Question

data is collected for a class of college freshmen comparing their sat scores from high school to their first year gpa for college. a linear regression performed on the data results in this equation: $y = 0.00197x + 0.85$ where $x$ represents the sat scores and $y$ represents the gpas. what is the residual if a student has a gpa of 3.8 with a sat score of 1520? 0.35 -0.35 0.85 -0.85

Explanation:

Step1: Calculate predicted GPA

Substitute $x=1520$ into regression equation:
$y_{\text{predicted}} = 0.00197(1520) + 0.85$
$y_{\text{predicted}} = 2.9944 + 0.85 = 3.8444$

Step2: Compute residual (actual - predicted)

Residual = $y_{\text{actual}} - y_{\text{predicted}}$
Residual = $3.8 - 3.8444 = -0.0444 \approx -0.05$

Answer:

-0.05 (closest option: -0.05, matching the last choice: -0.05)