Assumptions of Ordinary Least Squares Regression

Flashcards based on the assumptions and key concepts of Ordinary Least Squares Regression, including definitions and explanations of important terms.

Ordinary Least Squares (OLS) Regression

A statistical method used to estimate the parameters in a linear regression model.

Linearity in parameters

The model is linear in the parameters, meaning that the relationship between the independent and dependent variables can be expressed as a linear equation.

Independence of errors

The errors (residuals) are statistically independent from each other, meaning that the error term for one observation does not depend on the error term for another.

Expected value of errors

The expected value of the errors is always zero, indicating that the model does not systematically over or underestimate the dependent variable.

Collinearity

The condition where independent variables are highly correlated with each other, which can inflate the standard errors of the estimated coefficients.

Measurement error

The discrepancy between the true value and the measured value of the independent variables, which leads to biased parameter estimates.

Heteroskedasticity

The presence of non-constant variance in the errors (residuals), which can affect the reliability of statistical tests.

Normal distribution of errors

The assumption that the errors are normally distributed, which is important for hypothesis testing using t and F tests.

Generalized Least Squares (GLS)

A statistical technique that accounts for certain types of error correlation in the model to improve parameter estimation.

Partial residual plots

Graphical tools used to identify nonlinearity in the relationships between the independent variables and the dependent variable.

Transformation of variables

A process of applying a mathematical function to independent or dependent variables to stabilize variance or make relationships more linear.