What are the assumptions of linear regression?

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Linear regression relies on several key assumptions to produce valid and reliable results. These assumptions ensure the model’s predictions and statistical inferences are accurate:

1. Linearity: The relationship between the independent variables (predictors) and the dependent variable (response) is linear. This means the effect of the predictors on the outcome is additive and proportional.

2. Independence: The residuals (errors) are independent of each other. This means observations should not be correlated, which is especially important in time series data where autocorrelation can violate this assumption.

3. Homoscedasticity: The residuals have constant variance across all levels of the independent variables. If the variance of errors changes (i.e., heteroscedasticity), it can lead to inefficient estimates and biased standard errors.

4. Normality of Errors: The residuals should be approximately normally distributed, particularly important when constructing confidence intervals or conducting hypothesis tests.

5. No Multicollinearity: Independent variables should not be highly correlated with each other. High multicollinearity can make it difficult to determine the effect of each predictor and can inflate the variance of coefficient estimates.

6. No Autocorrelation: Especially relevant in time series data, this assumes that residuals are not correlated with each other over time.

Violating these assumptions can lead to biased estimates, unreliable predictions, and invalid statistical tests. Diagnostic tools like residual plots, variance inflation factors (VIF), and the Durbin-Watson test help detect assumption violations.

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