Fitting straight lines for each row and column of a data

I have two 1-dimensional arrays x[] and y[], which when plotted looks like the attached image: layout.

I wanted to fit straight lines to each row and column separately and display them all in a single image like in the attached image: output.

Finally, determine the error distance of each point to its fitted line.

I am looking for ideas to code the for loop to identify the right (x,y) points: first for fitting each line, and later for calculating the error distance of each point belonging to that line only.

Thanks very much