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 3.5 with a sat score of 1320? 0.35 -0.35 0.85 -0.85

Explanation:

Step1: Calculate predicted GPA

Substitute $x=1320$ into the regression equation:
$y_{\text{predicted}} = 0.00197(1320) + 0.85$
$y_{\text{predicted}} = 2.6004 + 0.85 = 3.4504$

Step2: Compute residual

Residual = Observed value - Predicted value
$\text{Residual} = 3.8 - 3.4504 = 0.3496 \approx 0.35$

Answer:

0.35