Stat 112: Lecture 12 Notes Fitting Curvilinear Relationships (Chapter 5): –Interpreting the slope coefficients in the log X transformation –The log Y – log X transformation

Log Transformation

Interpreting the Coefficient on Log X

Log Transformation of Both X and Y variables It is sometimes useful to transform both the X and Y variables. A particularly common transformation is to transform X to log(X) and Y to log(Y)

Heart Disease-Wine Consumption Data (heartwine.JMP)

Evaluating Transformed Y Variable Models The log-log transformation provides slightly better predictions than the simple linear regression Model.

Interpreting Coefficients in Log-Log Models

Another interpretation of coefficients in log-log models

Another Example of Transformations: Y=Count of tree seeds, X= weight of tree

By looking at the root mean square error on the original y-scale, we see that Both of the transformations improve upon the untransformed model and that the transformation to log y and log x is by far the best.

Prediction using the log y/log x transformation What is the predicted seed count of a tree that weights 50 mg? Math trick: exp{log(y)}=y (Remember by log, we always mean the natural log, ln), i.e.,