# 15.2.3 The Polynomial Regression Dialog Box

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

y = β0 + β1x + β2x2 + .. + βnxn

where βn 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.

## Supporting Information

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

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

## Recalculate

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

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 X column of the curve. Y 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 $\chi ^2=\sum_{i=1}^n \frac 1{\sigma _i^2} (y_i-\hat y_i)^2$ For more information, see: Weighted Fitting.