In terms of predictive modeling, how can I calculate the bias and variance in a given model (e.g. simple linear regression)? I know that the bias and variance of an estimator (linear regression model) for a single prediction is:
$Bias(\hat Y)=E \hat Y-Y$
$Var(\hat Y) = E(E\hat Y-\hat Y)^2$
and that the Mean Squared Error can be decomposed into
$MSE = Bias^2 + Var + error$
But these are all theoretical formulas. I can't seem to apply any of these quantities to evaluate my linear regression model. To my understanding, these quantities can only be calculated if I know the true distribution of $\hat Y$ for a given X, which we never do when we are working with real, sampled data. From this question, I learnt that the bias for a single prediction isn't something that you can calculate because you need to know the true distribution of our estimator (model). As for the variance of my estimator, I still don't know whether it can be calculated or not.
Let's say I have $\hat Y = 0.3 + 0.7X$. For X=5, I know that the actual value is $Y=4$, while my estimator/model predicts $\hat Y=3.8$. For this single prediction, can I calculate the variance of my model? My goal is to decompose the MSE for this single prediction into bias and variance.
My question is then, how are these formulas useful for practical applications if we aren't able to quantify them?