Which of the following is an assumption of linear regression?

The assumption that the errors are normally distributed is fundamental to the validity of linear regression analysis. This means that the residuals, which are the differences between the observed values and the predicted values from the regression model, should follow a normal distribution. This assumption is important because many inferential statistics related to regression, such as hypothesis tests and confidence intervals regarding the model parameters, rely on this normality. If the errors are not normally distributed, it can affect the accuracy and reliability of the regression coefficients and the conclusions drawn from them.

The other options do not reflect essential assumptions of linear regression. For example, varied sample sizes are not a requirement for linear regression analysis, as regression analysis can be performed with different sample sizes, provided the data meets other important assumptions like homoscedasticity and independence. Additionally, while outliers can significantly influence the results of regression analysis, a linear regression model does not inherently depend on outliers to be effective; rather, the presence of outliers can distort findings and should typically be examined as part of the analysis process. Lastly, linear regression is designed to handle continuous variables and can include categorical variables through techniques like dummy coding; thus, stating that all variables must be categorical is incorrect.