If you really want to do linear regression by hand, check out Chapter 1 of Stephen Stigler's History of Statistics: https://www.amazon.com/History-Statistics-Me

If you really want to do linear regression by hand, check out Chapter 1 of Stephen Stigler's History of Statistics: https://www.amazon.com/History-Statistics-Measurement-Uncertainty-before/dp/067440341X https://www.amazon.com/History-Statistics-Measurement-Uncert.... You can do least squares on astronomical data the way Legendre did it.