Linear extrapolation and standard deviation At $t = 1$, I have $y_1 = 4$ with the corresponding standard deviation $0.08$, and at $t = 3$, I have $y_2 = 9$ with the standard deviation $0.09$.
I want to obtain the value of $y$ at $t = 8$. We assume linear extrapolation works: one obtains first the slope of the line and then construct it and read off the $y$ value for $t = 8$.
My question is: How can one obtain also the corresponding standard deviation?

If you are willing to assume a linear model of the standard deviation, the approach is the same as modeling the "value".
You have two points: $(1, 0.08)$ and $(9, 0.09)$. Calculate the line between these two points using the standard methods from algebra that you applied to calculating the line between the "values". Then use this line to predict the standard deviation.
When you have multiple points, you can apply the usual methods of regression, with ordinary least squares (OLS) being among the easiest and most common approaches. OLS can be used to model both the "value" and the standard deviation.
