best fit linear filter

I have an image that I'm told I need to do a best fit linear filter on, but

I'm not exactly sure what that means and searches on it keep leading me to

linear regression, which I don't think is what I want, but maybe it is.

Can someone give me some help here? If it's a linear regression and the 
pixel brightness (they're 8-bit greyscale) is X, what is Y?

Thanks.