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%% Assess Significance of Regression Coefficients Using t-statistic % This example shows how to test for the significance of the regression % coefficients using t-statistic. % Copyright 2015 The MathWorks, Inc. %% % Load the sample data and fit the linear regression model. load hald mdl = fitlm(ingredients,heat) %% % You can see that for each coefficient, |tStat = Estimate/SE|. The $p$-values % for the hypotheses tests are in the |pValue| column. Each $t$-statistic % tests for the significance of each term given other terms in the model. % According to these results, none of the coefficients seem significant % at the 5% significance level, although the R-squared value for the model % is really high at 0.97. This often indicates possible multicollinearity % among the predictor variables. %% % Use stepwise regression to decide which variables to include in the model. load hald mdl = stepwiselm(ingredients,heat) %% % In this example, |stepwiselm| starts with the constant model (default) % and uses forward selection to incrementally add |x4| and |x1|. Each predictor % variable in the final model is significant given the other one is in the % model. The algorithm stops when adding none of the other predictor variables % significantly improves in the model. For details on stepwise regression, % see |stepwiselm|.