In linear regression, what needs to be normally distributed for the model to meet its assumptions?

In linear regression, one of the key assumptions is that the residuals, which are the differences between the observed values and the values predicted by the model, need to be normally distributed. This assumption is critical because it ensures that the statistical tests relying on the linear regression model (such as hypothesis tests for coefficients) will yield valid results.

When the residuals are normally distributed, it indicates that the model properly captures the relationship between the dependent and independent variables without significant bias. If the residuals are not normally distributed, it suggests that there may be issues with the model, such as omitted variable bias, incorrect functional form, or the presence of outliers, all of which can affect the validity of the regression results.

In contrast, while the independent and dependent variables themselves can have any distribution, it's primarily the residuals that need to adhere to normality for the reliability of inference in linear regression. This distinction is crucial for understanding the assumptions underlying the model and correctly interpreting the results obtained from regression analysis.