I'm trying to find the uncertainty values for a set of data points' slope and intercept. The values are:
$(0.18751,0.512332), (0.17076, 0.511825), (0.23204,0.513665), (0.20878, 0.512986), (0.17172, 0.511855), (0.19006, 0.512479)$
and the equation for linear regression is $y = 0.03x + 0.5607$, with $R^2$ = $0.99827$.
How do I go about obtaining uncertainty values for the slope and intercept? Is it simply $1 - R^2$?
If you look here, you will find how are computed the confidence intervals for the parameters of a linear regression.
Applied to your data points, this should give (at the level of $95$%) $$\begin{array}{clclclclc} \text{} & \text{Estimate} & \text{Standard Error} & \text{Confidence Interval} \\ a & 0.030023 & 0.000721 & \{0.027728,0.032319\} \\ b & 0.506715 & 0.000140 & \{0.506268,0.507162\} \\ \end{array}$$
