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? \bigcirc 0.35 \bigcirc -0.35 \bigcirc -0.85 \bigcirc 0.85

Explanation:

Step1: Calculate predicted GPA

Substitute $x=1820$ into the regression equation.
$y = 0.00197\times1820 + 0.85$
First compute $0.00197\times1820 = 3.5854$, then $3.5854 + 0.85 = 4.4354$

Step2: Calculate residual

Residual = Observed GPA - Predicted GPA
$\text{Residual} = 3.9 - 4.4354$

Answer:

-0.535 (closest to option: -0.55)
The matching option is: $\boldsymbol{-0.55}$