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Polynomial Multiple Regression - Which function to use and how ?

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Priya
Priya 2013-8-20
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.

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回答（1 个）

Shashank Prasanna
Shashank Prasanna 2013-8-20
编辑：Shashank Prasanna 2013-8-20
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
  2 个评论
Priya
Priya 2013-8-21
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
Shashank Prasanna 2013-8-21
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')

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