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 22, 2021

Answer the following questions based on Section 4.1.4: Natural logarithm transformation for the response.

Consider the following data:

X 0.8 0.6 0.8 0.2 0.5 1.0 0.3 0.1 0.2 0.5
Y 3.3 2.3 2.2 1.3 1.7 2.3 1.5 1.0 1.0 1.5
Use statistical software to fit a simple linear regression model with response variable, Y, and predictor variable, X (call this model 1). Then fit another simple linear regression model with response variable, loge(Y), and predictor variable, X (call this model 2). Use the fitted models to answer the following questions.
1. 

Model 2 with response variable, loge(Y), provides a more useful description of the association between Y and X than that of model 1 with predictor variable, X, because:

2. 

True or False? The fact that the regression standard error, s, is lower in model 2 (0.1904) than in model 1 (0.4106) indicates that model 2 provides a more useful description of the association between Y and X than that of model 1.

3. 

True or False? The fact that for model 2 the variation of the residuals remains constant as X increases, whereas for model 1 the variation of the residuals tends to increase as X increases, indicates that model 2 provides a more useful description of the association between Y and X than that of model 1.

4. 

True or false? Model 2 is not a linear regression model because the logarithmic transformation is non-linear.

5. 

In model 2, if X increases by one unit, we estimate Y to increase by:

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