15.2.3 The Polynomial Regression Dialog Box

Polynomial regression in Origin performs fit to data using the following model:

y = β₀ + β₁x + β₂x² + .. + β_nxⁿ

where β_n are the coefficients.

Polynomial regression can fit data with polynomial up to 9th order and it also supports fitting with fixed intercept or slope and apparent fit.

1 Supporting Information
2 Recalculate
3 Input
4 Fit Control

Supporting Information

Origin's polynomial regression dialog box can be opened from an active worksheet or graph. From the menu:

Click Analysis: Fitting: Polynomial Fit (Open Dialog...).

See Also:

Recalculate

Controls recalculation of fitting results upon changes to source data

None
Auto
Manual

For more information, see: Recalculating Analysis Results

Input

Multi-Data Fit Mode

This control is available only when there is more than one input dataset.

Independent-Consolidated Report

The input datasets are fitted separately. The reports are consolidated into one sheet.

Independent-Separate Report

The input datasets are fitted separately. The reports are output to different worksheets.

Concatenate

All input datasets are concatenated and fitted as one curve.

Input Data

Range

Specify the input XY data range

X column of the curve.

Y column of the curve.

Error

The Y error column.

Rows

Specify the range of the X column to be fitted. When Rows is set to By Row or By X, you can use the From and To textboxes to specify the range to be fitted.

All

Specify all rows of the dataset to be fitted.

By Row

Specify the range of the X column by row index. Use To = 0 to specify "the last row" in the input data range.

By X

Specify the range of the X column by X value. The By X option supports use of a named range in place of actual X values. For more information, see this OriginLab blog post.

When fitting multiple XY datasets from either worksheet or graph, click Apply Row Range to All to apply the same X row range to all input data. Specify a row range for the input colum for Range 1, click the

button to the right of Range 1, and then select Apply Row Range to All.

For more information, see: Specifying Your Input Data.

Polynomial Order

Polynomial Order	Specifies the order (1 through 9) of polynomial curve.

Fit Control

Errors as Weight

Use error bars as value for weights. Only available when a designated error column (yEr±) is selected.

No Weighting
Do not apply weighting.
Direct Weighting
Let $w_i$ stands for the ith weighting factor. It equals the ith row of the Error column. Then

$\chi^2=\sum_{i=1}^n w_i (y_i-\hat y_i)^2$
Instrumental
$w_i=\frac{1}{\sigma _i^2}$

where $\sigma _i$ stands for the value of the ith row of the Error column. Then we have

$\chi ^2=\sum_{i=1}^n \frac 1{\sigma _i^2} (y_i-\hat y_i)^2$