a. develop a regression model that could be used to predict the number of victor
ID: 3274934 • Letter: A
Question
a. develop a regression model that could be used to predict the number of victories based on the ERA
b) develop a regression model that could be used to predict the number of victories based on the runs scored
c.) develop a regression model that could be used to predict the number of victories based on the batting average
d.) develop a regression model that could be used to predict the number of victories based on the on-base percentage e.0 which of the four models is better for predicting the number of victories? find the best multiple regression model to predict the number of wins. use any combination of the variables to find the best model
TEAM W ERA R AVG OBP BALTIMORE ORIOLES 93 3.90 712 0.247 0.311 BOSTON RED SOX 69 4.70 734 0.260 0.315 CHICAGO WHITE SOX 85 4.02 748 0.255 0.318 CLEVELAND INDIANS 68 4.78 667 0.251 0.324 DETROIT TIGERS 88 3.75 726 0.268 0.335 KANSAS CITY ROYALS 72 4.30 676 0.265 0.317 LOS ANGELES ANGLES 89 4.02 767 0.274 0.332 MINNESTOA TWINS 66 4.77 701 0.260 0.325 NEW YORK YANKEES 95 3.85 804 0.265 0.337 OAKLAND ATHLETICS 94 3.48 713 0.238 0.310 SEATTLE MARINERS 75 3.76 619 0.234 0.296 TAMPA BAY RAYS 90 3.19 697 0.240 0.317 TEXAS RANGERS 93 3.99 808 0.273 0.334 TORONTO BLUE JAYS 73 4.64 716 0.245 0.309Explanation / Answer
a)
Regression Analysis: W versus ERA
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 1 1014.40 1014.40 22.16 0.001
ERA 1 1014.40 1014.40 22.16 0.001
Error 12 549.31 45.78
Lack-of-Fit 11 541.31 49.21 6.15 0.305
Pure Error 1 8.00 8.00
Total 13 1563.71
Model Summary
S R-sq R-sq(adj) R-sq(pred)
6.76580 64.87% 61.94% 52.95%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 155.1 15.6 9.94 0.000
ERA -17.87 3.80 -4.71 0.001 1.00
Regression Equation
W = 155.1 - 17.87 ERA
Fits and Diagnostics for Unusual Observations
Obs W Fit Resid Std Resid
11 75.00 87.90 -12.90 -2.01 R
b)
Regression Analysis: W versus R
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 1 518.8 518.76 5.96 0.031
R 1 518.8 518.76 5.96 0.031
Error 12 1045.0 87.08
Total 13 1563.7
Model Summary
S R-sq R-sq(adj) R-sq(pred)
9.33163 33.18% 27.61% 17.50%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant -6.9 36.6 -0.19 0.854
R 0.1235 0.0506 2.44 0.031 1.00
Regression Equation
W = -6.9 + 0.1235 R
c)
Regression Analysis: W versus AVG
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 1 13.58 13.58 0.11 0.751
AVG 1 13.58 13.58 0.11 0.751
Error 12 1550.14 129.18
Lack-of-Fit 10 1281.14 128.11 0.95 0.614
Pure Error 2 269.00 134.50
Total 13 1563.71
Model Summary
S R-sq R-sq(adj) R-sq(pred)
11.3657 0.87% 0.00% 0.00%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 62.2 61.4 1.01 0.331
AVG 78 240 0.32 0.751 1.00
Regression Equation
W = 62.2 + 78 AVG
d)
Regression Analysis: W versus OBP
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 1 152.0 152.0 1.29 0.278
OBP 1 152.0 152.0 1.29 0.278
Error 12 1411.7 117.6
Lack-of-Fit 11 1249.7 113.6 0.70 0.742
Pure Error 1 162.0 162.0
Total 13 1563.7
Model Summary
S R-sq R-sq(adj) R-sq(pred)
10.8463 9.72% 2.20% 0.00%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant -10.3 81.4 -0.13 0.901
OBP 289 254 1.14 0.278 1.00
Regression Equation
W = -10.3 + 289 OBP
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