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 5.2.3: Regression pitfalls - multicollinearity.

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 1.0 0.6 0.8 0.3 0.6 1.0 0.4 0.2 0.1 0.4
Y 0.6 0.5 0.5 0.3 0.3 0.6 0.5 0.1 0.1 0.5
Use the data to answer the following questions.

1. 

Construct a scatterplot of X1 and X2. What do you include from this plot?

2. 

Use statistical software to fit a multiple linear regression model with response variable, Y, and predictor variables, X1 and X2. Obtain the Variance Inflation Factor for X1 or X2 (they’re both the same). Round your answer to 2 decimal places.

3. 

How do we know there is a multicollinearity issue for the multiple linear regression model with response variable, Y, and predictor variables, X1 and X2.? (Select all that apply.)

4. 

Use statistical software to fit a simple linear regression model with response variable, Y, and predictor variable, X1. Obtain the two-tailed p-value for the regression parameter for X1. Round your answer to 4 decimal places.

5. 

Compare the standard error for the regression parameter for X1 in the multiple linear regression model with predictor variables, X1 and X2 (from Q2) and the simple linear regression model predictor variable, X1 (from Q4).

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