As a concrete example, I have four points:
x | y
---+------
1 | 1854
2 | 2174
3 | 2258
4 | 2953
The best linear fit for these four points is f(x) = 338.1x + 1464.5 with R² = 0.889467.
Knowing that, I can predict f(5) = 3155.0, but can I use f and R² to determine an error or standard deviation function σ(x) on f(x), e.g. f(5) = 3155.0 ± σ(5)? I guess the farther out you go from the known data, the larger σ(x) will be.