Statistics MCQs, Data Analysis, Stat Software
Lecture notes about Heteroscedasticity, its consequences, detection, and remedy. Hetero or Heteroscedasticity is a violation of the OLS assumption of consistent variance.
The usual Ordinary Least Squares (OLS) method assigns equal weight (or importance) to each observation. But generalized least squares (GLS) take such information into account explicitly and are therefore capable of producing BLUE estimators. Consider following two-variable model, \begin{align}Y_i &= \beta_1 + \beta_2 X_i + u_i\nonumber\\\text{or}\\Y_i &= \beta_1X_{0i} + \beta_2 …
The post is about the White test of heteroscedasticity. One important assumption of Regression is that the variance of the Error Term is constant across observations. If the error has a constant variance, then the errors are called homoscedastic, otherwise heteroscedastic. In the case of heteroscedastic errors (non-constant variance), the …
The Breusch Pagan test (named after Trevor Breusch and Adrian Pagan) is used to check for the presence of heteroscedasticity in a linear regression model. Assume our regression model is $Y_i = \beta_1 + \beta_2 X_{2i} + \mu_i$ i.e we have simple linear regression model, and $E(u_i^2)=\sigma_i^2$, where $\sigma_i^2=f(\alpha_1 + …
The following are some key points about heteroscedasticity. These key points are about the definition, example, properties, assumptions, and tests for the detection of heteroscedasticity (detection of hetero in short). One important assumption of Regression is that the One important assumption of Regression is that the variance of the Error …