Regression and ANOVA does not stop when the model is fit. You should examine residual plots and other diagnostic statistics to determine whether your model is adequate and the assumptions of regression are met. If your model is not adequate, it will incorrectly represent your data. For example:

- The standard errors of the coefficients might be biased, leading to incorrect t- and p-values.
- Coefficients can have the wrong sign.
- The model can be affected by one or two points.

Use the following table to determine whether your model is adequate.

Characteristics of an adequate regression model | Check using | Possible solutions |
---|---|---|

Functional form accurately models any curvature that is present. |
Lack-of-fit-test Residuals vs variables plot |
Add higher-order term to model Transform variables Nonlinear regression |

Residuals have constant variance. |
Residuals vs fits plot |
Transform variables Weighted least squares |

Residuals are independent of (not correlated with) each other. |
Durbin-Watson statistic Residuals vs order plot |
Add new predictor Use time series analysis Add lag variable |

Residuals are normally distributed. |
Histogram of residuals Normal plot of residuals Residuals vs fit plot Normality test |
Transform variables Check for outliers |

No unusual observations or outliers. |
Residual plots Leverages Cook's distance DFITS |
Transform variables Remove outlying observation |

Data are not ill-conditioned. |
Variance inflation factor (VIF) Correlation matrix of predictors |
Remove predictor Partial least squares regression Transform variables |

If you determine that your model does not meet the previous criteria, you should:

- Determine whether your data are entered correctly, especially observations identified as unusual.
- Try to determine the cause of the problem. You may want to determine how sensitive your model is to the issue. For example, if you have an outlier, do the regression analysis without that observation and determine how the results differ.
- Consider using one of the possible solutions listed earlier.