Regression Analysis vs Newton's Law of Cooling

Nonlinear Least Squares Regression - CurveFitter 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".

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 generates plots of the data points and the fitted equation. In addition, it plots 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.

In one of real world situations, Newton's Law of Cooling corresponds to an example of the temperature of a cup of water as it cools from boiling hot to room temperature over the course of an hour:
Temp = ( Tboiling - Troom ) * Exp( - k * Time ) + Troom

Category:

Science & Technology

Tags:

• Save-the-Children
• regression
• analysis
• data
• curve
• fitting
• Newton's
• law
• least
• squares
• parameters
• nonlinear
• function