Linear regression relies on several key assumptions to produce reliable predictions. Here's why option D is correct:

• A. The observations are dependent on each other. (Incorrect) Linear regression assumes that observations are independent, meaning the outcome of one does not affect another.
• B. The relationship between the independent and dependent variables is non-linear. (Incorrect) The model assumes a linear relationship, where changes in the independent variable(s) proportionally affect the dependent variable.
• C. The variance of the errors is not constant. (Incorrect) The assumption of homoscedasticity requires that the error variance remains constant across all levels of the independent variable(s).
• D. The errors are normally distributed. (Correct) This assumption is vital for conducting statistical tests and interpreting the confidence intervals of the model's coefficients accurately.

Understanding these assumptions helps in assessing the appropriateness of linear regression for your data and in interpreting the results more effectively. For more details, refer to Databricks documentation.