Applied Regression Modeling

Consider the following data:

X	2.3	1.8	2.2	1.2	1.6	2.6	1.4	1.1	1.2	1.6
Y	1.7	1.6	2.6	0.9	1.8	3.1	1.4	1.0	1.1	1.4

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, log_e(Y), and predictor variable, log_e(X) (call this model 2). Use the fitted models to answer the following questions.

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

True or False? Comparing the magnitude of the regression standard error, s, in model 2 (0.1687) with that in model 1 (0.3292) tells us nothing about which model provides a more useful description of the association between Y and X.

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 1 provides a more useful description of the association between Y and X than that of model 2.

True or false? The reason that model 2 is a linear regression model is because the logarithmic transformations to Y and X “cancel out.”

True or false? The natural logarithm transformation tends to "spread out" lower values and "pull in" higher values.