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If I have a linear relation (or wish to prove such a relation): y = k x where k = constant. I have a set of n experimental data points ...(y0, x0), (y1, x1)... measured with some error estimates.

Is there some way to present how well the n data points shows that the relation: y = kx is proven. What I have in mind is that the regression line will give an error intercept of the Y-axis, say e. Say e = 1.0 x 10^-5. What is the "confidence" for this error estimate.

I want to show error e to be very small say <1.0 10^-7. If I the measurement errors of (yi,xi) ... are very small, how will it help to show y=kx to be "very good" where y=k(1+e)x where e is very small.