Question

suppose the least square regression line \\( \hat { y } = 2.8333 x - 22.4967 \\) describes the relation between the club - head speed (in miles per hour), \\( x \\) and the distance a golf ball travels (in yards), \\( y \\).
(a) predict the distance a golf ball will travel if the club - head speed is 100 mph.
(b) suppose the observed distance a golf ball traveled when the club - head speed was 100 mph was 265 yards. what is the residual?
(a) the golf ball will travel \\( \square \\) yards
(round to the nearest tenth as needed.)
(b) the residual is \\( \square \\)
(round to the nearest tenth as needed )

Explanation:

Step1: Predict the distance for part (a)

Substitute \(x = 100\) into the regression line \(\hat{y}=2.8333x - 22.4967\).

$$
LATEXBLOCK0
$$

Step2: Calculate the residual for part (b)

The formula for the residual is \(e=y-\hat{y}\). We know \(y = 265\) (observed value) and \(\hat{y}\approx260.8\) (predicted value from part (a)).

$$ e=265 - 260.8=4.2 $$

Answer:

(a) \(260.8\)
(b) \(4.2\)