This function can form an X matrix with predictor values, their squares, their cubes, and so on. 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. Matrix X has a column of ones, and then one column of values for each of the five predictor variables. The data set (originally from Moore (1975)) has five predictor variables and one response. PolyTools provides a collection of functions intended to expand the existing collection of polynomial (poly) functions already available in MATLAB®, which include, for example, polyval, polyder, polyfit, etc, and to extend, in a simple way, this type of functionality to bipolynomials (or bivariate polynomials). The example comes from Chatterjee and Hadi (1986) in a paper on regression diagnostics.

A polynomialRegressor object encapsulates a set of polynomial regressors. For example, y(t1) 2 and y(t1) u(t1) are both polynomial regressors with orders of 2 and variable delays of one sample. Using the Statistics Toolbox (Statistics Toolbox) Statistics Toolbox Polynomial regressors are polynomials that are composed of delayed input and output variables.

Matlab polytool regress