Given only the shown residual plot for a linear regression model, what is the MOST likely issue with the model?
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Correct answer: Linear regression is inappropriate because the residuals do not have constant variance (heteroscedasticity)..
Why this is the answer
The residual plot shows a fanning-out pattern, where the spread of the residuals increases as the predicted values increase. This indicates that the variance of the errors is not constant across all levels of the independent variable, a condition known as heteroscedasticity. Linear regression assumes homoscedasticity (constant variance of residuals) for valid inference. Therefore, the presence of heteroscedasticity suggests that linear regression may be inappropriate or that the model's assumptions are violated, leading to inefficient parameter estimates and incorrect standard errors. While outliers can affect linear regression, the primary and most evident issue from this specific residual plot pattern is heteroscedasticity, not just the presence of outliers. The residuals having a mean of zero is a desirable property but doesn't negate the issue of non-constant variance. The residuals clearly do not exhibit constant variance, making that option incorrect.
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