Regression & Data Analysis

See Also: Data Table  Linear & Polynomial Regression  Multiple Linear Regression  Nonlinear Regression

All of the regression and data analysis options within Polymath are available from the Data Table which is used for input, manipulation and storage of numerical data.  This Data Table is much like a spreadsheet; however, it has more powerful and easy to use capabilities.  Data can be entered directly into the Data Table, or it can be copied into the Data Table from spreadsheets or other tables. Several of the Polymath programs also place their output results within the Data Table. Options that are available from the Data Table includes: interpolation, differentiation, integration, graphical presentation, and data column analysis.

The Linear & Polynomial Regression capability from the Data Table allows the fitting of data to a polynomial of degree n with the general form: 

        P(x) = a₀ + a₁*x + a₂*x^2 + . . . + a_n*x^n

or to a linear equation when the equivalent first degree polynomial is specified:

        P(x) = a₀ + a₁*x

The Multiple Linear Regression capability from the Data Table will fit a linear function of the form: 

        y(x₁, x₂, ..., x_n) = a₀ + a₁*x₁ + a₂*x₂ + ... + a_n*x_n 

where a₀, a₁, ..., a_n are regression parameters, to a set of N tabulated values of x₁, x₂, ..., x_n (independent variables) versus y (dependent variable).

The Nonlinear Regression option from the Data Table will fit a general nonlinear function of the form:

        y = f (x₁, x₂, …, x_n, a₀, a₁, a₂, …, a_m)

where a₀, a₁, …, a_n are regression parameters to a set of N tabulated values of x₁, x₂, …, x_n (independent variables) versus y (dependent variable).

Summary:

	Data Table      Interpolation      Differentiation      Integration      Graphical Presentation      Data Column Statistical Analysis
	Linear & Polynomial Regression
	Multiple Linear Regression
	Multiple Nonlinear Regression