What are the assumptions of linear regression?

What are the assumptions of linear regression?

What are the assumptions of linear regression?

Answer: "Linear regression relies on several assumptions to ensure that the model produces accurate, reliable, and interpretable results. These assumptions help guarantee that the estimates of the regression coefficients are unbiased and efficient. The key assumptions of linear regression are:

1. Linearity:

• The relationship between the independent variables (predictors) and the dependent variable (outcome) is assumed to be linear. This means that the effect of the predictors on the dependent variable is constant, and the regression line is the best fit for the data.

2. Independence of Errors:

• The residuals (errors), or the differences between the observed and predicted values, should be independent of each other. In other words, the error for one observation should not influence the error for another. This assumption is crucial, especially in time series data, to avoid autocorrelation (where errors are correlated over time).

3. Homoscedasticity (Constant Variance of Errors):

• The residuals should have constant variance across all levels of the independent variables. This means that the spread of residuals should be the same across the range of predicted values. If the variance of the residuals changes at different levels of the independent variables (a condition called heteroscedasticity), it can lead to inefficient estimates and unreliable hypothesis tests.

4. No Multicollinearity:

• There should be no perfect multicollinearity between the independent variables, meaning that the predictors should not be too highly correlated with each other. High multicollinearity can make it difficult to determine the individual effect of each predictor and can lead to unstable estimates of regression coefficients. Multicollinearity can be detected using measures like the Variance Inflation Factor (VIF).

5. Normality of Errors:

• The residuals (errors) should be normally distributed. This assumption is particularly important for making valid inferences about the regression coefficients, such as confidence intervals and hypothesis tests. If the residuals deviate significantly from normality, the conclusions drawn from the model might be inaccurate.

6. No Endogeneity:

• The independent variables should be exogenous, meaning they are not correlated with the residuals. If any of the predictors are correlated with the errors, this would lead to endogeneity, which causes biased and inconsistent coefficient estimates. Endogeneity can result from omitted variables, measurement errors, or reverse causality.

Conclusion:

These assumptions are critical for the proper application of linear regression. Violating these assumptions can lead to biased estimates, invalid inferences, or inefficient models. Therefore, it's important to check for violations using diagnostic tools such as residual plots, tests for multicollinearity, and normality checks before interpreting the results of a linear regression model."