MATLAB: Ridge regression y=a1x1+a2x2+a3*x3+C

MATLABridge regression

hi, I want to calculate the coefficient of equation using Ridge regression according to the following equation, y=a1*x1+a2*x2+a3*x3+C C is a constant i am using the command, a=ridge(y,[1 x1 x2 x3],0.5)

when I try to regenerate y using the coefficient and the x's it is not giving me the same values. Although the trend is looking same but values are scaled up. The data file containing y,x1,x2,x3 are attached. Please have a look and give me you expert opinion. I will be very thankful to you. SSR

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From

help ridge
"B1 = ridge(Y,X,K) returns ... regression coefficients...
      ... The results are computed after centering and scaling 
      the X columns so they have mean 0 and standard deviation 1."

It goes on to point out that to avoid using the scaling internally, add a fourth argument

doc ridge

for details.

Related Solutions

MATLAB: Ridge regression coefficient question

Good question! This took a while to figure out, and I can see the help text is not clear about it. The calculations are actually always based on a scaled X under the hood, but the results are adjusted later to be usable with the unscaled data. In particular, the ridge parameter is interpreted as applying to the scaled data. You can reproduce the ridge results by computing R in your code as follows:

R = X'*X + lambda*diag(var(X));

MATLAB: How to do parameter fitting for a system of equations with 3 independent variables

xdata = horzcat(x1,x2,x3);
ydata = horzcat(y1,y2,y3);
fun=@(b,xdata) horzcat((b(1)+b(4))*x1./(1+b(1)*x1+b(2)*x2+b(3)*x3),(b(2)+b(5))*x2./(1+b(1)*x1+b(2)*x2+b(3)*x3),(b(3)+b(6))*x3./(1+b(1)*x1+b(2)*x2+b(3)*x3));
b0=[1 ; 1 ; 1 ; 1 ; 1 ; 1];
[x,resnorm] = lsqcurvefit(fun,b0,xdata,ydata);

Best wishes

Torsten.

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Related Solutions

MATLAB: Ridge regression coefficient question

MATLAB: How to do parameter fitting for a system of equations with 3 independent variables

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