(e) Which of the four models is better for predicting the number of victories? (
ID: 3353349 • Letter: #
Question
(e) Which of the four models is better for predicting the number of victories? ( what is better for predicting the number of victories: ERA, Runs, AVG, or OBP?
(f) Find the best multiple regression model to predict the number of wins. Use any combination of the variables to find the best model
This question is in relation to a textbook solution for quantitative analysis for management, 12th edition, chapter 4. problem 31
Data set:
Wins ERA Runs AVG OBP
93 3.90 712 .247 .311
69 4.70 734 .260 .315
85 4.02 748 .255 .318
68 4.78 667 .251 .324
88 3.75 726 .268 .335
72 4.30 676 .265 .317
89 4.02 767 .274 .332
66 4.77 701 .260 .325
95 3.85 804 .265 .337
94 3.48 713 .238 .310
75 3.76 619 .234 .296
90 3.19 697 .240 .317
93 3.99 808 .273 .334
73 4.64 716 .245 .309
Explanation / Answer
e)
Wins Vs ERA
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
Wins = 155.1 - 17.87 ERA
Wins vs Runs
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
Runs 0.1235 0.0506 2.44 0.031 1.00
Regression Equation
Wins = -6.9 + 0.1235 Runs
Wins Vs AVG
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
Wins = 62.2 + 78 AVG
Wins Vs OBP
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
Wins = -10.3 + 289 OBP
Wins Vs ERA is the best prediction model with R-squared value 64.87% and Coefficient is significant to output.
F) Multiple regressions:
Below specified models are highest variance covered(R-squared models)
To find the best model have to look R-squared value and variables are coefficient to the regression model output or not.
Wins vs ERA and Runs
Model Summary
S R-sq R-sq(adj) R-sq(pred)
3.65161 90.62% 88.91% 85.52%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 72.3 17.3 4.19 0.002
ERA -16.88 2.06 -8.21 0.000 1.01
Runs 0.1093 0.0199 5.50 0.000 1.01
Regression Equation
Wins = 72.3 - 16.88 ERA + 0.1093 Runs
Wins Vs ERA, Runs and AVG
Model Summary
S R-sq R-sq(adj) R-sq(pred)
3.74640 91.02% 88.33% 85.11%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 79.5 20.7 3.84 0.003
ERA -16.18 2.35 -6.88 0.000 1.25
Runs 0.1235 0.0295 4.19 0.002 2.10
AVG -80 119 -0.67 0.517 2.25
Regression Equation
Wins = 79.5 - 16.18 ERA + 0.1235 Runs - 80 AVG
Wins Vs ERA, Runs and OBP
Model Summary
S R-sq R-sq(adj) R-sq(pred)
3.81031 90.72% 87.93% 82.46%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 80.2 30.4 2.64 0.025
ERA -16.77 2.17 -7.71 0.000 1.03
Runs 0.1164 0.0304 3.83 0.003 2.17
OBP -42 131 -0.32 0.755 2.16
Regression Equation
Wins = 80.2 - 16.77 ERA + 0.1164 Runs - 42 OBP
Wins Vs ERA, Runs, AVG and OBP
Model Summary
S R-sq R-sq(adj) R-sq(pred)
3.94012 91.06% 87.09% 79.88%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 74.6 32.8 2.27 0.049
ERA -16.06 2.54 -6.32 0.000 1.32
Runs 0.1215 0.0326 3.73 0.005 2.33
AVG -105 177 -0.59 0.568 4.52
OBP 39 192 0.20 0.844 4.34
Regression Equation
Wins = 74.6 - 16.06 ERA + 0.1215 Runs - 105 AVG + 39 OBP
Conclusion:
Wins Vs ERA and Runs is the best predicting model with R-squared value 90.62% and Variables are significant to the output variable.
The other models gave the best accuracy but not significant to the output variable.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.