Working my way through a copy of Draper and Smith's Applied Regression Analysis. I am on the first chapter and looking at the section that involves deriving the OLS equations. No linear algebra has been used yet.
The section I am looking at has started by presenting the sum of squared deviations equation, which has then been differentiated for the intercept and slope parameters and set to 0 to end with the formula for the intercept:
And the slope:
The next step is to substitute $\beta_0$ for $b_0$ and $\beta_1$ for $b_1$ which apparently leads you to:
I really am at a loss in understanding how the authors got from the first two equations to the second two. They say that they simply substituted $β_0$ for $b_0$ and $β_1$ for $b_1$. Not sure how this changes anything. Can anyone explain?