When a Regressor is correlated with the error term then?

If the independent variable is correlated with the error term in a regression model then the estimate of the regression coefficient in an ordinary least squares (OLS) regression is biased; however if the correlation is not contemporaneous, then the coefficient estimate may still be consistent.

What assumptions must be met if one wants to use ordinary least squares regression OLS )?

Assumptions of OLS Regression

• OLS Assumption 1: The linear regression model is “linear in parameters.”
• OLS Assumption 2: There is a random sampling of observations.
• OLS Assumption 3: The conditional mean should be zero.
• OLS Assumption 4: There is no multi-collinearity (or perfect collinearity).

Why might a variable be correlated with the error term?

If an independent variable is correlated with the error term, we can use the independent variable to predict the error term, which violates the notion that the error term represents unpredictable random error. We need to find a way to incorporate that information into the regression model itself.

What are the consequences of using OLS in the presence of heteroscedasticity?

Heteroskedasticity has serious consequences for the OLS estimator. Although the OLS estimator remains unbiased, the estimated SE is wrong. Because of this, confidence intervals and hypotheses tests cannot be relied on. In addition, the OLS estimator is no longer BLUE.

What assumptions do you make when using the method of least squares to estimate a population regression line?

Assumptions for Ordinary Least Squares Regression

• Your model should have linear parameters.
• Your data should be a random sample from the population.
• The independent variables should not be strongly collinear.
• The residuals’ expected value is zero.
• The residuals have homogeneous variance.

Is error term correlated with dependent variable?

The error term accounts for the variation in the dependent variable that the independent variables do not explain. Random chance should determine the values of the error term. For your model to be unbiased, the average value of the error term must equal zero.