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Is the error term in regression normally distributed?
In the very simplest case of linear regression if your model is y=Xβ+ϵ then the only stochastic component in your model is the error term. As such it determines the sampling distribution of y.
Does the error term have to be normally distributed?
OLS Assumption 7: The error term is normally distributed (optional) OLS does not require that the error term follows a normal distribution to produce unbiased estimates with the minimum variance. If the residuals follow the straight line on this type of graph, they are normally distributed.
What does it mean if errors are not normally distributed?
When the residuals are not normally distributed, then the hypothesis that they are a random dataset, takes the value NO. This means that in that case your (regression) model does not explain all trends in the dataset.
When is the condition of normality of the OLS residuals not?
The condition of normality of the residuals is useful when residuals are also homoskedastic. The result is then that OLS has the smallest variance between all of the estimator (linear OR non-linear). The extended OLS assumptions: $E(u|X_i = x) = 0$. $(X_i,Y_i), i=1,…,n,$ are i.i.d. Large outliers are rare. u is homoskedastic.
What are the assumptions for linear OLS regression?
In order to present the context for non-normality it may help to review the assumptions for linear OLS regression, which are: Weak exogeneity. This essentially means that the predictor variables, x, can be treated as fixed values, rather than random variables.
How is serial correlation used in the presence of lagged dependent variables?
Serial correlation in the presence of lagged dependent variables A case of particular interest, even in the con- text of simple yon xregression, is that where the \\explanatory variable” is a lagged depen- dent variable. the lagged value of the dependent variable.
What is the relationship between error terms and regressors?
Bayesian linear regression is a general way of handling this issue. The statistical relationship between the error terms and the regressors plays an important role in determining whether an estimation procedure has desirable sampling properties such as being unbiased and consistent.