Question

The number of victories (W), earned run average (ERA), runs scored (R), batting average (AVG), and on-base percentage (OBP) for each team in the American League in the 2012 season are provided in the following table. The ERA is one measure of the effectiveness of the pitching staff, and a lower number is better. The other statistics are measures of effectiveness of the hitters, and higher numbers are better for each of these.

	W	ERA	R	AVG	OBP
Team 1	93	3.9	712	0.247	0.311
Team 2	69	4.7	734	0.26	0.315
Team 3	85	4.02	748	0.255	0.318
Team 4	68	4.78	667	0.251	0.324
Team 5	88	3.75	726	0.268	0.335
Team 6	72	4.3	676	0.265	0.317
Team 7	89	4.02	767	0.274	0.332
Team 8	66	4.77	701	0.26	0.325
Team 9	95	3.85	804	0.265	0.337
Team 10	94	3.48	713	0.238	0.31
Team 11	75	3.76	619	0.234	0.296
Team 12	90	3.19	697	0.24	0.317
Team 13	93	3.99	808	0.273	0.334
Team 14	73	4.64	716	0.245	0.309

Develop a regression model that could be used to predict the number of victories based on the ERA.

Develop a regression model that could be used to predict the number of victories based on the runs scored.

Develop a regression model that could be used to predict the number of victories based on the batting average.

Develop a regression model that could be used to predict the number of victories based on the on-base percentage.

Which of the four models is better for predicting the number of victories?

Develop a regression model that could be used to predict the number of victories based on the ERA, runs scored, batting average, on-base percentage

Develop the best regression model that can be used to predict the number of victories

Discuss the accuracy of the regression model you developed in section g, and the significance of independent variables

Answer 1

1)

Regression Model for the prediction of no. of victories over ERA would be as followed:

Y= 155.09-17.87X ...... (Here Y=no. of victories and X=ERA)

2)

Regression Model for the prediction of no. of victories over R would be as followed:

Y= -6.88+0.12X ...... (Here Y=no. of victories and X=R)

3)

Regression Model for the prediction of no. of victories over AVG would be as followed:

Y= 62.25+77.903X ...... (Here Y=no. of victories and X=AVG)

4)

Regression Model for the prediction of no. of victories over OBP would be as followed:

Y= -10.341+289.01X ...... (Here Y=no. of victories and X=OBP)

5) The best model for prediction of victories would be the model over ERA, because the highest percentage of variability explained in the ERA model i.e, 64.87%

6)

Regression Model for the prediction of no. of victories over ERA, R, AVG, OBP would be as followed:

Y= 74.58-16.06X₁+0.12X₂-105.09X₃+38.898X₄ ...... (Here Y=no. of victories and X₁=ERA ,X₂= R ,X₃= AVG, X₄=OBP)