# How to select the degree of polynomial multiple regression?

I have around 50 dependent quantities (regressor variables).

I want to find the best relation between the response variable data and regressor variable data.

I tried multiple linear regression with 3 combinations but could not get correlation coefficient between original and predicted y variable greater than 0.5.

Hence, I am trying polynomial fit.

Starting from simple Quadratic Equation.

y = a.x1^2 + b.x2 + c

y, x1,x2,x3 ......... x50 is a matrix of 100 X 1 order.

Please help.

Can anyone suggest till which polynomial degree shall I go to find best correlation value between original and predicted y variable?

Which model is statistically better linear or polynomial?

Secondly, which matlab function can I use for this purpose?

Thanks

• (1) Don't you mean independent quantities? (2) If so, a polynomial of degree 49 will get you perfect correlation :-). (3) What do you mean by "statistically better"? (4) Please review our threads on model selection before modifying this question further. – whuber Aug 20 '13 at 20:19