I have to estimate $y = f(x)$ as a linear function of $x$ on a given range.
I can measure $y$ for as many $x$ values as I want. Each measure has its own measurement error. Assuming this error is random.
How should I choose the distribution of the $x$? Normal distribution? Uniform distribution?
My guess is that with Uniform distribution, the measures of $y$ for the $x$ close to both edges of the range will have more weight than the ones in the middle.
That's why I'm guessing normal distribution of $x$ should be better.
Is that true?
Any pointers to literature on this matter?