![]() ![]() # lm(formula = food_exp ~ income, data = food) One informal way of detecting heteroskedasticity is by creating a residual plot where you plot the least squares residuals against the explanatory variable or \(\hatįirst, let’s check the standard errors of our estimators for our original model. However, one can still use ordinary least squares without correcting for heteroskedasticity because if the sample size is large enough, the variance of the least squares estimator may still be sufficiently small to obtain precise estimates. Most real world data will probably be heteroskedastic. This can affect confidence intervals and hypothesis testing that use those standard errors, which could lead to misleading conclusions. The standard errors computed for the least squares estimators are incorrect.That is, there is another estimator with a smaller variance. The least squares estimator is still a linear and unbiased estimator, but it is no longer best.In the presence of heteroskedasticity, there are two main consequences on the least squares estimators: ![]() Why should we care about heteroskedasticity? Because it is a violation of the ordinary least square assumption that \(var(y_i)=var(e_i)=\sigma^2\). Conversely, when the variance for all observations are equal, we call that homoskedasticity. As mentioned previously, heteroskedasticity occurs when the variance for all observations in a data set are not the same. ![]()
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