solving coefficient with linear algebra

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

Answer 1

[James Tursa]

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?