best fit linear filter

I have an image that I need to normalize the brightness on. The image is 
greyscale 8-bit. I'm told I need to do a best fit linear filter. How do I
do 
this? Is this just a linear regression? If so, I need X&Y values and I'm
not 
sure what should be X vs. what should be Y. I assume one of them is the 
pixel brightness. What's the other?

Thanks