Which of the following is not an assumption for simple linear regression?

In the context of simple linear regression, several key assumptions are essential for the validity of the model. The option indicating that the residuals are all greater than 0 is not a valid assumption of this statistical method.

In simple linear regression, residuals are the differences between the observed values and the values predicted by the model. These residuals can take on any value, including negative values, as they represent deviations from the predicted line. Assuming that all residuals are positive would be overly restrictive and not reflective of the nature of variability in data. In fact, one of the reasons for analyzing residuals is to check for their distribution and properties.

On the other hand, the other assumptions—such as the normal distribution of residuals, independence of observations, and constant variance of residuals (homoscedasticity)—are critical for ensuring that the regression analysis provides valid results. Normality of residuals is often checked to confirm that the data fits a linear model well. Independence ensures that each data point contributes uniquely to the model, while constant variance implies that the spread of residuals remains consistent across all levels of the independent variable, which is necessary for reliable predictions. Thus, the requirement that all residuals be greater than 0 does not