For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners ( ) are recorded along with the attractiveness
ratings by females of their male date partners (y); the ratings range from 1 to 10 . The 50 paired ratings yield ,
P-value , and . Find the best predicted value of (attractiveness rating by female of male) for a date in which the attractiveness
rating by the male of the female is . Use a 0.05 significance level.
The best predicted value of when is
(Round to one decimal place as needed.)

Ask by Parry Nguyen. in the United States

Mar 24,2025

Question

For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners ( ) are recorded along with the attractiveness
ratings by females of their male date partners (y); the ratings range from 1 to 10 . The 50 paired ratings yield ,
P-value , and . Find the best predicted value of (attractiveness rating by female of male) for a date in which the attractiveness
rating by the male of the female is . Use a 0.05 significance level.
The best predicted value of when is
(Round to one decimal place as needed.)

Ask by Parry Nguyen. in the United States

Mar 24,2025

UpStudy AI · Accepted Answer

We are given the regression equation

$$
\hat{y} = 7.50 - 0.228x.
$$

To predict the attractiveness rating $$ \hat{y} $$ (rated by the female) when $$ x = 5 $$, substitute $$ x = 5 $$ into the equation:

$$
\hat{y} = 7.50 - 0.228(5).
$$

Calculate the product:

$$
0.228 \times 5 = 1.14.
$$

Then subtract:

$$
7.50 - 1.14 = 6.36.
$$

Rounding $$ 6.36 $$ to one decimal place gives:

$$
\hat{y} \approx 6.4.
$$

Thus, the best predicted value of $$ \hat{y} $$ when $$ x = 5 $$ is $$ 6.4 $$.
The best predicted value of $$ \hat{y} $$ when $$ x = 5 $$ is **6.4**.