Once you create your scatter plot add the regression equation and R-squared. Do
ID: 3068732 • Letter: O
Question
Once you create your scatter plot add the regression equation and R-squared. Do a regression analysis using the Excel Data Analysis tool. Highlight the "important" numbers: R-squared value, F-test number, Coefficients. Create the regression equation. For Years of experience tell me what sales should be if years of experience is 10 years. For Value tell me what a team would be worth is revenue was $250 million. Write a more than 100 word interpretation of what we have learned for each of the regression models.
is there a relationship between years of experience and sales.? Sales is Why we are doing to regression?
know if annual revenue in baseball is related to the value of the team. Value is why we are doing this.??
Arizona Diamondbacks Atlanta Braves Baltimore Orioles Boston Red Sox Chicago Cubs Chicago White Sox Cincinnati Reds Cleveland Indians Colorado Rockies Detroit Tigers Houston Astros Kansas City Royals Los Angeles Angels of Anaheim Los Angeles Dodgers Miami Marlins Revenue (S millions) Value (S millions) 584 629 618 1,312 1,000 692 546 559 537 643 626 457 718 1,615 520 562 578 811 2,300 468 225 336 245 201 Minnesota Twins New York Mets New York Yankees Oakland Athletics Philadelphia Phillies Pittsburgh Pirates San Diego Padres San Francisco Giants Seattle Mariners St Louis Cardinals Tampa Bay Rays Texas Rangers Toronto Blue Jays 471 173 479 786 716 262 764 568 631 Washington Nationals 225Explanation / Answer
Answer:
Here, we have to see two regression models. First of all, we have to see the regression model for the prediction of dependent variable sales based on the independent variable number of years. The regression model by using Excel data analysis is given as below:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.964564633
R Square
0.93038493
Adjusted R Square
0.922649923
Standard Error
4.346134937
Observations
11
ANOVA
df
SS
MS
F
Significance F
Regression
1
2272
2272
120.2823529
1.65082E-06
Residual
9
170
18.88888889
Total
10
2442
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
80
2.869698344
27.87749457
4.77671E-10
73.50829135
86.49170865
Years
4
0.364719542
10.96733117
1.65082E-06
3.174947077
4.825052923
From the above model, it is observed that the correlation coefficient between the two variables years and sales is given as 0.9646, which means there is a strong positive linear relationship exists between these two variables. The value for R square or coefficient of determination is given as 0.9304, which means about 93.04% of the variation in the dependent variable sales is explained by the independent variable years. The test statistic value F is given as 120.28 with the P-value of 0.00 approximately. So, we conclude that the given regression model is statistically significant. The regression model is given as below:
Sales = 80 + 4*years
If experience is given as 10 years,
Sales = 80 + 4*10 = 80 + 40 = 120
Now, we have to see another regression model for the prediction of the dependent variable ‘value’ based on independent variable revenue. Excel output is given as below:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.906166659
R Square
0.821138014
Adjusted R Square
0.814750086
Standard Error
165.6580782
Observations
30
ANOVA
df
SS
MS
F
Significance F
Regression
1
3527616.598
3527616.598
128.5452815
5.616E-12
Residual
28
768392.7687
27442.59888
Total
29
4296009.367
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-601.4814186
122.4288201
-4.912907091
3.51908E-05
-852.2654848
-350.6973524
Revenue
5.927062655
0.522770953
11.33778115
5.616E-12
4.856214917
6.997910394
Correlation coefficient = r = 0.9062
Coefficient of determination = R-square = 0.8211
F test statistic = 128.54
P-value = 0.00 approximately
So, we conclude that the given regression model is statistically significant.
Regression equation is given as below:
Value = -601.48 + 5.9271*Revenue
For revenue = $250 million
Value = -601.48 + 5.9271*250
Value = $880.295 million
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.964564633
R Square
0.93038493
Adjusted R Square
0.922649923
Standard Error
4.346134937
Observations
11
ANOVA
df
SS
MS
F
Significance F
Regression
1
2272
2272
120.2823529
1.65082E-06
Residual
9
170
18.88888889
Total
10
2442
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
80
2.869698344
27.87749457
4.77671E-10
73.50829135
86.49170865
Years
4
0.364719542
10.96733117
1.65082E-06
3.174947077
4.825052923
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