# solving coefficient with linear algebra

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Nicholas Deosaran on 15 Sep 2020
Edited: James Tursa on 15 Sep 2020
How can I determine the coefficients, p, of the least squares fit of a plane through the data defined as:
data = p(1) + p(2)*x + p(3)*y.
Useing the data given by the following code.
x=1:10;
y=x;
[X,Y]=meshgrid(x,y); % make a grid of x and y
valuesX=X(:); % turns the matrix into a long vector instead
Y=Y(:); % turns the matrix into a long vector
insteaddata=cumsum(ones(10,10))+(1-rand(10,10)); % fake elevation data
data=data(:); % turns the matrix into a long vector instead

James Tursa on 15 Sep 2020
Edited: James Tursa on 15 Sep 2020
You basically have this:
[ONES_COLUMN, X_COLUMN, Y_COLUMN] * p = DATA
You know all the CAPS stuff. So just use the standard least squares solution to find p. I.e., if you had the generic problem A*x = b, how would you find the least squares solution for x?

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