Hello,
I have a question about lsfit().
I have a set of equations :
var(x_i) + var(x_j) - 2 cov(x_i,x_j) = var(x_i - x_j) for all i != j,
i,j = [1,..,7]
var(x_i - x_j) is what I have as input (simultaneously measured) data to
the model.
I therefor have a system of equations A.x = b = var(x_i - x_j) where A
is a (nx21) x 28 matrix, with n being equal (>1) to the amount of times
I measured these var(x_i - x_j) simultaneously.
When I use lsfit on this I get warnings about collinearity and
consequently certain variables are not determined (set to zero).
My question is, what does this mean? Does it mean that lsfit has removed
the mutually dependent columns (or rows) and the remaining set was
determined well or does it mean that the outcome of lsfit is not to be
trusted at all?
And what does 'collinear' exactly mean in this lsfit context? Is it that
rows or columns are linear combinations of others in the matrix A or in
t(A)A, the matrix used for a Least Squares solution? Or something else.
I ask this because I cannot see that the matrix A above is collinear;
each row or column contains elements that are not present in any other
row or column.I am confused...(due to my limited knowledge of applied
linear algebra)
any help is greatly appreciated
Sicco Schets
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