A journey into the derivation of the parts of Pearson's R
Most students might just want to jump to the 20-minute mark to see the one worked example in this video.
Being old-fashioned, I like to use the standard formulas for variance and standard deviation. The machine formulas provided by the book and used throughout chapter 3 for standard deviation and the rest of regression have only become popular since the days of computers and calculators. While using computer power is fine, it robs the learner of the discovery of what is actually going on.
But one other problem with the machine formulas is that one gets the impression that the heavens opened up one day and like manna from heaven, the machine formulas came upon us. Why are the machine formulas presented as if they were divorced from the older formulas?
This video shows that they are mathematically identical, and even better, that the old formulas can be used to actually derive the machine formulas.
At the end of the video (around the 20-minute mark), we talk about an example taken from the text, solved using the standard formulas, showing that the results are identical to the machine formulas used in the text.