Question

Major League Baseball (MLB) consists of teams that play in the American League and the National League. MLB collects a wide variety of team and player statistics. Some of the statistics often used to evaluate pitching performance are as follows:

• ERA: The average number of earned runs given up by the pitcher per nine innings. An earned run is any run that the opponent scores off a particular pitcher except for runs scored as a result of errors.
• SO/IP: The average number of strikeouts per inning pitched.
• HR/IP: The average number of home runs per inning pitched.
• R/IP: The number of runs given up per inning pitched.

Complete the equation below for an estimated regression equation developed to predict the average number of runs given up per inning pitched (R/IP) given the average number of strikeouts per inning pitched (SO/IP) and the average number of home runs per inning pitched (HR/IP) (to 3 decimals).

R/IP =(___) + (___) SO/IP + (___) HR/IP

1. Use the  test to determine the overall significance of the relationship.

   Compute F test statistic (to 2 decimals).

   (___)

   The p-value is  (to 3 decimals).
   
   (___)

2. Use the t test to determine the significance of each independent variable.

   Compute the  test statistic for the significance of SO/IP (to 2 decimals).

   (___)

   The p-value is  (to 3 decimals).
   
   (___)

3. Compute the t-test statistic for the significance of HR/IP (to 2 decimals).

   (__)

   The p-value is  (to 3 decimals).

   (__)
   

   Player	Team	W	L	ERA	SO/IP	HR/IP
   Verlander, J	DET	24	5	2.39	1.00	0.10
   Beckett, J	BOS	13	7	2.88	0.90	0.11
   Wilson, C	TEX	16	7	2.93	0.92	0.07
   Sabathia, C	NYY	19	8	3.00	0.96	0.06
   Haren, D	LAA	16	10	3.16	0.81	0.07
   McCarthy, B	OAK	9	9	3.32	0.71	0.05
   Santana, E	LAA	11	12	3.38	0.78	0.11
   Lester, J	BOS	15	9	3.46	0.95	0.10
   Hernandez, F	SEA	14	14	3.47	0.94	0.08
   Buehrle, M	CWS	13	9	3.58	0.52	0.09
   Pineda, M	SEA	9	10	3.73	1.01	0.10
   Colon, B	NYY	8	10	3.99	0.82	0.13
   Tomlin, J	CLE	12	7	4.24	0.53	0.15
   Pavano, C	MIN	9	13	4.29	0.46	0.09
   Danks, J	CWS	8	12	4.32	0.78	0.11
   Guthrie, J	BAL	9	17	4.32	0.63	0.12
   Lewis, C	TEX	14	10	4.40	0.83	0.17
   Scherzer, M	DET	15	9	4.42	0.89	0.15
   Davis, W	TB	11	10	4.45	0.57	0.12
   Porcello, R	DET	14	9	4.74	0.57	0.10

Answer 1

Answers:

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Regression Equation:

HR/IP (Y) = -0.0772 + 0.0575 SO/IP (X1) + 0.0366 ERA (X2)

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Ans a) Excel Output:

F test statistic = 6.02

The p-value is = 0.249

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.643777
R Square	0.414449
Adjusted R Square	0.34556
Standard Error	0.024955
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	2	0.007493	0.003747	6.016238	0.010576
Residual	17	0.010587	0.000623
Total	19	0.01808
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-0.07718	0.064609	-1.19459	0.24865	-0.2135	0.059132
SO/IP (X1)	0.057508	0.04059	1.416797	0.174607	-0.02813	0.143147
ERA (X2)	0.036628	0.010818	3.385856	0.003514	0.013804	0.059451

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Ans b)

The t-test statistic for the significance of SO/IP is = 1.42

The p-value is = 0.175

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Ans c)

The t-test statistic for the significance of HR/IP is = 3.39

The p-value is = 0.014

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