Question

The value of a sports franchise is directly related to the amount of revenue that a franchise can generate. The file here represents the value in 2013 (in $millions) and the annual revenue (in $millions) for the 30 Major League Baseball franchises. (Data extracted from www.forbes.com/mlb-valuations/list.) Suppose you want to develop a simple linear regression model to predict franchise value based on annual revenue generated. What are the values for (1) the proportion of variation in value of a sports franchise that is explained by annual revenue , (2) the sum of squares Y , (3) the sum of squares predicted , (4) the sum of squares error , (5) the intercept A , (6) the slope b , (7) the predicted value of a sports franchise (in $millions) that generates $300 millions of annual revenue , and (8) the standard error of estimate ?

Team	Revenue	Value
Baltimore	206	618
Boston	336	1312
Chicago White Sox	216	692
Cleveland	186	559
Detroit	238	643
Kansas City	169	457
Los Angeles Angels	239	718
Minnesota	214	578
New York Yankees	471	2300
Oakland	173	468
Seattle	215	644
Tampa Bay	167	451
Texas	239	764
Toronto	203	568
Arizona	195	584
Atlanta	225	629
Chicago Cubs	274	1000
Cincinnati	202	546
Colorado	199	537
Houston	196	626
Los Angeles Dodgers	245	1615
Miami	195	520
Milwaukee	201	562
New York Mets	232	811
Philadelphia	279	893
Pittsburgh	178	479
St. Louis	236	716
San Diego	189	600
San Francisco	262	786
Washington	225	631

Answer 1

(1) the proportion of variation in value of a sports franchise that is explained by annual revenue ,

0.822

(2) the sum of squares Y ,

42,96,009.3667

(3) the sum of squares predicted ,

35,30,836.8306

(4) the sum of squares error ,

7,65,172.5361

(5) the intercept A ,

-601.9291

(6) the slope b ,

5.9316

(7) the predicted value of a sports franchise (in $millions) that generates $300 millions of annual revenue ,

1,177.566

and (8) the standard error of estimate ?

165.311

The regression output is:

	r²	0.822
	r	0.907
	Std. Error	165.311
	n	30
	k	1
	Dep. Var.	Value
ANOVA table
Source	SS	df	MS	F	p-value
Regression	35,30,836.8306	1	35,30,836.8306	129.20	5.29E-12
Residual	7,65,172.5361	28	27,327.5906
Total	42,96,009.3667	29
Regression output					confidence interval
variables	coefficients	std. error	t (df=28)	p-value	95% lower	95% upper
Intercept	-601.9291
Revenue	5.9316	0.5218	11.367	5.29E-12	4.8627	7.0006
Predicted values for: Value
		95% Confidence Interval		95% Prediction Interval
Revenue	Predicted	lower	upper	lower	upper	Leverage
300	1,177.566	1,077.870	1,277.261	824.571	1,530.560	0.087