Curvilinear Regression

1 / 24

# Curvilinear Regression - PowerPoint PPT Presentation

Curvilinear Regression. Monotonic but Non-Linear. The relationship between X and Y may be monotonic but not linear. The linear model can be tweaked to take this into account by applying a monotonic transformation to Y, X, or both X and Y.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Curvilinear Regression' - snowy

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Curvilinear Regression

Monotonic but Non-Linear
• The relationship between X and Y may be monotonic but not linear.
• The linear model can be tweaked to take this into account by applying a monotonic transformation to Y, X, or both X and Y.
• Predicting calories consumed from number of persons present at the meal.

Calories

Log Model

Persons

• A monotonic transformation will not help here.
• A polynomial regression will.
• Copp, N.H. Animal Behavior, 31, 424-430
• Subjects = containers, each with 100 ladybugs
• Y = number of ladybugs free (not aggregated)
• X = temperature
Polynomial Models
• Cubic:
• For each additional power of X added to the model, the regression line will have one more bend.
Using Copp’s Data
• Compute Temp2, Temp3 and Temp4.
• Conduct a sequential multiple regression analysis, entering Temp first, then Temp2, then Temp3, and then Temp4.
• At each step, evaluate whether or not the last entered predictor should be retained.
SAS
• Curvi -- Polynomial Regression, Ladybugs.
• Refer to it and the output as Professor Karl goes over the code and the output
Which Model to Adopt?
• Adding Temp2 significantly increased R2, by .838-.615 = .223, keep Temp2.
• Adding Temp3significantly increased R2, by .861-.838 = .023 – does this justify keeping Temp3?
• Adding Temp4 did not significantly increase R2.
• Somewhat reluctantly, I went cubic.
Phototaxis
• Subjects = containers, each with 100 ladybugs
• Containers lighted on one side, dark on the other
• Y = number on the lighted side
• X = temperature

R2

Linear = .137

• The quadratic model clearly fits the data better than does the linear model.
• Phototaxis is positive as temps rise to about 18 and negative thereafter.
A Cubic Model
• R2 has increased significantly, from .601 to .753, p < .001
• Does an increase of 15.2% of the variance justify making the model more complex?
• I think so.
Interpretation
• Ladybugs buried in leaf mold in Winter head up, towards light, as temperatures warm.
• With warming beyond 12, head for some shade – the aphids are in the shade under Karl’s tomato plant leaves.
• With warming beyond 32, this place is too hot, lets get out of here.
A Quartic Model
• R2=.029, p = .030
• Does this small increase in R2 justify making the model more complex?
• Can you make sense of a third bend in the curve.
Multicollinearity
• May be a problem whenever you have products or powers of predictors in the model.
• Center the predictor variables,
• Or simply standardize all variables to mean 0, standard deviation 1.