Which of the following can be an assumption of linear regression?

• A. Independence of residuals.
• B. Normal distribution of the dependent variable.
• C. Linear relationship between predictors and the dependent variable.
• D. All of the above.

Answer: (D)

In linear regression analysis, several critical assumptions must be met to ensure that the model produces valid and reliable results. One of these key assumptions is the independence of residuals. This means that the errors or residuals should not be correlated with one another, ensuring that each observation contributes uniquely to the prediction.

Another important assumption is that the dependent variable is normally distributed, especially when it comes to the residuals rather than the dependent variable itself, since linear regression focuses on predicting the average outcome. This assumption is crucial for hypothesis testing regarding the regression coefficients.

Additionally, there must be a linear relationship between the predictors (independent variables) and the dependent variable. This ensures that changes in predictor values are associated with proportional changes in the predicted outcome.

By considering all these elements, it's clear that all three are fundamental assumptions of linear regression. Therefore, selecting the option that includes all of these assumptions reflects a comprehensive understanding of linear regression requirements.