Implications of Systematic Residual Patterns in Regression Analysis

Very Hard Multiple Regression Analysis Model Assumptions

A researcher conducted a multiple regression analysis to examine the impact of various economic indicators on GDP growth. The model included three independent variables: consumer spending (X1), business investment (X2), and government expenditure (X3). After running the regression, the researcher checked the assumptions necessary for a valid multiple regression analysis. Among the assumptions considered are linearity, independence of errors, homoscedasticity, and normality of residuals.

Assuming all relevant independent variables have been included in the model, the researcher found that the residuals showed a systematic pattern when plotted against the predicted values. In light of this finding, which of the following statements best describes the implications for the regression model?

The linearity assumption is violated, indicating that a non-linear model may provide a better fit.

The independence of errors assumption is violated, leading to biased parameter estimates.

The homoscedasticity assumption is violated, suggesting that standard errors and hypothesis tests may be unreliable.

Hint

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