Question

Assignment 7: Problem 14 Previous Problem Problem List Next Problem (1 point) The following data represents the winning percentage (the number of wins out of 162 games in a season) as wel as the teams Earned Run Average ERA The ERA is a pitching statistic. The lower the ERA, the less runs an opponent will score per game. Smaller ERA's reflect a good pitching staff and ) a goo team defense. You are to investigate the relationship between a team's winning percentage-Y, and its Earned Run Average (ERA) - X Winning Proportion -Y Earned Run Average (ERA) 0.623457 0.512348 0.635802 0.604938 0.518519 0.580247 0.413580 0.407407 0.462963 0.450617 0.487654 0.456790 0.574047 3.13 3.97 3.68 3.92 4.00 4.12 4.29 4.62 3.89 5.20 4.38 4.91 3.75 (a) Using MINITAB, create a scatter-plot of the data. What can you conclude from this scatter-plot? A. There is not a linear relationship between the a teams winning percentage and its ERA. o B. There is a negative linear relationship between a teams winning percentage and its ERA o C. There is a positive linear relationship between a teams winning percentage and its ERA. (b) Use MINITAB to find the least squares estimate of the linear model that expressed a teams winning percentage as a linear function of is ERA. Use four decimals in each of your answers. (c) Find the value of the coefficient of determination, then complete its interpretation. l(use four decimals) The percentage of? V in 2 Vthat is explained by its linear relationship with (d) Interpret the meaning of the slope term in the estimate of the linear model, in the context of the data. As a teams? increases by? the teams? will lI.(use four decimals) (e) A certain professional basebal team had an earned run average of 3.45 this past season. How many games out of 162 would you expect this team to win Use two decimals in your answer. lgames won (f) The team mentioned in part (e) won 91 out of 162 games. Find the residual, using two decimals in your answer

Answer 1

2964144776541 7049015230672 0051001517042 1 0 0 0 0 0 0 0 0 0 0 0 0 2431252933753 3919002830703 2224 .00262495 00 .000 .201051 0 .0 001000 0 234179167775 5587023046916 0018060156265 1010 .01100000 1762424755169 0142101420273 1000000001000

Sum of X-53.84 Sum of Y-6.7278 Mean X- 4.1415 Mean Y-0.5175 Sum of squares (SSx) 3.5614 sum of products (SP) =-0.3828 Regression Equation -y- bX+ a b- SPISSx--0.38/3.56 -0.10748 a-My-bMx = 0.52-(-0.1 1 *4.14) :096264 у--0.1 0748X+ 0.96264

0.65 0.6 0.55 0.5 0.45 0.41 3.5 4 4.5 5.5 x-Independent Regression Line ()--0.1 1X + 0.96)

7159015341672 0051001517042 1000000000000 1048041234143 1010001100000 3939002930813 2214202262495 020000201051 1000000001000 6587134057027 0018060156365 1010001100000 2222228828882 1762424755169 0142101420273 1000000001000

X Values Σ = 53.84 Mea n = 4.1 42 Σ(X-MJ2 SSx = 3.561 Y Values Σ = 6.728 Mean = 0.518 Xand Y Combined N= 13 Σ(X-Mx)(Y-My) =-0.383 R Calculation r =-0.383 / V(3.561)(0.075)) =-0.7403 Meta Numerics (cross-check) r--0.7403

The value of R is-0.7403. The value of R2, the coefficient of determination, is 0.548.

The percentage of variation in a teams winning percentage ' that is explained by its linear relationship with is54.76 the teams earned run average (d) Interpret the meaning of the slope term in the estimate of the linear model, in the context of the data. As a teams earned run average increases by one earned runt the teams winning percentage 7 will will decrease by an average of0.1073 , (use four decimals) (e) A certain professional baseball team had an earned run average of 3.45 this past season. How many games out of 162 would you expect this team to win? Use two decimals in your answer 95.87 games won

Residual Observed value predicted value e y -y-hat f) we want to find, the residual for x 3.45 observed value of y is, 91/162 0.5617 and predicted value of y for x -3.45 is, y-hat 0.962 (0.1073* 3.45) 0.5918 y-hat 0.5918 Therefore, residual 0.5617- 0.5918--0.0301 residual -0.03 (rounded to two decimal places) ei-0.03