4. A baseball analytics specialist 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 per game for a recent season (stored in Baseball.xlsx). Develop a model to predict the number of wins based on ERA and runs scored per game.

a. (5 points) State the multiple regression equation and interpret the meaning of the slopes in this equation.

b. (5 points) Is there a significant relationship between the number of wins and the two independent variables (ERA and runs scored per game) at the 0.05 level of significance? Explain.

c. (5 points) At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. Explain.

d. (5 points) Construct a 95% confidence interval estimate of the population slope between wins and ERA.

Suppose the analytics specialist decides to drop runs scored per game and to include the league (0 = American, 1 = National) as an independent variable in addition to ERA. Develop a model to predict wins based on ERA and league.

e. (5 points) State the multiple regression equation and interpret the meaning of the slopes in this equation.

f. (5 points) At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. Explain.

Suppose the analytics specialist decides to add an interaction term between ERA and league. Develop a model to predict wins based on ERA, league and the interaction term.

g. (5 points) At the 0.05 level of significance, determine whether the interaction term makes a significant contribution to the model.

Team	Wins	League	E.R.A.	Interaction	Runs Scored	Hits Allowed	Walks Allowed	Saves	Errors
Baltimore	64	0	5.15	0.00	741	1633	546	31	90
Boston	95	0	4.35	0.00	872	1494	530	41	82
Chicago White Sox	79	0	4.14	0.00	724	1438	507	36	113
Cleveland	65	0	5.06	0.00	773	1570	598	25	97
Detroit	86	0	4.29	0.00	743	1449	594	42	88
Houston	74	1	4.54	4.54	643	1521	546	39	78
Kansas City	65	0	4.83	0.00	686	1486	600	34	116
Los Angeles Angels	97	0	4.45	0.00	883	1513	523	51	85
Minnesota	86	0	4.50	0.00	817	1542	466	48	76
New York Yankees	103	0	4.26	0.00	915	1386	574	51	86
Oakland	75	0	4.26	0.00	759	1486	523	38	105
Seattle	85	0	3.87	0.00	640	1359	534	49	105
Tampa Bay	84	0	4.33	0.00	803	1421	515	41	98
Texas	87	0	4.38	0.00	764	1432	531	45	106
Toronto	75	0	4.47	0.00	798	1509	551	25	76
Arizona	70	1	4.42	4.42	720	1470	525	36	124
Atlanta	86	1	3.57	3.57	735	1399	530	38	96
Chicago Cubs	83	1	3.84	3.84	707	1329	586	40	105
Cincinnati	78	1	4.18	4.18	673	1420	577	41	89
Colorado	92	1	4.22	4.22	804	1427	528	45	87
Florida	87	1	4.29	4.29	772	1425	601	45	106
Los Angeles Dodgers	95	1	3.41	3.41	780	1265	584	44	83
Milwaukee	80	1	4.83	4.83	785	1498	607	44	98
New York Mets	70	1	4.45	4.45	671	1452	616	39	97
Philadelphia	93	1	4.16	4.16	820	1479	489	44	76
Pittsburgh	62	1	4.59	4.59	636	1491	563	28	73
St. Louis	91	1	3.66	3.66	730	1407	460	43	96
San Diego	75	1	4.37	4.37	638	1422	603	45	94
San Francisco	88	1	3.55	3.55	657	1268	584	41	88
Washington	59	1	5.00	5.00	710	1533	629	33	143