Discuss the role of the error term in a regression model.

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Role of the error term in a regression model:

An error term refers to a variable in a mathematical or statistical model, which is created when the model is incapable in full representation of the actual relationship among the independent variables and the dependent variables. Due to the incomplete relationship, the error term is termed to be the amount at which the equation may differ during empirical analysis. We need the error term in a regression model because these are based on samples not populations. These sample estimators usually aren't closer to the mean of population. To account for this, an error term is incorporated. Furthermore we are not modelling the dependent variable as a function of all the variables due to limitations in the data. Moreover models are simplifications of reality and, thus aren't right.

The error term displays the combined effect of the omitted variables, on an assumption that:

(i) the combined effect of the omitted variables is independent of each variable that are inclusive in the equation,

(ii) the combined effect of the omitted variables has an expectation zero.

(iii) the combined effect of the omitted variables across the subjects is independent

Rahul Sunny answered 1 year ago

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