CODEWITHSUNDEEP
validationsas
PwL
PwL

Reputation: 11

How to validate of quality of polynomial model based on known model formula

I want to validate polynomial model which working on production based on known formula. I mean how check in SAS that model parameters is correct (significant different by 0) based on p-value (t-Student). Model has example character. I have only two variables Y and X.
Y - it's dependent variable
X - it's independent variable to proc reg in SAS I Modeller will defined 3 new variable 

x1=1/X
x2=1/x^^2 
x3=1/x^^3

and obtained this function

y=0,00519+2,1873*x1+(-3,63807*x2)+2,06002*x3

The most important is analysis of residual. R2 is almost equal 1, so model it's very fitted.
Corellation and Multicollinearity is very high.

So it's my question:

  1. How check p-value for parameter of regression (0,00519;2,1873;-3,63807;2,06002)?

  2. Normal distribution must be preserved for residual for polynomial model?

  3. Homoscedasticity (test White) is necessary?

Upvotes: 0

Views: 128

Answers (1)

user10502805
user10502805

Reputation: 18

I'm assuming you're using a regression (e.g. proc reg, proc genmod, proc glm) to model y based on your x1, x2, and x3 variables?

Before you start: how many data points do you have? If you have only four points, then the regression will produce an R^2 of 1 even if they're not on any sort of curve. This does not mean you have good fit; it means that you can define any 4 points using a model with 3 parameters plus an intercept.

The p-value for the parameters in the regression should be provided by the regression model procedure you used to obtain your estimates - could you post your output?

Yes, it is true that the residuals should be normally distributed, even if the regression is a polynomial.

Depending on which regression model you're using, the code differs a bit, but you need to plot your residual against your Y value to look for indications of heteroscedasticity or non-normal residuals. I would look at the standard fit diagnostic residuals for this, see this page for more details: How to plot standard diagnostics for proc reg

Upvotes: 0

Related Questions