A random sample of 10 NBA teams was selected. Their average points per game and the total number of regular season wins for the $2018 / 19$ season were recorded. The results are listed in the table below.
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|}
\hline $\begin{array}{l}\text { Points/Game, } \\
\text { X }\end{array}$ & 104.2 & 105.3 & 107.5 & 110.7 & 113.3 & 112.4 & 113.9 & 114.4 & 115.2 & 117.5 \\
\hline Wins, y & 19 & 39 & 19 & 54 & 29 & 49 & 53 & 58 & 48 & 57 \\
\hline
\end{tabular}
(Note: $\sum x y=47,799.1$ )
a) Find the regression equation for the above data. Round in such a way that prediction made from this equation will be reliable to at least 1 decimal place.
b) Use the equation to predict the average number of wins for an NBA team that average 113 points per game. Round your answer to 1 decimal place.
c) Find $r \& r^{2}$

Step 1 ：We are given a random sample of 10 NBA teams with their average points per game (X) and the total number of regular season wins (y) for the 2018/19 season. We are also given that the sum of the product of X and y, denoted as \(\sum xy\), is 47799.1.

Step 2 ：We need to find the regression equation for the above data. The regression equation is of the form \(y = bx + a\), where b is the slope and a is the y-intercept.

Step 3 ：The formula for the slope (b) is given by \[b = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}\] and the formula for the y-intercept (a) is given by \[a = \frac{\sum y - b(\sum x)}{n}\]

Step 4 ：First, we need to calculate \(\sum x\), \(\sum y\), and \(\sum x^2\) from the given data. After calculating, we get \(\sum x = 1114.4\), \(\sum y = 425\), and \(\sum x^2 = 124364.98\).

Step 5 ：Substituting these values into the formulas, we get the slope (b) as approximately 2.48 and the y-intercept (a) as approximately -233.88.

Step 6 ：Therefore, the regression equation is \[y = 2.48x - 233.88\]

Step 7 ：Final Answer: The regression equation for the above data is \(\boxed{y = 2.48x - 233.88}\).