Regression Analysis in Mathcad

While processing experimental data in Mathcad with the purpose of investigating their nature, a necessity occurs in expressing the dependent variable in the form of a certain mathematical function with one or several independent variables. The mentioned correlation is known as regression model or regression equation, and methods which help obtain this correlation are called regression analysis methods in Mathcad. Regression analysis methods make it possible to: figure out regression models of various kinds; verify the hypothesis of model adequacy in compliance with available observation data; use the model for predicting the dependent variable values in correlation with the new values of the independent variable. Mathcad offers a set of functions, which make it possible to figure out various regression models. The table contains functions, used for regression models creation.

 

Regression Analysis in Mathcad.

Let’s study the parameters used as arguments in functions. Every Mathcad function uses two vectors of initial data, vx – vector of independent variables, vy –vector of dependent variables. The quantity of vector elements of vx and vy should be identical. Functions regress and loess are used only together with function interp. Functions regress and loess calculate only vector demanded by function interp for figuring out the polynomial itself. In Mathcad parameter span of function loess determines the size of the domain, in which the specified fragment of polynomial to the power of two is being built. The optimal value of span, offered by the reference system Mathcad, equals to 0.75, but it is recommended to select the best value of span by means of variant calculations in every particular case. Parameter g is vector of initial approximation for the unknown variables of the regression function. Regression correlations in Mathcad being defined, it is of current importance to choose the best function from collection of functions, choice based on the adequacy of initial experimental data description. A criterion for the best regression model choice can be the coefficient of determination which is numerically equal to the coefficient of correlation squared. Coefficient of correlation value in Mathcad can be calculated with the help of function corr(A,B), where A and B are two value vectors. The programme listing shows the example of various regression models figured out and the best model chosen. Listed data illustrate that the best results are shown by a polynomial model based on function loess. This model is characterized by coefficient of determination value equal to 0.984.

Regression Analysis in Mathcad