Problem:1 A) Crazy Dave, a well-known baseball analyst, wants to determine which variables are important in predicting a team’s wins in a given season. He has collected data related to wins, earned run average (ERA), and runs scored for the 2009 season (stored BB2009). Develop a model to predict the number of wins based on ERA and runs scored. State the multiple regression equation. Interpret the meaning of the slopes in this equation. Predict the number of wins for a team that has an ERA of 4.50 and has scored 750 runs. Perform a residual analysis on the results and determine Is there a significant relationship between number of wins and the two independent variables (ERA and runs scored) at the 0.05 level of significance? Determine the p-value in (e) and interpret its meaning. Interpret the meaning of the coefficient of multiple determination in this problem. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. Indicate the most appropriate regression model for this set of data. Determine the p-values in (i) and interpret their meaning. Construct a 95% confidence interval estimate of the population slope between wins and ERA. Compute and interpret the coefficients of determination. Which is more important in predicting wins—pitching, as measured by ERA, or offense, as measured by runs scored? Explain.

Problem:1 A) Crazy Dave, a well-known baseball analyst, wants to determine which variables are important in predicting a team’s wins in a given season. He has collected data related to wins, earned run average (ERA), and runs scored for the 2009 season (stored BB2009). Develop a model to predict the number of wins based on ERA and runs scored.

1. State the multiple regression equation.
2. Interpret the meaning of the slopes in this equation.
3. Predict the number of wins for a team that has an ERA of 4.50 and has scored 750 runs.
4. Perform a residual analysis on the results and determine
5. Is there a significant relationship between number of wins and the two independent variables (ERA and runs scored) at the 0.05 level of significance?
6. Determine the p-value in (e) and interpret its meaning.
7. Interpret the meaning of the coefficient of multiple determination in this problem.
8. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. Indicate the most appropriate regression model for this set of data.
9. Determine the p-values in (i) and interpret their meaning.
10. Construct a 95% confidence interval estimate of the
11. population slope between wins and ERA.
12. Compute and interpret the coefficients of determination.
13. Which is more important in predicting wins—pitching, as measured by ERA, or offense, as measured by runs scored? Explain.
    
    
    
    

    Team	League	Wins		Runs Scored	Hits Allowed	Walks Allowed	Saves	Errors	E.R.A.
    Baltimore	0	64		741	1633	546	31	90	5.15
    Boston	0	95		872	1494	530	41	82	4.35
    Chicago White Sox	0	79		724	1438	507	36	113	4.14
    Cleveland	0	65		773	1570	598	25	97	5.06
    Detroit	0	86		743	1449	594	42	88	4.29
    Kansas City	0	65		686	1486	600	34	116	4.83
    Los Angeles Angels	0	97		883	1513	523	51	85	4.45
    Minnesota	0	86		817	1542	466	48	76	4.50
    New York Yankees	0	103		915	1386	574	51	86	4.26
    Oakland	0	75		759	1486	523	38	105	4.26
    Seattle	0	85		640	1359	534	49	105	3.87
    Tampa Bay	0	84		803	1421	515	41	98	4.33
    Texas	0	87		764	1432	531	45	106	4.38
    Toronto	0	75		798	1509	551	25	76	4.47
    Arizona	1	70		720	1470	525	36	124	4.42
    Atlanta	1	86		735	1399	530	38	96	3.57
    Chicago Cubs	1	83		707	1329	586	40	105	3.84
    Cincinnati	1	78		673	1420	577	41	89	4.18
    Colorado	1	92		804	1427	528	45	87	4.22
    Florida	1	87		772	1425	601	45	106	4.29
    Houston	1	74		643	1521	546	39	78	4.54
    Los Angeles Dodgers	1	95		780	1265	584	44	83	3.41
    Milwaukee	1	80		785	1498	607	44	98	4.83
    New York Mets	1	70		671	1452	616	39	97	4.45
    Philadelphia	1	93		820	1479	489	44	76	4.16
    Pittsburgh	1	62		636	1491	563	28	73	4.59
    St. Louis	1	91		730	1407	460	43	96	3.66
    San Diego	1	75		638	1422	603	45	94	4.37
    San Francisco	1	88		657	1268	584	41	88	3.55
    Washington	1	59		710	1533	629	33	143	5.00

Problem:1 B) Suppose that in addition to using ERA to predict the number of wins, Crazy Dave wants to include the league (0=American, 1=National) as an independent variable. Develop a model to predict wins based on ERA and league.

1. State the multiple regression equation.
2. Interpret the slopes in (a).
3. Predict the number of wins for a team with an ERA of 4.50 in the American League. Construct a 95% confidence interval estimate for all teams and a 95% prediction interval for an individual team.
4. Perform a residual analysis on the results