Question

The value of a sports franchise is directly related to the amount of revenue that a franchise can generate. Below is the data that represents the value (in $millions) and the annual revenue (in $millions) for 30 Major League Baseball franchises. Suppose you want to develop a simple linear regression model to predict franchise value based on annual revenue generated.

Team	Revenue	Value
Baltimore	179	460
Boston	310	1000
Chicago White Sox	214	600
Cleveland	178	410
Detroit	217	478
Kansas City	161	354
Los Angeles Angels	226	656
Minnesota	213	510
New York Yankees	439	1850
Oakland	160	321
Seattle	210	585
Tampa Bay	161	323
Texas	233	674
Toronto	188	413
Arizona	186	447
Atlanta	203	508
Chicago Cubs	266	879
Cincinnati	185	424
Colorado	193	464
Houston	196	549
Los Angeles	230	1400
Miami	148	450
Milwaukee	195	448
New York Mets	225	719
Philadelphia	249	723
Pittsburgh	168	336
St. Louis	233	591
San Diego	163	458
San Francisco	230	643
Washington	200	480

(a ) Use the least-squares method to determine the regression coefficients (intercept and slope).

(b) Interpret the meaning of the intercept and slope in this problem.

(c) Predict the value of a baseball franchise that generates $150 million of annual revenue.

Answer 1

Using Excel<data<megastat<correlation/regression<regression

Regression Analysis
	r²	0.790
	r	0.889
	Std. Error	150.955
	n	30
	k	1
	Dep. Var.	Value y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	24,04,121.3683	1	24,04,121.3683	105.50	5.31E-11
Residual	6,38,045.3317	28	22,787.3333
Total	30,42,166.7000	29
Regression output					confidence interval
variables	coefficients	std. error	t (df=28)	p-value	95% lower	95% upper
Intercept	-496.3022	110.71	-4.48	0.00	-723.09	-269.51
Revenue x	5.1961	0.5059	10.271	5.31E-11	4.1599	6.2324

a)

Intercept (b0) -496.3022

Slope (b1) 5.1961

b)

A practical interpretation of the​ Y-intercept,b0​, is not meaningful because no value is going to have a revenue of zero. The​ slope,b1​, implies that for each increase of 1 million dollars in annual​ revenue, the value is expected to increase by the value of b1​, in millions of dollars.

c)

Y=5.196 x-496.302 = 5.196*150-496.302=283.098

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