Polynomial Multiple Regression - Which function to use and how ?

I have around 50 dependent quantities (regressor variables).

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

Which combination shall I try ?

starting from simple Quadratic Equation.

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

Which matlab function can i use ? How to use it ?

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

Please help.

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

Answer 1

[Shashank Prasanna]

How do I go about doing it?

LinearModel.fit: http://www.mathworks.com/help/stats/linearmodel.fit.html

Implement on your own using backslash: http://www.mathworks.com/help/matlab/ref/mldivide.html

How do I choose the polynomial order?

That is problem dependent. Without looking at the data and without understanding the application area and requirements there is no way anyone can give you a fixed answer.

However you could use STEPWISE to automatically choose the model for you:

http://www.mathworks.com/help/stats/linearmodel.stepwise.html

[Priya]

For multiple Linear regression I used the function - regress for two and three predictors. Then I substituted the coefficients in the linear equation and calculate the predicted value of y and found correlation coefficient between original and predicted y dataset. Correlation was around 0.5 (max)

Is it different from Linear Model Fit function ?

Secondly: equation of the form Linear regression model: y ~ 1 + x1*x2 + x2^2

Does it come in Linear Model ? I think it is quadratic equation and should have been included in polynomial model .. Please explain.

[Shashank Prasanna]

LinearModel.fit is newer and easier to use and is the recommended approach. REGRESS is a relatively older function in the Stats Tbx.

mdl = LinearModel.fit(X,y,'quadratic')