# appiled linear regression

**Topics:**Linear regression, Regression analysis, Simple linear regression

**Pages:**98 (3500 words)

**Published:**February 11, 2014

Solutions Manual

to accompany

Applied Linear

Regression Models

Fourth Edition

Michael H. Kutner

Emory University

Christopher J. Nachtsheim

University of Minnesota

John Neter

University of Georgia

2004

McGraw-Hill/Irwin

Chicago, IL

Boston, MA

PREFACE

This Student Solutions Manual gives intermediate and ﬁnal numerical results for all starred (*) end-of-chapter Problems with computational elements contained in Applied Linear Regression M odels, 4th edition. No solutions are given for Exercises, Projects, or Case Studies.

In presenting calculational results we frequently show, for ease in checking, more digits than are signiﬁcant for the original data. Students and other users may obtain slightly diﬀerent answers than those presented here, because of diﬀerent rounding procedures. When a problem requires a percentile (e.g. of the t or F distributions) not included in the Appendix B Tables, users may either interpolate in the table or employ an available computer program for ﬁnding the needed value. Again, slightly diﬀerent values may be obtained than the ones shown here.

The data sets for all Problems, Exercises, Projects and Case Studies are contained in the compact disk provided with the text to facilitate data entry. It is expected that the student will use a computer or have access to computer output for all but the simplest data sets, where use of a basic calculator would be adequate. For most students, hands-on experience in obtaining the computations by computer will be an important part of the educational experience in the course.

While we have checked the solutions very carefully, it is possible that some errors are still present. We would be most grateful to have any errors called to our attention. Errata can be reported via the website for the book: http://www.mhhe.com/KutnerALRM4e. We acknowledge with thanks the assistance of Lexin Li and Yingwen Dong in the checking of this manual. We, of course, are responsible for any errors or omissions that remain. Michael H. Kutner

Christopher J. Nachtsheim

John Neter

i

ii

Contents

1 LINEAR REGRESSION WITH ONE PREDICTOR VARIABLE

1-1

2 INFERENCES IN REGRESSION AND CORRELATION ANALYSIS

2-1

3 DIAGNOSTICS AND REMEDIAL MEASURES

3-1

4 SIMULTANEOUS INFERENCES AND OTHER TOPICS IN REGRESSION ANALYSIS 4-1

5 MATRIX APPROACH TO SIMPLE LINEAR REGRESSION ANALYSIS

5-1

6 MULTIPLE REGRESSION – I

6-1

7 MULTIPLE REGRESSION – II

7-1

8 MODELS FOR QUANTITATIVE AND QUALITATIVE PREDICTORS 8-1

9 BUILDING THE REGRESSION MODEL I: MODEL SELECTION AND

VALIDATION

9-1

10 BUILDING THE REGRESSION MODEL II: DIAGNOSTICS

10-1

11 BUILDING THE REGRESSION MODEL III: REMEDIAL MEASURES

11-1

12 AUTOCORRELATION IN TIME SERIES DATA

12-1

13 INTRODUCTION TO NONLINEAR REGRESSION AND NEURAL NETWORKS

13-1

14 LOGISTIC REGRESSION, POISSON REGRESSION,AND GENERALIZED LINEAR MODELS 14-1

iii

iv

Chapter 1

LINEAR REGRESSION WITH ONE

PREDICTOR VARIABLE

1.20. a.

d.

1.21. a.

b.

c.

d.

1.24. a.

ˆ

Y = −0.5802 + 15.0352X

ˆ

Yh = 74.5958

ˆ

Y = 10.20 + 4.00X

ˆ

Yh = 14.2

4.0

¯ ¯

(X, Y ) = (1, 14.2)

i:

1

ei : -9.4903

2

...

0.4392 . . .

44

1.4392

45

2.4039

e2 = 3416.377

i

Min Q =

b.

1.25. a.

b.

1.27. a.

b.

e2

i

M SE = 79.45063,

√

M SE = 8.913508, minutes

e1 = 1.8000

e2 = 17.6000, M SE = 2.2000, σ 2

i

ˆ

Y = 156.35 − 1.19X

ˆ

(1) b1 = −1.19, (2) Yh = 84.95, (3) e8 = 4.4433,

(4) M SE = 66.8

1-1

1-2

Chapter 2

INFERENCES IN REGRESSION

AND CORRELATION ANALYSIS

2.5. a.

t(.95; 43) = 1.6811, 15.0352 ± 1.6811(.4831), 14.2231 ≤ β1 ≤ 15.8473

b.

H0 : β1 = 0, Ha : β1 = 0. t∗ = (15.0352 − 0)/.4831 = 31.122. If |t∗ | ≤ 1.681 conclude H0 , otherwise Ha . Conclude Ha . P -value= 0+

c.

Yes

d.

H0 : β1 ≤ 14, Ha : β1 > 14. t∗ = (15.0352 − 14)/.4831 = 2.1428. If t∗ ≤ 1.681 conclude H0 , otherwise Ha . Conclude Ha . P -value= .0189

2.6. a.

t(.975; 8)...

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