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Post regression analysis has its own importance in econometrics. It involves using various plots and tests to check the validity and reliability of the regression model. Some of the common post regression analysis tools are residual plots, influence plots, VIF, R-squared, and p-values.
How would you interpret the residual plot, if residuals of regression are scattered and variance of residuals are non-constant and what would you do if you find outliers and non-constant variance in it.
If the residuals of a regression model are scattered and the variance of the residuals is non-constant, this indicates the presence of heteroscedasticity. Heteroscedasticity means that the spread or dispersion of the residuals is not the same across all levels of the independent variables.
Interpreting a residual plot with heteroscedasticity involves observing the pattern of the residuals. Typically, you would notice that the scatter of the residuals widens or narrows as you move along the predicted values of the dependent variable. This pattern can take different forms, such as a cone shape, a fan shape, or an irregular pattern.
When encountering heteroscedasticity, there are several steps you can take:
Try to identify the potential reasons for heteroscedasticity. It can be caused by omitted variables, model misspecification, or the nature of the data itself.
If you identify a specific independent variable that is causing heteroscedasticity, you can try transforming it. Common transformations include taking logarithms, square roots, or reciprocals of the variable.
If the heteroscedasticity is not easily addressed through variable transformation, you can consider using weighted least squares (WLS) regression. WLS assigns different weights to observations based on their estimated variances, giving more weight to observations with lower variance. This method can help mitigate the impact of heteroscedasticity on the regression results.
Another option is to calculate robust standard errors, which provide adjusted standard errors that take into account the presence of heteroscedasticity. Robust standard errors allow for valid hypothesis testing and confidence interval estimation even in the presence of heteroscedasticity.
In some cases, heteroscedasticity may indicate the need for a nonlinear regression model. Exploring nonlinear relationships between the dependent and independent variables might help capture the varying spread of the residuals.
Regarding outliers in the residual plot, you should investigate them further. Outliers can have a significant impact on the regression results and should not be ignored. It is important to understand the reasons behind their occurrence and assess whether they are influential observations that can affect the model's overall fit. You may consider removing outliers if they are data entry errors or extreme values that do not reflect the underlying relationship.
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