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 the equation: ( hat{y} = 0.0019x + 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 1820?
options: 0.35, -0.85, -0.35, 0.85

Explanation:

Step1: Calculate predicted GPA

Substitute $x=1820$ into the regression equation:
$y = 0.00187(1820) + 0.86$
First compute $0.00187 \times 1820 = 3.4034$, then add 0.86:
$y = 3.4034 + 0.86 = 4.2634$

Step2: Calculate residual

Residual = Observed GPA - Predicted GPA
Residual = $3.8 - 4.2634$

Answer:

-0.46 (closest to -0.45, so the correct option is: B. -0.45)