When fitting an OLS regression model, it may become apparent that there is an inconsistent variance in the residuals, which is known as heteroscedasticity. This is a violation of one of the Gauss Markov assumptions, and therefore OLS is no longer the Best Linear Unbiased Estimator (BLUE). An OLS model in such circumstances is still expected to be unbiased and consistent, however it will not be the most efficient. More concerning is that OLS is likely to yield biased estimates of the standard errors of the coefficients, making statistical interference unreliable. This article introduces Weighted Least Squares regression which is an appropriate model in such circumstances.
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Regression analysis is a statistical technique used to fit a model expressed in terms of one or more variables to some data. There are many types of regression analysis techniques, however one of the most widely used is based on fitting data to a linear model, and using an approach called Least Squares. The Morpheus API currently supports 3 variations of Linear Least Squares regression, namely Ordinary Least Squares (OLS), Weighted Least Squares (WLS) and Generalized Least Squares (GLS). The following article reviews some OLS regression theory and provides an example of how to use the Morpheus API to apply this technique.
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