Least squares problems fall into two categories: linear or ordinary least squares and nonlinear least squares, depending on whether or not the residuals are linear in all unknowns. The linear least-squares problem occurs in statistical regression analysis; it has a closed-form solution.
Non-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters (m ≥ n). It is used in some forms of nonlinear regression.
In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables. The data are fitted by a method of successive approximations (iterations).
Create a bell curve data set (x,y). Add a small random amount to each y value. Fit a curve to the data. Plot the data points and the curve.
Y = Ke-(X-M)2/(2σ2)
| X,Y | are the curve's x,y coordinates (used for plotting, etc.) |
| K | is the maximum Y coordinate; used to scale the Y coordinates
(height in Y units) |
| M | is the curve's mathematical mean (X coordinate of the mean) |
| σ | is the curve's standard deviation;
determines how fat or skinny the curve is (width in X units) |
| e | is Euler's number; is a constant; is an irrational number (defined in the Python numpy module and other libraries) |
Least squares (Wikipedia)
Non-linear least squares (Wikipedia)
Nonlinear Regression (Wikipedia)
Python for Data Analysis - Using scipy for data fitting
Is there a way to plot a curve of best fit without function? Python