How do I calculate the error $(\triangle) \space$of coefficients $a, b $ from $$ y = a + bx $$ if $$ \triangle y = \sqrt{\frac{1}{(n-2)} \sum_{i= 1}^n {(y_i - a - bx_i )^2}} $$

using the least squares method.

I have the answers from my textbook, but I'd still like to understand how they are found $$\triangle a= \triangle y\sqrt{\frac{\sum_{i= 1}^n {x_i^2}}{n\sum_{i= 1}^n{(x_i -\widetilde{x})^2}}{}}$$

$$\triangle b= \triangle y\sqrt{\frac{1}{\sum_{i= 1}^n{(x_i -\widetilde{x})^2}}{}}$$


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