What is the function of residual plots in multiple linear regression models, and how are they interpreted?

Residual plots in multiple linear regression models are used to validate model assumptions and detect possible issues such as heteroscedasticity or nonlinearity. These graphs show the discrepancies between observed and expected values (residues) vs independent variables or predicted values. A randomly distributed plot indicates that the model's assumptions have been satisfied. However, patterns or trends in the plot suggest breaches of assumptions, prompting more study or model modification. Nonlinearity, for example, can be represented by a curved pattern, but heteroscedasticity is represented by a widening or narrowing spread of residuals.
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