Solutions Manual to accompany Introduction to Linear Regression Analysis

Douglas C. Montgomery, Elizabeth A. Peck, G. Geoffrey Vining

• Publisher: Wiley
• Year: 2013
• ISBN:
  9781118548509
• Edition: 5
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

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.

Chapter 3

Multiple Linear Regression

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 R²_Adj = 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 y_i 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 R²_Adj = 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 R²_Adj = 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 x_1...