1
$\begingroup$

I am working on a linear regression project where I first removed insignificant variables, then looked at a possible transform of the data. I performed the variable selection smoothly, however am having trouble interpreting an effective transform for the data to fit the assumptions of a linear model.

I after identifying that my data-set requires transformation (as some of the 4 assumptions of linear regression were violated for the original dataset), I tried 4 transformations:

  1. log model (log response variables)
  2. log-log model (log response variables and log explanatory variables)
  3. Box-Cox on Y
  4. Box-Cox on X & Y

I found that the Box-Cox on X & Y produced the highest R2, and thus selected that as the 'best' transformation.

Upon re-checking the assumptions under the transformed data-set, I found from the partial residual plots that one of the explanatory variables still displayed non-linear relationship with the residuals.

Partial Residual plot before transformation: enter image description here

Partial Residual plot after transformation: enter image description here

As well, the QQ-plot of residuals confirming normality of the data is changed to have more extreme tails rather than more skew, and is still not 'perfect' to a normal distribution

QQ-plot before transformation: QQ-plot before transformation:

QQ-plot after transformation: QQ-plot after transformation:

Finally, the residuals plotted against the fitted to check for constant variance seem to be worse off after the transformation than before:

Residuals vs Fitted before transformation: enter image description here

Residuals vs Fitted after transformation: enter image description here

From looking at these concerns, how would I interpret the effectiveness of this transform on the data?

$\endgroup$
0
$\begingroup$
  • After you applied your 4 transformation, you must have should check if the model assumptions are satisfied (you did not do this step, you directly selected the transformation based on $R^2$. Hence your partial residual plot showed the non linear trend).
  • Also $R^2$ is never to be used for selection of transformation.
  • If all the transformations equally satisfy the assumptions, then you must choose the transformation which makes the interpretation of the transformed variables the easiest.
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.