Question

In: Statistics and Probability

The value of a sports franchise is directly related to the amount of revenue that a...

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.

Solutions

Expert Solution

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

Regression Analysis
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

Please do the comment for any doubt or clarification. Please upvote if this helps you out. Thank You!


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