Lecture 40: Example 2 Beta hedge's problem

Hello, In Lecture 40, Example 2 Beta hedge, notebook shows the residual equation is

$r_{resid,i}=r_i-\beta*r_i$

In my opinion, the residual equation should be written like

$r_{resid,i}=r_i-\beta*r_m$

because the [CAPM](https://financeformulas.net/Capital-Asset-Pricing-Model.html)'s equation is

$r_i=r_f+\beta*(r_m-r_f)$ or

$r_i=\alpha+\beta*(r_m-r_f)+\epsilon$

if I want to cancel the market risk, I can minus $\beta*(r_m-r_f)$ or $\beta*r_m$ . Can someone please explain what I misunderstood?

Thank you

quantopian / research_public