Novice here: Nonlinear Regression - fitting my data to a nonlinear line

[gan024059]

Hi all - 

I have run a linear regression on my students' test score data and the r-squared value is high and p-value is low which would be great - except my residuals plot showed a different story. The residual plots did not show uniform randomness, my data appeared to be curved/not-linear. My residuals histogram is skewed a bit to the right.

Seems as though I need to transform a variable or create a nonlinear model. But I need help with SAS on how to do this. Some random, sample data is attached here that shows the types of data i'm using. I am using the following variables:

Dependent Variable: Mean Test Score

Independent Variable: % Free and Reduced Lunch

& I am separating my analyses by test subject (literacy or math).

I have NO idea how to run a procedure in SAS to help me build a nonlinear model. Is anyone able to assist me or point me in the right direction?

I tried PROC NLIN, but get lost with the parameters...

[PGStats]

To give us an idea of the type of model required, could you post the graph resulting from a loess fit, something like:

proc sort data=myData; by subject frl; run;

proc sgpanel data=myData;
panelby subject / onepanel;
loess y=score x=frl;
run;

[gan024059]

Absolutely! See attached for the Loess graphs.

[PGStats]

Those relationships look fairly linear to me.Try exploring the linear effects with something like

proc glm data=myData plots=(diagnostics residuals);
where subject ne "Spanish Language Art...";
class subject level;
model ssAvg = FRLPercent subject|level FRLPercent*subject FRLPercent*level;
output out=myOutput r=resid p=pred;
run;

[gan024059]

Hmmmm, yeah the residuals look pretty good when I do the proc glm like that, see attached. What do you think?

[StatDave]

Very flexible models can be fit by using splines. Models with splines can be easily fit in PROC GAMPL. See the examples in the GAMPL documentation in the SAS/STAT documentation.

[gan024059]

Hi Dave, thanks so much for responding.

Does this look right?

proc gampl data=cmasRegAnalysis;
class subject level;
model ssAvg = spline(FRLPercent);
run;

[gan024059]

However the proc gampl doesn't allow me to separate the output by subject and level?

[StatDave]

If you want to fit separate spline models for each subject and level combination, then specify BY SUBJECT LEVEL; rather than CLASS SUBJECT LEVEL; .  If instead you want a single model including those variables as predictors, then keep the CLASS statement and add PARAM(SUBJECT LEVEL) in your MODEL statement.

[gan024059]

Thank you! Attached is my output. Do you have any good resources to help me understand my output from proc gampl?

[StatDave]

GAMPL looks for a form of the spline that fits the shape of your data. The linear shape of what it decided on and the Effective degrees of freedom equal to 1 indicates that there is no nonlinearity. In the examples in the GAMPL documentation you will see examples where the plotted spline shape and the degrees of freedom are quite nonlinear.