X Weight,Horsepower,Acceleration; Fit a linear regression model by using fitlm.The model formula in the display, y 1 x1 x2 x3, corresponds to y 0 1 X 1 2 X 2 3 X 3.The model display also shows the estimated coefficient information, which is stored in the Coefficients property.Display the Coefficients property.
![]() ![]() Value p -value for the t -statistic of the hypothesis test that the corresponding coefficient is equal to zero or not. For example, the p -value of the t -statistic for x2 is greater than 0.05, so this term is not significant at the 5 significance level given the other terms in the model. The summary statistics of the model are: Number of observations Number of rows without any NaN values. For example, Number of observations is 93 because the MPG data vector has six NaN values and the Horsepower data vector has one NaN value for a different observation, where the number of rows in X and MPG is 100. Error degrees of freedom n p, where n is the number of observations, and p is the number of coefficients in the model, including the intercept. For example, the model has four predictors, so the Error degrees of freedom is 93 4 89. Root mean squared error Square root of the mean squared error, which estimates the standard deviation of the error distribution. R-squared and Adjusted R-squared Coefficient of determination and adjusted coefficient of determination, respectively. For example, the R-squared value suggests that the model explains approximately 75 of the variability in the response variable MPG. F-statistic vs. constant model Test statistic for the F -test on the regression model, which tests whether the model fits significantly better than a degenerate model consisting of only a constant term. For example, the model is significant with a p -value of 7.3816e-27. You can find these statistics in the model properties ( NumObservations, DFE, RMSE, and Rsquared ) and by using the anova function. For example, lm2 fitlm(tbl, linear ); If you use a character vector for model specification and you do not specify the response variable, then fitlm accepts the last variable in tbl as the response variable and the other variables as the predictor variables. Fit Linear Regression Using Specified Model Formula Open Live Script Fit a linear regression model using a model formula specified by Wilkinson notation. Remove Acceleration from the model, and try improving the model by adding the predictor variable ModelYear. First define ModelYear as a categorical variable. ModelYear categorical(tbl.ModelYear). It also creates the necessary two dummy indicator variables for the categorical variable ModelYear. Fit Linear Regression Using Terms Matrix Open Live Script Fit a linear regression model using a terms matrix. Terms Matrix for Table Input If the model variables are in a table, then a column of 0 s in a terms matrix represents the position of the response variable. The response variable is in the second column of the table, so the second column of the terms matrix must be a column of 0 s for the response variable. Load the carsmall data set and define the matrix of predictors.
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