solving general linear models
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I need to solve a general linear model in the form of
Y = X*C+E to calibrate a load-cell. I can not measure the individual force and torques independently, such that I could use functions like regress().
The model looks like this : [F_x,F_y,F_z,T_x,T_y,T_z;... n observations] = [V1,V2,V3,V4,V5,V6;...n observations]*C + Error
What is the best solution in Matlab to perform a linear regression and solve for the 6x6 calibration matrix C?
I don't want to use the pseudo-inverse, as the voltage measurements might be erroneous.
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Tom Lane
am 4 Apr. 2012
The mvregress function comes at this a little differently, but it is possible to set up the problem using mvregress. For this sample problem:
n = 100; p = 3; d = 4;
x = randn(n,p);
c = rand(p,d)
e = randn(n,d)/10;
y = x*c + e;
I can use backlash to get a matrix of coefficients:
x\y
and I can get the same coefficients from mvregress this way:
for j=1:n; X{j} = kron(eye(d),x(j,:)); end
mvregress(X,y)
This will give you some additional outputs, though not all you may be looking for. For example, the fourth output is the estimated covariance of the coefficient estimates, so you can take the square root of the diagonal values to get standard errors.
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Tom Lane
am 4 Apr. 2012
I think you want
C = X\Y
if you just need estimates, no other statistical information. If not, please explain specifically what else you need.
The mvregress function is another possibility.
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tang
am 4 Apr. 2012
Hi Richard, do you have try the command regress? If the quality of data is good,the outcome may be ok
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