# Confidence in linear regression results

I have two sequences of x and y values x[1]...x[n] y[1]...y[n]. I know that for some k and j, y[t]=mX[t]+b when k<t<j (m and b are unknown). That is, y is linearly dependent on x for some subsequence. My goal is to find the subsequence that is most likely to have that linear relation. Obviously, finding a subsequence of length 2 is meaningless.

I was thinking about using a t-test, but I'm far from an expert. What would you do?

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