47 Exercises which assumption fails

This video teaches how to diagnose violations of key OLS assumptions by carefully examining graphical patterns in the data. Framed as a game called “Which Assumption Failed?”, it walks through four common problems using intuitive visual clues rather than heavy mathematics. First, a funnel-shaped residual plot reveals heteroscedasticity, where error variance changes with the level of 𝑥, leading to unreliable standard errors. Second, a clear trend between 𝑥 and residuals signals a violation of the zero conditional mean assumption, producing biased OLS estimates, often due to omitted variables or misspecification. Third, a strong linear relationship between two regressors highlights perfect (or near-perfect) collinearity, causing unstable and imprecise coefficient estimates. Finally, patterned residuals over time illustrate serial correlation in time series data, which creates misleading statistical confidence. Overall, the video emphasizes that visual inspection of residual and variable plots is a powerful tool for identifying assumption failures and understanding their consequences for estimation and inference.