Question

> The accompanying data are the number of wins and the earned run averages (mean number of earned runs allowed per nine innings pitched) for eight baseball pitchers in a recent season. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not (a)x=5 wins (b) x = 10 wins (c)x= 21 wins (d) x = 15 wins Click the icon to view the table of numbers of wins and earned run average. The equation of the regression line is ĝ=x+ (Round to two decimal places as needed.) Construct a scatter plot of the data and draw the regression line. Choose the correct graph below OA. AERA 6- ОВ. AERA 6- OC. AERA 6- Q a D. AERA 6- a 4- a 4- 4- Q 4- 2- 24 2- 2 2 0 6 12 18 24 12 18 24 6 12 18 24 6 12 18 24 (a) Predict the ERA for 5 wins, if it is meaningful. Select the correct choice below and, if necessary, fill in the answer box within your choice

Answer 1

Let, The number of wins earned run averages (ERA) The we know that, the pitted prediction is, linear regression line for y = 6x ta Where cî- estimate of yointercept of regression line ń - estimate of slope of regression line Vaso we show that Ô ssay ssa and a = 7 - Ôx where, ssay = {(xi-x) (Hi-F) = [ (xi-7) 2 SSH 1 Here, n=8, x = Zai {ali=117 {y} = 29.53 Eli = 3.6913 140625 17. CSS

(xi-*) 28.8906 11.3906 (x1 - x) Iti-7.) froze 81 - 5.0055 bi -1.4555 So 0408 -2.7342 0.122 . 0.0742 1,8900 0:3906 6.8900 13. 1405 31.6406 99.875 -1.763 - 0.648 -803188 Total -19.8163" Here, Ssa=99.875 Ssxyz --19-8163 i = ssay SSA os -19.8163 99.875 n 1,' b = -0.1984 ♡ - 0:20 and bo = 3.6913- (-0.1984X 14.625 6.5930 m 6.59 Mint . The equation of equation of the regression line is. Y -0.20 x + 6. 59. CS Sad With CMS

Mi xi 20 18 2.6248 300215 3-2200 17. 3:4184 3.8153 14 12 4+ 21 21 U 4.4105 4.8073 or Scatter plot of given data and regression line Y 6 Elearned Run Average 4 2 6 12 14 16 2 18 8 10 wins Ans B CS

의 Here, we have to predict the ERA for 5 wing. 1 . : 6.50 + (- 024 x ) when, =s. -:Y: 6:59 -0.2015) Û = 5.60 B x = 10 for :: 6:59 - 0-20110) 4.61 ri Ansil ý 24.61 for : 6S - O-10 (21) 2.43 .: Ans: Ô 9 = 2.43 co x=15. À 3.6.59-0.20 (15) 1. Ya 3.62 1. Ansia 23.62 CSS