Calculation of Beta

Hello Mr Moffat
Hope you are fine and thank you for your nice lectures.
I am just wondering how Beta is calculated.
It it correct?

We have to find the return of an stock as well as the return of the index for a specific period (say last year)

Then draw the plotted diagram and calculate regression line.(from what we learnt in F2). X axis is the return of index, Y axis is the return of stock. Now beta is the slope of regression line. Yes?

My only question is that should we deduct risk free rate from the return of stock and index and then calculate regression of them or there is no need to deduct risk free rate?

Thank you in advance Sir. I know it must be out of syllabus. Its just for better understanding.