FC2Video

Linear Regression Pt 1

DataFitting program performs statistical regression analysis to estimate the values of parameters for linear, multivariate, polynomial, exponential and nonlinear functions. The regression analysis determines the values of the parameters that cause the function to best fit the observed data that you provide. This process is also called curve fitting. DataFitting gives engineers and researchers the power to find the ideal model for even the most complex data, by putting a large number of equations at their fingertips. DataFitting's built-in library includes a wide array of linear and nonlinear models from simple linear equations to high order polynomials. DataFitting has the following capabilities: A 38-digit precision math emulator for properly fitting high order polynomials and rationals. A robust fitting capability for nonlinear fitting that effectively copes with outliers and a wide dynamic Y data range. Once your data have been fit, DataFitting automatically sorts and plots the fitted equations by the statistical criteria of Standard Error. You can preview your graph and output publication-quality graphs in several different configurations. A residual graph as well as parameter output is generated for the selected fitted equation. Data, statistical and numeric summaries are also available from within the report-panel.

CurveFitter is a powerful statistical analysis program that performs linear and nonlinear regression analysis (i.e. curve fitting). CurveFitter determines the values of parameters for an equation, whose form you specify, that cause the equation to best fit a set of data values. CurveFitter can handle linear, polynomial, exponential, and general nonlinear functions. Unlike many "nonlinear" regression programs that can only handle a limited set of function forms, CurveFitter can handle essentially any function whose form you can specify algebraically. CurveFitter performs true nonlinear regression analysis, it does not transform the function into a linear form. As a result, it can handle functions that are impossible to linearize such as ("Newton's Law of Cooling"): y = (a - c) * exp(-b * x) + c Another advantage of handing the function in true nonlinear form is that the minimization of the sum of squared residual values (i.e., "least squares") is based on the true nonlinear value rather than some linearized transformation. In addition to computing the optimal values of the parameters to best fit the function to the data, CurveFitter can generate plots of the data points and the fitted equation. In addition, it can plot the distribution of residual values. This state-of-the-art data fitting includes the following capabilities: * Any user-defined equations of up to nine parameters and eight variables. * Unlimited length of dataset. * A 38-digit precision math emulator for properly fitting high order polynomial and rational coefficients. * A robust fitting capability for nonlinear fitting that effectively copes with outliers and a wide dynamic Y data range. CurveFitter is an indispensable curve fitting tool for scientists, researchers, engineers, students, teachers and other professionals.

A simple (two-variable) regression has three standard errors: one for each coefficient (slope, intercept) and one for the predicted Y (standard error of regression). While the population regression function (PRF) is singular, sample regression functions (SRF) are plural. Each sample produces a (slightly?) different SRF. So, the coefficients exhibit dispersion (sampling distribution). The standard error is the measure of this dispersion: it is the standard deviation of the coefficient.