I need a simple clarification on how one line turns into the next, and what the general rule is. Help would be much appreciated. This is in relation to a proof for an expression of sum of squared errors of prediction (SSE).
$$ \sum_i \mathrm{Var}[Y_i - \overline Y - b_1(X_i - \overline X)]$$
$$ \sum_i [\mathrm{Var}(Y_i - \overline Y) - 2\mathrm{Cov}(Y_i - \overline Y, b_1(X_i - \overline X)) + (X_i - \overline X)^2\mathrm{Var}(b_1)]$$
Hint 1:
$$ \mathbb{V}[X+Y] = \mathbb{V}[X] + \mathbb{V}[Y] + 2\mathrm{Cov}(X,Y) $$
if $X$ and $Y$ are two correlated random variables.
Hint 2:
$$ \mathbb{V}[a X] = a^2 \mathbb{V}[X] $$
if $a$ is a constant.
remains for you to find to what $X$ and $Y$ here correspond in your case (last hint, it's not $X_i$ and $Y_i$).