I am trying to find out Historical Alphas of a bunch of fund returns ${F_i}$ by Using Regression Model$(stepwise)$ with regressors as its underlying exposure-returns(risk-free rate subtracted) i.e. $$ \mathrm{E_i = X_i-R_f} $$ $$ \mathrm{F_i} = {a_i + \beta_{1i}E_{1}+\beta_{2i}E_{2}...} $$
Here, I assume that this regression model is representative of a Multi-factor CAPM model and the obtained ${\beta_i}$ are the CAPM-${\beta}$ i.e. systemic risk of ${F_i}$ w.r.t. ${E_i}$.
Then, I use these models to calculate average historical ${\alpha_i}$ which is excess return for fund ${F_i}$ using below formula.
$$ \mathrm{\alpha_i} = avg({F_i - F_i^{estimated})} $$
Is this simplistic approach correct, if not, what is the correct way?