

ΔcolGPA = 0.3 + (-0.03)

ΔcolGPA = 0.27

Therefore, the predicted difference in college GPAs between the two students, with one having a 0.5 higher high school GPA and 3 lower ACT score, is 0.27 points.