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

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

1 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

2 Log Transformation

3 Interpreting the Coefficient on Log X

4 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)

5 Heart Disease-Wine Consumption Data (heartwine.JMP)

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

7 Interpreting Coefficients in Log-Log Models

8 Another interpretation of coefficients in log-log models

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

10

11 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.

12 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.,


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