Editing Least squares (section)

==Limitations==
This regression formulation considers only observational errors in the dependent variable (but the alternative [[total least squares]] regression can account for errors in both variables). There are two rather different contexts with different implications:

*Regression for prediction. Here a model is fitted to provide a prediction rule for application in a similar situation to which the data used for fitting apply. Here the dependent variables corresponding to such future application would be subject to the same types of observation error as those in the data used for fitting. It is therefore logically consistent to use the least-squares prediction rule for such data.
*Regression for fitting a "true relationship". In standard [[regression analysis]] that leads to fitting by least squares there is an implicit assumption that errors in the [[independent variable]] are zero or strictly controlled so as to be negligible. When errors in the [[independent variable]] are non-negligible, [[Errors-in-variables models|models of measurement error]] can be used; such methods can lead to [[parameter estimation|parameter estimates]], [[hypothesis testing]] and [[confidence interval]]s that take into account the presence of observation errors in the independent variables.<ref>For a good introduction to error-in-variables, please see {{cite book |last=Fuller |first=W. A. |author-link=Wayne Fuller |title=Measurement Error Models |publisher=John Wiley & Sons |year=1987 |isbn=978-0-471-86187-4 }}</ref> An alternative approach is to fit a model by [[total least squares]]; this can be viewed as taking a pragmatic approach to balancing the effects of the different sources of error in formulating an objective function for use in model-fitting.