Python Plotting Tutorial -- Part 8

Fitting data with error bars

Suppose you have data $(x_i,y_i)$, with uncertainties $\sigma_i$ in the y-values. Let
$$U_n = \sum_i \frac{x_i^n}{\sigma^2_i}, \qquad W_n = \sum_i   \frac{y_i  \, x_i^n}{\sigma^2_{i} } ,$$
and let
$$D = U_0 U_2 - U_1^2  .$$
Then the best fit line is given by
$$slope = \frac{U_0 W_1 - U_1 W_0}{D}, \qquad intercept = \frac{U_2 W_0 - U_1 W_1}{D},$$
with uncertainties
$$\sigma_{slope}^2 = \frac{U_0}{D}, \qquad \sigma_{intercept}^2 = \frac{U_2}{D}.$$

As part of your homework, you will write a function which implements this method.