Extract linear region of data (stress-strain data)

Hi all. I have experience in about 1 class with Matlab but I'm stumped right now. I know I could do this manually, but I'm trying to practice with Matlab.

My problem is that stress-strain data is usually approximately linear up to a point, then it becomes non-linear. Is there a way to "extract" the linear portion of data and put it in a matrix?

Here's some example data:

   clear; clc; close all;
     A= [0 0
    331 0.156
    669 0.315
    1022 0.493
    1140 0.554
    1175 0.581
    1167 0.776
    1177 1.294
    1193 2.16
    1207 2.98
    1217 3.85
    1221 4.77
    1200 6.02
    1129 7.51
    1045 9.03
    944 10.60
    829 12.00];

 stress = A(:,1); 
 strain = A(:,2)/100; 
 plot(strain,stress)

I was thinking about trying to do something like "find the first place where the gradient switches from positive to negative"... but my real-world data isn't strictly increasing since there's errors in measurements.

I almost feel like I'm thinking too hard about it and there might be a completely different way that's more efficient...

Anyone have an idea?