Question

The value of a sports franchise is directly related to the amount of revenue that a franchise can generate.  The data below represents the value in 2017 ($ in millions) and the annual revenue ($ in millions) for the 30 Major League Baseball teams.

Team	Revenue ($ in millions)	Value ($ in millions)
Baltimore Orioles	253	1175
Boston Red Sox	434	2700
Chicago White Sox	269	1350
Cleveland Indians	271	920
Detroit Tigers	275	1200
Houston Astros	299	1450
Kansas City Royals	246	950
Los Angeles Angels	350	1750
Minnesota Twins	249	1025
New York Yankees	526	3700
Oakland Athletics	216	880
Seattle Mariners	289	1400
Tampa Bay Rays	205	825
Texas Rangers	298	1550
Toronto Blue Jays	278	1300
Arizona Diamondbacks	253	1150
Atlanta Braves	275	1500
Chicago Cubs	434	2675
Cincinnati Reds	229	915
Colorado Rockies	248	1000
Los Angeles Dodgers	462	2750
Miami Marlins	206	940
Milwaukee Brewers	239	925
New York Mets	332	2000
Philadelphia Phillies	325	1650
Pittsburgh Pirates	265	1250
St. Louis Cardinals	310	1800
San Diego Padres	259	1125
San Francisco Giants	428	2650
Washington Nationals	304	1600

1. Using Excel or JMP, construct a scatterplot of value versus the revenue for the 30 MLB teams in 2016.  Provide a copy of the resulting scatterplot. (3 points)

2. Based upon your scatterplot, does it appear that the linear model is a reasonable approximation of the data? Comment on the direction and form of the relationship. (2 points)

3.  Using Minitab provide (or attach) the simple linear regression analysis for predicting a team’s value based upon its revenue. (2 points)

4. State the slope for the simple linear regression analysis and interpret this value in this context. (2 points)

5. State the y-intercept for the simple linear regression analysis and interpret, if applicable. (1 point)

6.  State the standard error of the regression analysis and interpret that value.  (2 points)

7. State the coefficient of determination and interpret the value in this context. (2 points)

8. State the sum of square errors. (1 point)

SSE=504849.5953

9. State the standard error of the slope. (1 point)

SEb(1)=sqrt(504849.5953/30-2)/sqrt(186742.7)=134.277/432.137=0.3107

Source: www.forbes.com

10. Calculate and interpret the 95% confidence interval for slope.   (2 points)

8.6507+-2.048(0.3107)=8.6507+-0.6363=(8.0144,

   We are 95% confident that the slope of the interval is between 8.0144 and 9.287.

11.  From the coefficient of determination, standard error of regression, and the confidence interval for slope does that model appear to fit well?  Explain.  (2 points)

Answer 1

## 1. Using Excel or JMP, construct a scatterplot of value versus the revenue for the 30 MLB teams in 2016.  Provide a copy of the resulting scatterplot.

## 2. Based upon your scatterplot, does it appear that the linear model is a reasonable approximation of the data? Comment on the direction and form of the relationship.

Answer : from scatter plot we can say that all points are in linear pattern , if we draw line there is linear relationship occur .

there is positive relationship between Revenue and value , as Revenue value increases Value is increases .

## 3) Using Minitab provide (or attach) the simple linear regression analysis for predicting a team’s value based upon its revenue.

Regression Equation

value = -1066.2 + 8.651 Revenue

### 4) State the slope for the simple linear regression analysis and interpret this value in this context.

Answer : Slope is 8.651 as Revenue value increases as 1 then value increases as the 8.651 units .

slope is positive that means there is positive relationship between value and Revenue .

## 5)  State the y-intercept for the simple linear regression analysis and interpret, if applicable.

Answer : Yes it is applicable its value is : -1066.2 it is negative it is affect on value (y)

## 6)  State the standard error of the regression analysis and interpret that value.

Answer : S = standard error = 134.277

S represents the average distance that the observed values fall from the regression line.

Model Summary

S R-sq R-sq(adj) PRESS R-sq(pred)
134.277 96.51% 96.39% 612504 95.77%

## 7) State the coefficient of determination and interpret the value in this context.

Answer : it is R square value = 96.51 % it is very very good ,

variation explained by model is 96.51 % , if R square value is larger then model is good .

## 8) State the sum of square errors.

SSE=504849.5953

It is the sum of squared deviation of actual values from predicted values .

## 9) State the standard error of the slope. (1 point)

SEb(1)=sqrt(504849.5953/30-2)/sqrt(186742.7)=134.277/432.137

=0.3107

The standard error of the regression slope S represents the average distance that observed values deviate from the regression line

## 10. ) Calculate and interpret the 95% confidence interval for slope.   (2 points)

8.6507+-2.048(0.3107)=8.6507+-0.6363

=(8.0144, 9.287)

We are 95% confident that the slope of the interval is between 8.0144 and 9.287

## 11) From the coefficient of determination, standard error of regression, and the confidence interval for slope does that model appear to fit well?  Explain.

Answer : 1) overall model is significant ,  

2) it is variation explained by model is very very good .

3) there is significant linear regression occur .

## here attached Minitab output :