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 30 years. Is the result within 5 years of the actual Best Actor winner, whose age was 38 years? \begin{tabular}{cllllllllllll} \hline Best Actress & 29 & 30 & 30 & 61 & 34 & 34 & 46 & 30 & 62 & 22 & 46 & 52 \\ Best Actor & 45 & 36 & 38 & 43 & 52 & 48 & 61 & 49 & 37 & 54 & 46 & 34 \\ \hline \end{tabular} Find the equation of the regression line. \[ \hat{y}=\square+(\square) x \] (Round the $y$-intercept to one decimal place as needed. Round the slope to three decimal places as needed.)

Step 1 ：Given the ages of the Best Actress winners as the predictor (x) variable, and the ages of the Best Actor winners as the response (y) variable, we need to perform a linear regression analysis to find the equation of the regression line.

Step 2 ：The equation of the regression line is given by \(\hat{y} = a + bx\), where \(a\) is the y-intercept and \(b\) is the slope of the line.

Step 3 ：Using the given data, we find that the y-intercept \(a\) is approximately 16.5 and the slope \(b\) is approximately 0.618. Therefore, the equation of the regression line is \(\hat{y} = 16.5 + 0.618x\).

Step 4 ：We can use this regression equation to predict the age of the Best Actor winner when the age of the Best Actress winner is 30 years. Substituting \(x = 30\) into the equation, we get \(\hat{y} = 16.5 + 0.618 \times 30\), which gives a predicted age of approximately 47.0 years.

Step 5 ：Comparing this predicted age with the actual age of the Best Actor winner (38 years), we find that the prediction is not within 5 years of the actual age.