Assumptions of the classical linear regression model

Assumptions of the Classical Linear Regression Model The classical linear regression model assumes several underlying assumptions that ensure the accuracy an...

Assumptions of the Classical Linear Regression Model#

The classical linear regression model assumes several underlying assumptions that ensure the accuracy and reliability of the estimated model. These assumptions help in obtaining a consistent and efficient estimate of the population parameters.

1. Linearity:

The relationship between the dependent and independent variables is linear. This means that the points in the scatter plot tend to form a straight line.

2. Independence:

The observations are independent of each other. This means that the disturbance terms (errors) are randomly scattered across the entire sample, and each observation is affected by the same error term.

3. Normality:

The errors are normally distributed. This means that the mean of the error terms is equal to zero, and the variance is constant.

4. Homoscedasticity:

The error terms have constant variance. This means that the spread of the error terms is the same for all values of the independent variables.

5. No autocorrelation:

The error terms are not correlated with each other. This means that the estimated coefficients are independent of each other.

6. Perfect collinearity:

The independent variables are perfectly correlated. This means that the estimated coefficients are not independent, and the model will be less efficient.

7. Exogeneity:

The independent variables are exogenous, meaning that they are not correlated with the error terms. This assumption is not always tested in practice.

Consequences of non-compliance:

When these assumptions are not met, the classical linear regression model may produce biased or inefficient estimates. It can also lead to misleading results and incorrect conclusions.

By understanding and analyzing these assumptions, we can evaluate the accuracy and reliability of the estimated model and determine whether it can be used for practical decision-making