Chapter 9.2, Problem 10P

For Problems 7–18, please do the following.

1. (a) Draw a scatter diagram displaying the data.
2. (b) Verify the given sums ∑x, ∑y, ∑x², ∑y², and ∑xy and the value of the sample correlation coefficient r.
3. (c) Find $\bar{x}$, $\bar{y}$, a, and b. Then find the equation of the least-squares line $\hat{y}=a+bx$.
4. (d) Graph the least-squares line on your scatter diagram. Be sure to use the point $\left(\bar{x},\bar{y}\right)$ as one of the points on the line.
5. (e) Interpretation Find the value of the coefficient of determination r². 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?

10. Basketball: Fouls 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.

Complete parts (a) through (e), given ∑x = 13, ∑y = 154, ∑x² = 65, ∑y² = 6290, ∑xy = 411, and r ≈ 0.988.

1. (f) If a team had x = 4 fouls over and above the opposing team, what does the least-squares equation forecast for y?