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 \(\boxed{y = 2.48x - 233.88}\).