3.1 a.
= −1.8 + .0036x2 + .194x7 − .0048x8
b. Regression is significant.
c. All three are significant.
| Coefficient | test statistic | p-value |
| β2 | 5.18 | 0.000 |
| β7 | 2.20 | 0.038 |
| β8 | −3.77 | 0.001 |
d. R2 = 78.6% and R2Adj = 76.0%
e. F0 = (257.094 − 243.03)/2.911 = 4.84 which is significant at α = 0.05. The test statistic here is the square of the t-statistic in part c.
3.2 Correlation coefficient between yi and
i is .887. So (.887)2 = .786 which is R2.
3.3 a. A 95% confidence interval on the slope parameter β7 is
7 ± 2.064(.08823) = (.012, .376)
b. A 95%. confidence interval on the mean number of games won by a team when x2 = 2300, x7 = 56.0 and x8 = 2100 is
3.4 a.
= 17.9 + .048x7 − .00654x8 with F = 15.13 and p = 0.000 which is significant.
b. R2 = 54.8% and R2Adj = 51.5% which are much lower.
c. For β7, a 95% confidence interval is 0.484 ± 2.064(.1192) = (−.198, .294) and for the mean number of games won by a team when x7 = 56.0 and x8 = 2100, a 95% confidence interval is 6.926 ± 2.064(.533) = (5.829,8.024). Both lengths are greater than when x2 was included in the model.
d. It can affect many things including the estimates and standard errors of the coefficients and the value of R2.
3.5 a.
= 32.9 − .053x1 + .959x6
b. Regression is significant.
c. R2 = 78.6% and R2Adj = 77.3%. For the simple linear regression with x1, R2 = 77.2%.
d. A 95% confidence interval for the slope parameter β1 is −.053 ± 2.045(.006145) = (−.0656, −.0405).
e. x1 is significant while x6 is not.
| Coefficient | test statistic | p-value |
| β1 | -8.66 | 0.000 |
| β6 | 1.43 | 0.163 |
f. A 95% confidence interval on the mean gasoline mileage when x1...
Book description
As the Solutions Manual, this book is meant to accompany the main title, Introduction to Linear Regression Analysis, Fifth Edition. Clearly balancing theory with applications, this book describes both the conventional and less common uses of linear regression in the practical context of today's mathematical and scientific research. Beginning with a general introduction to regression modeling, including typical applications, the book then outlines a host of technical tools that form the linear regression analytical arsenal, including: basic inference procedures and introductory aspects of model adequacy checking; how transformations and weighted least squares can be used to resolve problems of model inadequacy; how to deal with influential observations; and polynomial regression models and their variations. The book also includes material on regression models with autocorrelated errors, bootstrapping regression estimates, classification and regression trees, and regression model validation.
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Description
As the Solutions Manual, this book is meant to accompany the main title, Introduction to Linear Regression Analysis, Fifth Edition. Clearly balancing theory with applications, this book describes both the conventional and less common uses of linear regression in the practical context of today's mathematical and scientific research. Beginning with a general introduction to regression modeling, including typical applications, the book then outlines a host of technical tools that form the linear regression analytical arsenal, including: basic inference procedures and introductory aspects of model adequacy checking; how transformations and weighted least squares can be used to resolve problems of model inadequacy; how to deal with influential observations; and polynomial regression models and their variations. The book also includes material on regression models with autocorrelated errors, bootstrapping regression estimates, classification and regression trees, and regression model validation.
About the Author
Douglas C. Montgomery, PhD, is Professor of Statistics in the Department of Industrial Engineering at Arizona State University. Elizabeth A. Peck, PhD, is Logistics Modeling Specialist at the Coca-Cola Company in Atlanta, Georgia. G. Geoffrey Vining, PhD, is Professor and Head of the Department of Statistics at Virginia Polytechnic and State University. All three coauthors have published extensively in both journals and books. Solutions prepared by Ann G. Ryan.
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Table of contents
Preface xiii
1. Introduction 1
2. Simple Linear Regression 13
3. Multiple Linear Regression 67
4. Model Adequacy Checking 131
5. Transformations and Weighting to Correct Model Inadequacies 173
6. Diagnostics for Leverage and Influence 207
7. Polynomial Regression Models 221
8. Indicator Variables 265
9. Variable Selection and Model Building 291
10. Multicollinearity 325
11. Robust Regression 382
12. Introduction to Nonlinear Regression 414
13. Generalized Linear Models 443
14. Other Topics in the Use of Regression Analysis 488
15. Validation of Regression Models 529
Appendix A. Statistical Tables 549
Appendix B. Data Sets For Exercises 567
Appendix C. Supplemental Technical Material 582
References 621
Index 637