What assumption is NOT typically associated with linear regression?

In the context of linear regression, the assumption that is not typically associated with the model is the random distribution of dependent variables. Linear regression primarily focuses on establishing a relationship between independent and dependent variables. The key assumptions related to linear regression include:

1. Linearity of relationships: This assumption states that the relationship between the independent and dependent variables should be linear. It implies that changes in the independent variable(s) will result in proportional changes in the dependent variable.

2. Independence of observations: This assumption ensures that the observations are independent of one another. In practical terms, one observation should not affect another, which is crucial for accurate statistical inference.

3. Homogeneity of variances: Also known as homoscedasticity, this assumption indicates that the variance of the residuals (errors) should be constant across all levels of the independent variable. When the variances vary (heteroscedasticity), it can impact the efficiency of the estimates and the validity of hypothesis tests.

The notion of a random distribution of dependent variables does not align with these foundational assumptions. In linear regression, we aim to understand how the dependent variable behaves in relation to the independent variables, and while certain distributions of residuals are expected