Question

find the regression equation, letting the first variable be the predictor (x) variable. using the listed actress/actor ages in various years, find the best predicted age of the best actor winner given that the age of the best actress winner that year is 45 years. is the result within 5 years of the actual best actor winner, whose age was 45 years? use a significance level of 0.05.
best actress: 27, 32, 29, 61, 34, 31, 45, 30, 65, 21, 45, 56
best actor: 42, 39, 37, 46, 50, 49, 62, 50, 39, 53, 45, 34
find the equation of the regression line.
ŷ = 50.9 + (-0.135)x
(round the y-intercept to one decimal place as needed. round the slope to three decimal places as needed.)
the best predicted age of the best actor winner given that the age of the best actress winner that year is 45 years is
□ years old.
(round to the nearest whole number as needed.)

Explanation:

Step1: Identify the regression equation

The regression equation is given as $\hat{y} = 50.9 + (-0.135)x$, where $x$ is the age of the Best Actress (predictor variable) and $\hat{y}$ is the predicted age of the Best Actor.

Step2: Substitute x = 45 into the equation

We need to find the predicted age when $x = 45$. Substitute $x = 45$ into the regression equation:
$\hat{y} = 50.9 + (-0.135)(45)$

Step3: Calculate the value

First, calculate $(-0.135)(45) = -6.075$. Then, add this to 50.9:
$\hat{y} = 50.9 - 6.075 = 44.825$

Step4: Round to the nearest whole number

Rounding 44.825 to the nearest whole number gives 45.

Answer:

45