Applied Regression Modeling

3rd edition

Iain Pardoe

A concise, comprehensive treatment of the application of statistical regression analysis suitable for undergraduate and graduate students. Covers simple linear regression, multiple linear regression, model building, and advanced regression topics.

by Iain P
on July 30, 2021

Answer the following questions based on Section 5.4: Model selection.

Consider the following data:

X1 0.8 0.6 0.8 0.2 0.5 1.0 0.3 0.1 0.2 0.5
X2 0.1 1.0 0.8 0.5 1.0 0.9 0.3 0.5 1.0 0.2
X3 0.3 0.6 0.6 0.6 0.8 0.7 0.2 0.1 0.9 0.4
X4 1.2 0.3 0.1 0.8 0.3 0.4 0.8 0.4 0.2 0.9
Y 0.8 0.5 0.7 0.5 0.8 1.1 0.3 0.1 0.5 0.3
Use the data to answer the following questions.

1. 

Use statistical software to find the best simple linear regression model with response variable, Y, and one of the four predictor variables, X1, X2, X3, or X4. Which of the four possible models fits the best?

2. 

Use statistical software to find the best multiple linear regression model with response variable, Y, and two of the four predictor variables, X1, X2, X3, or X4. Which of the six possible models fits the best?

3. 

Use statistical software to find the best multiple linear regression model with response variable, Y, and three of the four predictor variables, X1, X2, X3, or X4. Which of the four possible models fits the best?

4. 

Which of the following four multiple linear regression models has the highest value of adjusted R2?

5. 

Which of the following four multiple linear regression models has the lowest (most negative) value of AIC?

6. 

Which of the following four multiple linear regression models has the lowest (most negative) value of BIC?

7. 

Which of the following four multiple linear regression models has the lowest value of Mallows' Cp?

8. 

Which of the following four multiple linear regression models fits the data the best?

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