What to choose for the distribution of $x$ to estimate $f(x)$ as linear

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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?