Nonlinear Least Squares Regression


Description Usage Output Method See Also

Description

Nonlinear Least Squares (NLLS) Regression allows the estimation of paramters in user-defined equation. Draco uses a Generalized Least Squares method to estimate parameters, as described in the Method section.

Usage

The NLLS regression can be started by clicking Nonlinear Least Squares... in the Data Window's Regression menu. The NLLS regression dialog appears below:
NLLS Regression Window
The NLLS window has two basic panes, Model and Parameters. The Model window, shown above, is used to specify the equation to attempt to fit to the data.  The Combo Box on the far left specifies the dependent variable for the regression.  The equation to fit is entered in the center box.  Combo Boxes on the right are present for convenience to add existing variables and constants to the equation.  In the example above, alpha is a constant in the worksheet, prob is a variable from the worksheet, and b1 is a parameter to be fit.  This parameter is specified in the Parameters tab.

NLLS Parameters Tab

The Parameters tab lists all the parameters in the equation that will be estimated along with their initial estimates.  Paramters are added and removed from this pane using the toolbar buttons:
NLLS Toolbar Buttons
The Plus sign adds a new parameter, and the Subtract sign removes the selected parameter.  

Draco uses an iterative technique to arrive at the final estimates for the Non-Linear Least Squares regression.  The convergence criteria can be set in by clicking the Iterations and Convergence... item in the Options Menu; the default values are usually sufficient.

Once all parameters are specified along with the equation, the regression can be run by selecting Compute Regression... from the Preform Fit Menu.

Logit Regression Menu

While running, the iterative progress dialog will appear, showing progress of the regression.

Output

The Nonlinear Least Square Regression will generate output similar to the following:

Results of the Non-Linear Least Squares Regression Model

Regression Variable: ser1

Sum Squared of the Residuals:
1.88226
Standard Error of the Fit:
0.26403
R-Squared Value:
1
Adjusted R-Squared Value:
1

Coefficient Value Std. Err. t-Score
alpha
2.00019
.6331E-05
3.5508E04
beta
1.44938
0.07055
20.54421


Further information can be generated after the regression. By selecting Generate Column Data from the Perform Fit menu, the estimated dependent variable data will be output as a new variable in the Data window. The resulting covariance matrix can be viewed by selecting View Covariance Matrix... from the Supporting Data menu. The residuals from the regression can also be output to the Data window as a new variable by selecting Output Residuals to Column from the Supporting Data menu.

Method

The Nonlinear Least Squares Regression uses the Levenberg-Marquardt algorithm to solve for parameter estimates. The algorithm used is implemented in the Apache Commons Math, which itself is based on MINPACK code.

See Also

Least Squares Fit
Iteration Controls
Equations
Apache Commons Math (external link)

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