Answer true or false to each of the following statements and explain your answers. a. In using the method of transformations, we should only transform

(a)
The method of transformation may transform either one or both of the response and predictor variables, in an attempt to satisfy the assumptions of the regression model.
Thus, the statement “In using the method of transformations, we should only transform the predictor variable to straighten a scatterplot.” is False.
(b)
The conditional distribution of the response variable depends on the predictor variable and not on any transformation of the predictor variable. Whatever transformation is performed on the predictor variable, the conditional distribution of the response variable will continue to depend on the original distribution of the predictor variable.
Thus, the statement “In using the method of transformations, a transformation of the predictor variable will change the conditional distribution of the response variable.” is False.
(c)
Some non-linear equations in a regression can be transformed into linear equations or at least an equation that can be approximately linear, using transformations such as the power transformations. However, it is not possible to transform all non-linear equations to linear approximations using the power transformations.
Thus, the statement “It is not always possible to find a power transformation of the response variable or the predictor variable (or both) that will straighten the scatterplot.” is True.