This lecture by the instructor covers the essential regression diagnostics for linear models. It explains the assumptions to check for, including linearity, homoskedasticity, Gaussian distribution, and independent errors. The lecture details how to check these assumptions using residuals, standardised residuals, and various plots. It emphasizes the importance of identifying outliers, influential observations, and covariates left out of the model. Additionally, it discusses how to assess linearity, homoskedasticity, normality, and independence through graphical methods. The lecture concludes with a summary of diagnostic plots commonly used in regression analysis.