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.

The following data show values for these statistics for a random sample of 20 pitchers from the American League for a season.

Player	Team		W			L			ERA	SO/IP	HR/IP	R/IP
Verlander, J	DET			24			5		2.39	0.99	0.09	0.29
Beckett, J	BOS			13			7		2.90	0.92	0.11	0.35
Wilson, C	TEX			16			7		2.94	0.93	0.07	0.39
Sabathia, C	NYY			19			8		3.00	0.98	0.08	0.38
Haren, D	LAA			16			10		3.17	0.80	0.08	0.39
McCarthy, B	OAK			9			9		3.31	0.71	0.06	0.43
Santana, E	LAA			11			12		3.39	0.77	0.12	0.42
Lester, J	BOS			15			9		3.46	0.95	0.10	0.39
Hernandez, F	SEA			14			14		3.47	0.95	0.07	0.43
Buehrle, M	CWS			13			9		3.58	0.54	0.10	0.44
Pineda, M	SEA			9			10		3.74	1.00	0.11	0.43
Colon, B	NYY			8			10		4.00	0.82	0.14	0.51
Tomlin, J	CLE			12			7		4.26	0.55	0.16	0.47
Pavano, C	MIN			9			13		4.30	0.47	0.10	0.54
Danks, J	CWS			8			12		4.34	0.78	0.10	0.51
Guthrie, J	BAL			9			17		4.34	0.64	0.12	0.55
Lewis, C	TEX			14			10		4.41	0.83	0.18	0.51
Scherzer, M	DET			15			9		4.44	0.90	0.15	0.53
Davis, W	TB			11			10		4.45	0.58	0.12	0.52
Porcello, R	DET			14			9		4.75	0.56	0.10	0.56

An equation given below is 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). Enter negative value as negative number.

  +   +  

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

Compute  test statistic (to 2 decimals). Use F table.

The -value is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 5

What is your conclusion at the  level of significance?

There - Select your answer -is notisItem 6 a significant overall relationship.

b. Use the  test to determine the significance of each independent variable.

Compute the  test statistic for the significance of SO/IP (to 2 decimals). Enter negative value as negative number. Use t table.

The -value is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 8

What is your conclusion at the  level of significance?

SO/IP - Select your answer -is notisItem 9 significant.

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

The -value is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 11

What is your conclusion at the  level of significance?

HR/IP - Select your answer -is notisItem 12 significant.

Answer 1

The regression equation is defined as,

The regression analysis is done in excel by following these steps,

Step 1: Write the data values in excel. The screenshot is shown below,

Step 2: DATA > Data Analysis > Regression > OK. The screenshot is shown below,

Step 3: Select Input Y Range: 'R/IP' column, Input X Range: 'SO/IP and HR/IP' column then OK. The screenshot is shown below,

The result is obtained. The screenshot is shown below,

The regression equation is,

a)

Answer:

test statistic = 9.62

The p-value is less than .01

There is a significant overall relationship.

Explanation:

From the regression analysis (ANOVA table)

F-statistic = 9.61737

The p-value (significance F) = 0.0016 which is less than 0.01 at a 1% significance level which means the model fits the data value at the 1% significance level. Hence we can conclude that independent variables fit the model significantly.

b)

Answer:

t-statistic (SO/IP) = -3.32

The p-value is less than .01

SO/IP is significant.

t-statistic (HR/IP) = 2.18

The p-value is between .025 and .05

SO/IP is significant.

Explanation:

From the regression analysis (t value table)

	P-value
SO/IP	0.004026	<0.01	Significant at 1% significance level
HR/IP	0.043474	between 0.025 and 0.05	Significant at 5% significance level