Questions: (d) Find the value of the coefficient of determination r^2. (Round your answer to four decimal places.) r^2=0.8422 What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? (Round your answer to two decimal places.) 84.12 % What percentage is unexplained? (Round your answer to two decimal places.) 15.88 % (e) If a team had x=3 fouls over and above the opposing team, what does the least-squares equation forecast for y (in %)? (Round your answer to two decimal places.) 42.53 %

Find the value of the coefficient of determination \( r^{2} \).

Calculate \( r^{2} \).

The value of the coefficient of determination \( r^{2} \) is \( 0.8422 \).

\(\boxed{r^{2} = 0.8422}\)

What percentage of the variation in \( y \) can be explained by the corresponding variation in \( x \) and the least-squares line?

Calculate the explained variation percentage.

The percentage of the variation in \( y \) explained by the corresponding variation in \( x \) is given by \( r^{2} \times 100 = 84.22\% \).

\(\boxed{84.22\%}\)

What percentage is unexplained?

Calculate the unexplained variation percentage.

The percentage of the variation in \( y \) that is unexplained is \( 100\% - 84.22\% = 15.78\% \).

\(\boxed{15.78\%}\)

If a team had \( x = 3 \) fouls over and above the opposing team, what does the least-squares equation forecast for \( y \) (in \%)?

State the forecasted value of \( y \).

The least-squares equation forecasts \( y \) to be \( 42.53\% \).

\(\boxed{42.53\%}\)

The value of the coefficient of determination \( r^{2} \) is \( 0.8422 \).
The percentage of the variation in \( y \) explained by the corresponding variation in \( x \) is \( 84.22\% \).
The percentage of the variation in \( y \) that is unexplained is \( 15.78\% \).
The least-squares equation forecasts \( y \) to be \( 42.53\% \).