This presentation contains a new system of estimation, starting with correlation coefficients, that rivals least squares and for much data does better. One example of SAT and ACT data is used to illustrate minimization through the Correlation Estimation System (CES) in a two-variable linear regression; in this example the CES results give a better representation of the meaning of the data. All the regression model parameters, including variation and location, are estimated by this general CES process. The results from this example are completely typical; the example was not cherry-picked. If you are a least squares-bible toting statistician then what you see in this presentation is blasphemy, but if you are a more secular statistician then you may appreciate a rival estimation system that should be widely used.
The attached file (below) is the R program for five correlation coefficients and an explanation of use. It includes setup for linear regression and population values.
© 2014 Rudy Gideon
Gideon, Rudy, "THE MINIMIZATION PROCESS IN THE CORRELATION ESTIMATION SYSTEM (CES) COMPARED TO LEAST SQUARES IN LINEAR REGRESSION" (2014). Mathematical Sciences Faculty Publications. 6.