Matlab linear regression

As stated earlier, Matlab s philosophy is to read everything as a matrix. Consequently, the basic operators for multiplication, right division, left division, power (, /,, A) automatically perform corresponding matrix operations (A will be introduced shortly in the context of square matrices, / and will be discussed later, in the context of linear regression and the calculation of a pseudo inverse, see The Pseudo-Inverse, p.117). 

Matlab recognises the importance of linear regression calculations and introduced a very elegant and useful notation the / forward- and backslash operators, see p.l 17-118. 

We have encountered Excel s LINEST as a tool for linear regression. Unfortunately, LINEST cannot be generalised from vectors to matrices. To deal with matrices, we do not have an option but to use equations (4.59) and (4.61). It is possible to do so, but not as convenient as in Matlab. 

Other software packages that can be used to perform non-linear regression analysis are MathCad (MathSoft, Inc., 201 Broadway, Cambridge, MA 02139) and MatLab (Mathworks Inc., 24 Prime Park Way, Natick, MA 01760). 

Refer MATLAB program lin regres.m for the linear regression discussed in this section. 

From experimental data (file expdata.dat available on the worldwide web), we want to determine the best value of the product of the overall heat transfer coefficient times the heat transfer area (UA). You need to use the load command which will give you a two-dimensional array with time and temperature called exp-data. Is there a linear plot that allows for the use of linear regression MATLAB has the function polyfit that can perform this fit. What is the optimal vaue of UA for this system What do you think of the data MATLAB also has a function polyval that allows you to get best predicted values. 

This section presents three examples that show how to implement various forms of regression analysis in MATLAB. The topics considered are linear regression, nonlinear regression, and system identification. AH examples are based on real data obtained from experiments. Appropriate MATLAB code, as well as the final results, is provided so that the reader can modify these examples to fit their particular needs. 

Script for solving linear regression problems in MATLAB %Copyright 2 015 Yuri Shardt... 

Fig. 7.1 Linear regression example MATLAB plots of the (top, left) normal probability plot of the residuals, (top, centre) residuals as a function of y, (top, right) residuals as a function of the first regressor, Xj, (bottom, left) residuals as a function of x, (bottom, centre) residuals as a function of y, and (bottom, right) a time series plot of the residuals...

LIBSVM, http //www.csie.ntu.edu.tw/ cjlin/libsvm/. LIBSVM (Library for Support Vector Machines) was developed by Chang and Lin and contains C-classification, v-classification, s-regression, and v-regression. Developed in C++ and Java, it also supports multiclass classification, weighted SVMs for unbalanced data, cross-validation, and automatic model selection. It has interfaces for Python, R, Spins, MATLAB, Perl, Ruby, and LabVIEW. Kernels available include linear, polynomial, radial basis function, and neural (tanh). 

SVM Toolbox, http //asi.insa-rouen.fr/%7Earakotom/toolbox/index. This fairly complex MATLAB toolbox contains many algorithms, including classification using linear and quadratic penalization, multiclass classification. E-regression, v-regression, wavelet kernel, and SVM feature selection. 

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