03-16-2015 11:05 AM
I have a situation where three X variables are in "strange" curvilinear relationship with Y var., but, when i put those X vars. as predictors in multiple linear regression, as result i get high value of Adj.R Square, all X vars. are stat. significant (p<0,001) and all assumptions for linear regression are met except of linearity. How is it possible that the model is still good, despite the fact that the assumption of linearity is not fulfilled?
03-16-2015 11:17 AM
Because you are able to fit a linear model with high Adj R. Square does not imply that this is the best model ... you should get a better Adj R. Square if you fit the curvature properly.
The curvature may produce data that slopes up or slopes down, and hence the appearance of a good fit and significant coefficients.
03-16-2015 04:11 PM
Here's an example to look at:
do x= 0 to 10 by .1;
y = x + cos(x);
Where x has a somewhat "strange" curvilinear relationship with y but the R-square is 0.9385 and the parameter for x has a p-value < 0.0001;
The data bounces back and forth across the line y=x, not very far as all of the values are within the 95% prediction interval for individual values.