Question

1 2 (2 points) 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. Team Games Won Batting Average 90 284 94 260 74 267 62 280 112 263 78 274 60 259 112 288 3 4 5 6 7 8 Using games won as the explanatory variable x, do the following: (a) The correlation coefficient is r = (b) The equation of the least squares line is y =

Answer 1

-> Solution We use the following table for further calculation Team Batting average 22 y; 2 xiyi Games Won (Ri) 90 1 2 8 4 284 160 267 280 263 62 112 8100 8836 5476 38 44 12 544 6084 3600 80656 67600 71289 78400 69169 75096 67081 255 60 24440 19758 17360 29456 21372 15540 5 6 7 60 259 8 32256 288 82944 112 12544 Total. Exi= 682 247=21752x12 = 34:2-592215 ExiYi = 1857 42 61028 시 och 11 8. 682 lx 85.25. Y = ſy 8 2175 8 271.875

32 = 1 ²x; 2 – x2 = 1 $x;2_x2 8 S 1 X61028 - (85.25)? 82 3608375 2x = 18.9983, (1) by ² = 1. Y; 2 _ ý 2 = { x 592215 - (274:815) 8 143.4808 by 11.9783 Cox (x, y) = cha Exili S 1 8 8 EXi Yi 121 ху X 185742 - (85.25) (271.815) 8 Cov(x,y) = 45.5212

Q) > The correlation coefficientliga Con(x,y) Ex by 45.5212 18.9983 X 11.9783 Le> 0.2000 The value of a indicates that number of games won is related to team batting average. b)-> The equation of least square line is bo + b1a. where the least square estimator. 5o = 7 - bi and be = con(x, y) 822 Now', consider. bi CON (X,Y) 45.5212 360,9 375 ܨܬ = 0.1261 5o = g_bg = 271.815 - 0.1261 X 85.25. 0 = 261.06

From equation (5) and (6) equation (4) becomes ŷ tb, x Son bot co y = 261.00+ 0.1261 x The least - o quares line is ŷ - 261.0 6 +0:12 612 (up to bu