# How to find the appropriate fit?

Imagine we are given this set of data:

``data = {{0, 1}, {1, 0}, {3, 2}, {5, 4}, {6, 4}, {7, 5}}; ``

We fit the data with:

``nlm = NonlinearModelFit[data, Log[a + b x^2], {a, b}, x], ``

and we can obtain $$a$$ and $$b$$.

Now, if we are given that the $$y$$ coordinates in the data list have the variance of, for example, $$0.5$$, $$0.3$$, $$1.3$$, $$0.2$$, $$0.9$$, and $$0.7$$, can we use this additional information to improve fitting?