Log-likelihood is calculated under the assumption that errors follow normal distribution. Even though the assumption is not very reasonable, this statistic may still find its use in conducting LR tests. Durbin–Watson statistic tests whether there is any evidence of serial correlation between the residuals. As a rule of thumb, the value smaller than 2 will be an evidence of positive correlation. Akaike information criterion and Schwarz criterion are both used for model selection. Generally when comparing two alternative models, smaller values of one of these criteria will indicate a better model. Standard error of regression is an estimate of σ, standard error of the error term. Total sum of squares, model sum of squared, and residual sum of squares tell us how much of the initial variation in the sample were explained by the regression. F-statistic tries to test the hypothesis that all coefficients (except the intercept) are equal to zero. This statistic has F(p–1,n–p) distribution under the null hypothesis and normality assumption, and its p-value indicates probability that the hypothesis is indeed true. Note that when errors are not normal this statistic becomes invalid, and other tests such as Wald test or LR test should be used. Ordinary least squares analysis often includes the use of diagnostic plots designed to detect departures of the data from the assumed form of the model. These are some of the common diagnostic plots: Residuals against the explanatory variables in the model. A non-linear relation between these variables suggests that the linearity of the conditional mean function may not hold. Different levels of variability in the residuals for different levels of the explanatory variables suggests possible heteroscedasticity. Residuals against explanatory variables not in the model. Any relation of the residuals to these variables would suggest considering these variables for inclusion in the model. Residuals against the fitted values, . Residuals against the preceding residual. This plot may identify serial correlations in the residuals. An important consideration when carrying out statistical inference using regression models is how the data were sampled. In this example, the data are averages rather than measurements on individual women. The fit of the model is very good, but this does not imply that the weight of an individual woman can be predicted with high accuracy based only on her height. Sensitivity to rounding This example also demonstrates that coefficients determined by these calculations are sensitive to how the data