I am trying to map the pixels from one image to another image using two linear transformations, one to determine the new x position and one to determine the new y position within the image. I have come up with the following two equations for a direct mapping of pixels from one image to another using digital image correlation and least squares regression; however the mapping has an error associated with it represented by the standard deviation of how well the patches that were compared actually match up to the equation, please correct me if I am wrong on this.

x2 = a + b*x1 + c*y1 with a standard deviation of s over n given samples

y2 = d + e*x1 + f*y1 with a standard deviation of t with the same n samples

Given 3 images, I'm trying to understand how the error will propogate when I try to combine the linear equations from image 1 and 2 with the the linear equations from image 2 and 3 to get a direct mapping from image 1 and 3. I am able to obtain the new equations, but could somebody explain how the error is affected in these cases? Does the sample size have any affect on the error?