Polynomial Regression Dialog

1 Recalculate
2 Multi-Data Fit Mode
3 Input Data
4 Polynomial Order
5 Fit Options
6 Quantities to Compute
7 Residual Analysis
8 Output Settings
9 Fitted Curves Plot
10 Find X/Y
11 Residual Plots

Recalculate

Recalculate	Controls recalculation of fitting results upon changes to source data None Auto Manual

Controls recalculation of fitting results upon changes to source data

None
Auto
Manual

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.

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. By X Specify the range of the X column by X value 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.

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.

By X

Specify the range of the X column by X value

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.

Polynomial Order

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

Fit Options

Specifies the fitting options.

Errors as Weight	This is available only when Error column is specified. You can use it to control how the error values are used for weights. 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 $σ i$ stands for the value of the ith row of the Error column. Then we have $\chi ^2=\sum_{i=1}^n \frac 1{\sigma _i^2} (y_i-\hat y_i)^2$
Fix Intercept	Specify whether to restrict the intercept to the value specified.
Fix Intercept at	This is available only when the Fix Intercept check box is selected. It specifies the fixed intercept value.
Use Reduced Chi-Sqr	This is available only when Direct Weighting or Instrumental is selected for Error as Weight. It specifies whether to use reduced chi-square to calculate the errors of the parameters. This option does not affect the fitting process or the fitted curve. By default, it is checked, and the covariance matrix is calculated by: $\sigma (x'x)^{-1}\,\!$ , otherwise, $(x'x)^{-1}\,\!$ .
Apparent Fit	Specify whether to use the apparent values for fitting, according to the current axis scales. When this check box is selected and the data has error values associated with it, Origin uses the larger of the positive/negative errors as weight.

Apparent fitting is only useful when the fitting is started from a graph with non-linear axes (Log10, for example). If you check this option, the fitter will first transform raw data into a new data space according to the axis types, and then perform the fitting on the transformed data. As you can see, apparent fitting is equivalent to transforming the raw data in worksheet and then applying a direct fitting.

Quantities to Compute

Use this branch to specify the quantities to be computed and displayed:

Fit Parameters	Value Parameters' value. Standard Error Standard error of parameters LCL The lower confidence limit UCL The upper confidence limit Confidence level for Parameters (%) The confidence level for regression t-Value t-test value of parameters prob>\|t\| p-value of parameters CI Half-Width Half-width of the confidence interval
Fit Statistics	Number of Points Total number of fitting points Degrees of Freedom Model degrees of freedom Reduced Chi-Sqr The Reduced Chi-square value, equals to the residual sum of square divided by the degree of freedom. R Value The R value, equals to square root of R2 Residual Sum of Squares Residual sum of squares (RSS); or sum of square error. R-Square (COD) Coefficient of determination Adj. R-Square Adjusted coefficient of determination Root-MSE (SD) Standard deviation; or square root of mean square error. Norm of Residuals Norm of residuals; equals to square root of RSS. Polynomial order The chosen polynomial order.
Fit Summary	Check to output the fit summary table. This table organizes all the selected fit parameters in a row for each curve (dependent data).
ANOVA	Specifies whether or not to output the analysis of variance table.
Covariance matrix	Specifies whether or not to output the covariance matrix.
Correlation matrix	Specifies whether or not to output the correlation matrix.

Residual Analysis

Select methods to calculate and output the different kind of residuals.

Regular	Output the regular residuals
Standardized	Output the standardized residuals
Studentized	Output the studentized (internally studentized ) residuals
Studentized deleted	Output studentized deleted (externally studentized) residuals

Output Settings

Custom the output results and destination.

Graph Arrangement	Arrange Graphs into Columns Specify a number l. In any result sheet table, graphs will be arranged in rows of l graphs. Arrange Plots of Same Type in One Graph If this checkbox is selected, plots of the same type will be arranged in one graph
Fitted Results Sheet Arrangement	This drop-down list is only available when multiple datasets are input. It allows you to specify how to arrange the fitted result worksheets. Combined All results are combined in a worksheet. Separate The results are output to separate worksheets.
Report Tables	Specifies the destination of report tables. Book Specifies the destination workbook. <none> Do not output report worksheet tables <Source> The source data workbook <new> A new workbook. <existing> A specified existing workbook BookName The name of the destination workbook. Sheet The destination worksheet, always <new>. SheetName The desired name of the destination worksheet. Result Log Use this checkbox to Specify whether to output the report to Result Log Script Window Use this checkbox to specify whether to output the report to Script Window. Notes Window Use this drop-down list to specify the destination Notes Window: <none> Do not output to any Notes window. <new> Output to a new Notes window. You can enter the desired name of the Note window here.
Fitted Curves	Specifies the destination workbooks and worksheet for the fitted value. Book Specifies the destination workbook. <auto> The workbook that is automatically picked by the program. <source> The source data workbook. <report> The workbook containing the report tables. <new> A new workbook <existing> A specified existing workbook. BookName The name of the destination workbook. Sheet Specifies the destination worksheet. <source>' Source data worksheet. <new> A new worksheet. <existing> A specified existing worksheet. SheetName The name of the destination worksheet.
Fit Residuals	Specifies the destination workbook and worksheet for residual values Book Specifies the destination workbook. <fittedvalue> The workbook has the fitted values. <source> The source data workbook <new> A new workbook <existing> A specified existing workbook BookName The name of the destination workbook. Sheet Specifies the destination worksheet. <fittedvalue>' The worksheet has the fitted values. <new> A new worksheet <existing> A specified existing worksheet SheetName The name of the destination worksheet.
Find Specific X/Y Tables	Specifies the destination of Find Specific X/Y tables. This branch is only available when either the Find X from Y checkbox or the Find Y from X checkbox is selected. See: Find Specific X/Y, below. Book Specifies the destination workbook. <fittedvalue> The workbook has the fitted values. <source> The workbook has the source data. <new> A new workbook. <existing> A specified existing workbook BookName The name of the destination workbook. Sheet Specifies the destination worksheet. <fittedvalue> The worksheet that has the fitted values <new> A new worksheet. <existing> A specified existing worksheet. FindX SheetName The name of the destination Find X worksheet. FindY SheetName The name of the destination Find Y worksheet.
Optional Report Tables	Specifies what is output to report worksheet Notes Notes table Input Data Table for input data Masked Data Table for masked data Missing Data Table for missing data

Fitted Curves Plot

Settings for the output fitted curves

Plot in Report Table	When the checkbox is selected, fitted curves will be added to Report Table.
Plot on Source Graph	This option is available only when the input datasets are from a graph. It can be used to specify whether to add the fitted curve to the original graph. None The fitted curve is not added to the original graph. Fitted Curve The fitted curve is added to the original graph. Fitted Curve+Plot Type The fitted curve and the plot specified by the Plot Type drop-down list are added to the original graph. This option is available only when the input datasets are from a graph and the Concatenate Fit mode is chosen.
Update Legend on Source Graph	Check this check box to specify whether to update legend on the source graph.
Multiple Plots Use Source Graph Color	Check this check box to specify whether to use color settings of source graph to color multiple fitted curves.
X Data Type	Specify how to generate the X values of the fitted curve. Uniform Linear The X values of the fitted curve are plotted on an equally-spaced linear scale. Log The X values of the fitted curve are plotted on a logarithmic scale. Same as Input Data The X values of the fitted curve are the same as the input X values. Use Source Graph Scale Type The X values of the fitted curve are plotted using the scale type of the source graph. This option is available only when the input datasets are from a graph. Points This control is available only when X Data Type is either Uniform Linear or Log. It specifies the total number of data points in a fitted curve. Range This control is available only when X Data Type is either Uniform Linear or Log. It specifies the range of the X values of the fitted curve. Select one of the following options: Use Input Data Range + Range Margin Span to Full Axis Range Custom Range Margin This control is available only when X Data Type is either Uniform Linear or Log and Use Input Data Range + Range Margin is selected for Range. It specifies the range margin into which the fitted curves extend. Min/Max This control is available only when X Data Type is either Uniform Linear or Log and Custom is selected for Range. These two text boxes specify the minimum and maximum X value for fitted curves.
Confidence Bands	Specify whether or not the confidence bands are added to the output graph.
Prediction Bands	Specify whether or not the prediction bands are added to the output graph.
Confidence Level for Curves (%)	Specify the confidence level for confidence bands and prediction bands.

Find X/Y

Use this branch to specify whether to output Find Specific X/Y tables. A Find Y from X table is used to obtain a dependent variable value that corresponds to a given independent variable value; while a Find X from Y table can be used to obtain an independent variable value for a given dependent variable value.

Find X From Y	Use the checkbox to specify whether to generate a Find X From Y table. Number of X Columns Specifies the number of X columns.
Find Y From X	Use the checkbox to specify whether to generate a Find Y From X table. Number of Y Columns Specifies the number of Y columns.

Find X From Y

Use the checkbox to specify whether to generate a Find X From Y table.

Number of X Columns

Specifies the number of X columns.

Find Y From X

Use the checkbox to specify whether to generate a Find Y From X table.

Number of Y Columns

Specifies the number of Y columns.

Note: If you use Apparent Fit, the Find X From Y and Find Y from X table will find values on the transformed scale.

Residual Plots

Use the controls in this branch to customize the residual plots.

Residual Plots	Use the controls in this branch to customize the residual plots. Residual Type Specify the residual type from the drop-down list: Regular Standardized Studentized Studentized Deleted For the selected residual type, you can opt to output up to five residual plots: Residual vs. Independents Plot Histogram of the Residual Plot Residual vs. Predicted Values Plot Residual vs. the Order of the Data Plot Residual Lag Plot

Residual Plots

Use the controls in this branch to customize the residual plots.

Residual Type

Specify the residual type from the drop-down list:

Regular
Standardized
Studentized
Studentized Deleted

For the selected residual type, you can opt to output up to five residual plots:

Residual vs. Independents Plot

Histogram of the Residual Plot

Residual vs. Predicted Values Plot

Residual vs. the Order of the Data Plot

Residual Lag Plot

Polynomial Regression Dialog

Contents

Recalculate

Multi-Data Fit Mode

Input Data

Polynomial Order

Fit Options

Quantities to Compute

Residual Analysis

Output Settings

Fitted Curves Plot

Find X/Y

Residual Plots