1) Interpret the multiple coefficient of determination R-square. 2) Compare the R-square of the simple linear regression and the R-square of the multiple regression, what does the differences in R-squares tell us? 3) What does F-test for significance tell us? SUMMARY OUTPUTRegression StatisticsMultiple RR SquareAdjusted R SquareStandard ErrorObservationsANOVARegressionResidualTotalInterceptAgePressureSmoker (Yes=1)0.9252030310.8560006490.8290007716.141529119df2031619SSMSF3587.455921 1195.819 31.70387603.4940788 37.718384190.95Coefficients Standard Error t Stat P-value-107.53650381.222244070.2983520846.82635185114.71362875 -7.30863 1.76E-060.159044683 7.68491 9.3E-070.045408505 6.570401 6.44E-062.908212167 2.347267 0.032109Significance F5.76336E-07Lower 95%Upper 95%Lower 95.0%Upper 95.0%-138.7280033 -76.3450042 -138.7280033 -76.345004230.885084402 1.559403737 0.885084402 1.5594037370.202090353 0.394613815 0.202090353 0.3946138150.661217468 12.99148623 0.661217468 12.99148623

We are provided with summary output of regression as given in the question.

1) Interpret the multiple coefficient of determination R-square. 2) Compare the R-square of the simple linear regression and the R-square of the multiple regression, what does the differences in R-squares tell us? 3) What does F-test for significance tell us?

1) Interpret the multiple coefficient of determination R-square. 2) Compare the R-square of the simple linear regression and the R-square of the multiple regression, what does the differences in R-squares tell us? 3) What does F-test for significance tell us?

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter11: Data Analysis And Displays

Section: Chapter Questions

Problem 10CT

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Question

1) Interpret the multiple coefficient of determination R-square.

2) Compare the R-square of the simple linear regression and the R-square of the multiple regression, what does the differences in R-squares tell us?

3) What does F-test for significance tell us?

SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
ANOVA
Regression
Residual
Total
Intercept
Age
Pressure
Smoker (Yes=1)
0.925203031
0.856000649
0.829000771
6.141529119
df
20
3
16
19
SS
MS
F
3587.455921 1195.819 31.70387
603.4940788 37.71838
4190.95
Coefficients Standard Error t Stat P-value
-107.5365038
1.22224407
0.298352084
6.826351851
14.71362875 -7.30863 1.76E-06
0.159044683 7.68491 9.3E-07
0.045408505 6.570401 6.44E-06
2.908212167 2.347267 0.032109
Significance F
5.76336E-07
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
-138.7280033 -76.3450042 -138.7280033 -76.34500423
0.885084402 1.559403737 0.885084402 1.559403737
0.202090353 0.394613815 0.202090353 0.394613815
0.661217468 12.99148623 0.661217468 12.99148623

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