OLS regression
The OLS (ordinary least square) regression is described in Simple linear regression model. We’ll call this regression the -on- regression since we are using a value for to predict a value for .
Issues with -on- regression
- The regression-to-the-mean phenomenon means that the equation of the -on- regression is a biased estimate of the true functional relationship between and . Specifically, the the absolute value of the slope of the -on- regression is smaller than the absolute value of the slope of the true relationship between and .
- The -on- regression is not symmetric. Specifically, if you solve in terms of in the -on- regression, you do not end up with the -on- regression.
- If you plot the -on- and -on- regressions in the same plane, both regression lines go through the data centroid , but the slope of the -on- regression line is greater than or equal to the slope of the -on- regression line.
Reference
Simple linear regression model, https://functor.network/user/1751/entry/653