Just getting this out there; I'll try to fill in some explanations soon.

m = {{N\sum{xy} - \sum{x}\sum{y}}\over{N\sum{x^2}-(\sum{x})^2}}

b = {{\sum{x^2}\sum{y} - \sum{x}\sum{y}}\over{N\sum{x^2}-(\sum{x})^2}}

d = {\sum_{i=1}^N({y_i - mx_i -b})^2}

\sigma_m = {\sqrt{\left|{{d \times N}\over{(N\sum{x^2}-(\sum{x})^2) \times (N-2)}}\right|}}

\sigma_b = {\sqrt{\left|{{d \times {\sum{}x^2}}\over{(N\sum{x^2}-(\sum{x})^2) \times (N-2)}}\right|}}

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