If you need to investigate a fitted regression model further, create a linear regression model object LinearModel by using fitlm or stepwiselm. This function can form an X matrix with predictor values, their squares, their cubes, and so on. regress is useful when you simply need the output arguments of the function and when you want to repeat fitting a model multiple times in a loop. In problems with just a single predictor, it is simpler to use the polytool function (see The polytool Demo). The first observation is an outlier since its error bar does not cross the zero reference line. The 95% confidence intervals about these residuals are plotted as error bars.
The plot shows the residuals plotted in case order (by row). The F statistic of about 12 and its p-value of 0.0001 indicate that it is highly unlikely that all of the regression coefficients are zero. R 2 is 0.8107 indicating the model accounts for over 80% of the variability in the observations. The elements of the vector stats are the regression R 2 statistic, the F statistic (for the hypothesis test that all the regression coefficients are zero), and the p-value associated with this F statistic. The y-intercept is b (1), which corresponds to the column index of the column of ones. The column of ones is necessary for estimating the y-intercept of the linear model. Lets assume for the sake of argument that the 250th row of X is in fact a new data point. You have a new data point you would like to evaluate using the computed fit.
#MATLAB POLYTOOL REGRESS HOW TO#
Matrix X has a column of ones, and then one column of values for each of the five predictor variables. How to Use the Outputs regMultiPolyRegress(X,Y,2) PowerMatrix. The data set (originally from Moore (1975)) has five predictor variables and one response. The example comes from Chatterjee and Hadi (1986) in a paper on regression diagnostics. Using the Statistics Toolbox (Statistics Toolbox) Statistics Toolbox
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