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%% Assess Fit of Model Using F-statistic % This example shows how to use assess the fit of the model and the significance % of the regression coefficients using F-statistic. % Copyright 2015 The MathWorks, Inc. %% % Load the sample data. load carbig tbl = table(Acceleration,Cylinders,Weight,MPG); tbl.Cylinders = ordinal(Cylinders); %% % Fit a linear regression model. mdl = fitlm(tbl,'MPG~Acceleration*Weight+Cylinders+Weight^2') %% % The F-statistic of the linear fit versus the constant model is 139, with % a _p_-value of 2.94e-109. The model is significant at the 5% significance % level. The R-squared value of 0.741 means the model explains about 74% % of the variability in the response. %% % Display the ANOVA table for the fitted model. anova(mdl,'summary') %% % This display separates the variability in the model into linear and nonlinear % terms. Since there are two non-linear terms (|Weight^2| and the interaction % between |Weight| and |Acceleration|), the nonlinear degrees of freedom % in the |DF| column is 2. There are six linear terms in the model (four % |Cylinders| indicator variables, |Weight|, and |Acceleration|). The corresponding % F-statistics in the |F| column are for testing the significance of the % linear and nonlinear terms as separate groups. %% % The residual term is also separated into two parts; first is the error % due to the lack of fit, and second is the pure error independent from % the model, obtained from the replicated observations. The corresponding % F-statistics in the |F| column are for testing the lack of fit, that is, % whether the proposed model is an adequate fit or not. %% % Display the ANOVA table for the model terms. anova(mdl) %% % This display decomposes the ANOVA table into the model terms. The corresponding % F-statistics in the |F| column are for assessing the statistical significance % of each term. The F-test for |Cylinders| test whether at least one of % the coefficients of indicator variables for cylinders categories is different % from zero or not. That is, whether different numbers of cylinders have % a significant effect on |MPG| or not. The degrees of freedom for each % model term is the numerator degrees of freedom for the corresponding F-test. % Most of the terms have 1 degree of freedom, but the degrees of freedom % for |Cylinders| is 4. Because there are four indicator variables for this % term.