Please do the following. (a) Draw a scatter diagram...

Please do the following. (a) Draw a scatter diagram displaying the data. (b) Verify the given sums $\Sigma x, \Sigma y, \Sigma x^{2}, \Sigma y^{2},$ and $\Sigma x y$ and the value of the sample correlation coefficient $r$. (c) Find $\bar{x}, \bar{y}, a,$ and $b .$ Then find the equation of the least-squares line $\hat{y}=a+b x$. (d) Graph the least-squares line on your scatter diagram. Be sure to use the point $(\bar{x}, \bar{y})$ as one of the points on the line. (e) Interpretation Find the value of the coefficient of determination $r^{2} .$ What percentage of the variation in $y$ can be explained by the corresponding variation in $x$ and the least-squares line? What percentage is unexplained? Answers may vary slightly due to rounding. Data for this problem are based on information from STATS Basketball Scoreboard. It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let $x$ be the number of fouls that were more than (i.e., over and above) the number of fouls made the opposing team made. Let $y$ be the percentage of times the team with the larger number of fouls won the game. $$\begin{array}{c|cccc}\hline x & 0 & 2 & 5 & 6 \\\hline y & 50 & 45 & 33 & 26\end{array}$$ Complete parts (a) through (e), given $\Sigma x=13, \Sigma y=154, \Sigma x^{2}=65, \Sigma y^{2}=6290, \Sigma x y=411,$ and $r \approx-0.988$. (f) If a team had $x=4$ fouls over and above the opposing team, what does the least-squares equation forecast for $y ?$

Please do the following.
(a) Draw a scatter diagram displaying the data.
(b) Verify the given sums $\Sigma x, \Sigma y, \Sigma x^{2}, \Sigma y^{2},$ and $\Sigma x y$ and the value of the sample correlation coefficient $r$.
(c) Find $\bar{x}, \bar{y}, a,$ and $b .$ Then find the equation of the least-squares line $\hat{y}=a+b x$.
(d) Graph the least-squares line on your scatter diagram. Be sure to use the point $(\bar{x}, \bar{y})$ as one of the points on the line.
(e) Interpretation Find the value of the coefficient of determination $r^{2} .$ What percentage of the variation in $y$ can be explained by the corresponding variation in $x$ and the least-squares line? What percentage is unexplained?
Answers may vary slightly due to rounding.
Data for this problem are based on information from STATS Basketball Scoreboard. It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let $x$ be the number of fouls that were more than (i.e., over and above) the number of fouls made the opposing team made. Let $y$ be the percentage of times the team with the larger number of fouls won the game.
$$\begin{array}{c|cccc}\hline x & 0 & 2 & 5 & 6 \\\hline y & 50 & 45 & 33 & 26\end{array}$$
Complete parts (a) through (e), given $\Sigma x=13, \Sigma y=154, \Sigma x^{2}=65, \Sigma y^{2}=6290, \Sigma x y=411,$ and $r \approx-0.988$.
(f) If a team had $x=4$ fouls over and above the opposing team, what does the least-squares equation forecast for $y ?$

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