Confidence bands for a linear regression with X and Y errors

#1
Dear all,

I have been searching for a while without finding a solution, so I hope someone here can help.

Here is my problem:

I have (X, Y) data points. X is a roughness parameter for which I have several measurements, Y is the area of cells when they grow on a surface with the roughness X, for which I also have several measurements. Therefore for each pair (X;Y), X and Y are the mean values of a set of measurements, with standard deviations Sx for the X values and standard deviations Sy for the s values. One comment (I don't know if it matters): Sy does not correspond to an uncertainty in the measurement of a single cell, but to the variation of the area in a population of cells

To show the correlation between X and Y, I would like to perform a linear regression taking into account the standard deviations. I think I found a way to do that, using the approach described in the attached PDF.

First question: is that approach OK in my case ?
Second question : I would like to compute 90% confidence bands. Is there a simple way to do that ? I found the answer only for the case of a simple linear regression (with no standard deviations associated to X and Y measurements)

Thank your your help,

Quentin