Is the number of games won by a major league baseball team in a season related to the team batting average? The table below shows the number of games won and the batting average (in thousandths) of 8 teams.TeamGames WonBatting Average192262210225931022624622655102290683266780273865277Using games won as the explanatory variable ?, do the following:(a) The correlation coefficient is ?=(b) The regression equation is ?̂ =

The given paired observations are as follows:TeamGames WonBatting192262210225931022624622655102290683266780273865277Considering "games own" as the explanatory variable (i.e., denoted as x) the regression equation for estimating the "batting average" (i.e., denoted as y) is given as follows: y=a+bx. Calculation Table:TeamGames Won; xBatting Average; y(x−x¯)(y−y¯)(x−x¯)(y−y¯)(x−x¯)2(y−y¯)2x2xy1922626-7.25-43.53652.5625846424104210225916-10.25-164256105.06251040426418310226216-7.25-11625652.56251040426724462265-24-4.2510257618.062538441643051022901620.75332256430.56251040429580683266-3-3.259.75910.5625688922078780273-63.75-22.53614.0625640021840865277-217.75-162.7544160.0625422518005Total688215400-651866743.561034185179The number of paired observations, n=8.The averages are:x¯=∑xn=6888=86y¯=∑yn=21548=269.25Part (a)The correlation coefficient:rxy=∑(x−x¯)(y−y¯)∑(x−x¯)2×∑(y−xy¯)2=−651866×743.5≈−0.05518Part (b)The slope of the regression line is:b=n∑xy−∑x∑yn∑x2−(∑x)2=(8×185179)−(688×2154)(8×61034)−(688)2=−0.03483386924≈−0.0348And the y-intercept is calculated as:a=∑y−b∑xn=2154−(−0.0383386924×688)8≈272.2457The regression equation is: y=272.2457−0.0348x.(a) The correlation coefficient is r=−0.05518.(b) The regression equation is y=272.2457−0.0348x.