Question

Question was provided via image upload.

Explanation:

Step1: Recall Anscombe's Quartet Properties

Anscombe's quartet has four data sets with the same mean of \( x \) (\( \bar{x} = 9 \)), same mean of \( y \) (\( \bar{y} \approx 7.5 \)), same slope of regression line (\( m \approx 0.5 \)), and same y - intercept (\( b \approx 3 \)). The regression line for all four data sets is \( \hat{y}=3 + 0.5x \).

Step2: Substitute \( x = 10 \) into Regression Line

We use the regression line formula \( \hat{y}=b+mx \). For Anscombe's quartet, \( b = 3 \) and \( m = 0.5 \). Substitute \( x = 10 \) into the formula:
\( \hat{y}=3+0.5\times10 \)
First, calculate \( 0.5\times10 = 5 \). Then, \( 3 + 5=8 \).

Answer:

\( \hat{y} = 8 \) (when using the regression line for Anscombe's quartet data sets to predict \( y \) for \( x = 10 \))