[MINI] Heteroskedasticity

Linearity Issues

The pitfalls of assuming linearity in statistical models are highlighted through a discussion on income and traffic tickets. Linh Tran and Kyle Polich examine a graph depicting the relationship between average household income and the number of traffic tickets issued. Linh points out that the graph's linear assumption may not accurately represent the data, as it overlooks the potential for non-linear relationships.

This makes a linear assumption. It assumes that the right model to describe this is that as income goes up, that the chances you'll get a ticket goes down.

--- Linh Tran

Kyle agrees, noting that the graph's creator likely used ordinary least squares regression, which biases towards the densest areas of data 1.

   

Underfitting Risks

Underfitting in model predictions is a significant risk when assuming linearity. Linh and Kyle discuss how a linear model consistently underpredicts high incomes above $85,000 and fails to capture incomes below $40,000. This suggests that a linear fit may not be the best choice for this data set.

This model consistently under predicts for all high incomes.

--- Linh Tran

The conversation underscores the importance of selecting appropriate models to avoid underfitting and ensure accurate predictions 2.