Question

pizza - powered athletes the scatterplot shows the relationship between the number of slices of pizza eaten by each member of a football team (x) and the number of laps around the block the player could run immediately afterward (y). the equation of the regression line shown on the graph is $hat{y}=10 - 0.67x$. a) predict the number of laps a player who ate 7 slices can run. $hat{y}=10 - 0.67(7)=5.31$. b) one player ate 8.5 pieces of pizza and ran 2.75 laps. calculate the residual for this player. interpret the residual for this player.

Explanation:

Step1: Recall residual formula

Residual = Observed - Predicted.

Step2: Calculate predicted value for b

Given regression line $\hat{y}=10 - 0.67x$, when $x = 8.5$, then $\hat{y}=10-0.67\times8.5=10 - 5.695 = 4.305$.

Step3: Calculate residual

Observed $y = 2.75$, so residual $=2.75 - 4.305=-1.555$.

Step4: Interpret residual

The negative residual means the player ran 1.555 fewer laps than predicted by the regression - line model.

Answer:

a) 5.31
b) Residual: - 1.555. Interpretation: The player ran 1.555 fewer laps than predicted by the regression - line model.