15.2.4 The Multiple Linear Regression Dialog Box

Multiple Linear Regression fits multiple independent variables with the following model:

y = β₀ + β₁x₁ + β₂x₂ + .. + β_nx_n

where β_n are the coefficients.

An unique feature in Multiple Linear Regression is a Partial Leverage Plot output, which can help to study the relationship between the independent variable and a given dependent variable:

1 Supporting Information
2 Recalculate
3 Input
4 Fit Control
5 Quantities
6 Residual Analysis
7 Output
8 Plots

Supporting Information

Origin's multiple linear regression dialog box can be opened from an active worksheet. From the menu:

Click Analysis: Fitting: Multiple Linear Regression (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

For help with range controls, see: Specifying Your Input Data.

Range

The XY data range.

Dependent Data

Data range for the dependent variable.

Independent Data

Data range for the Independent variable(s).

Error Bar / Weight

Range of error bar/weight data.

If you pre-select data before opening the Multiple Regression dialog box, your X columns will be entered as Independent Data and your Y column will be entered as Dependent Data. Columns designated as yEr± will be entered into the Error/Bar Weight box. To learn more, see Column Plot Designations.

Fit Control

Beginning with Origin 2022b, the MLR dialog supports use of a named range in place of numeric input (e.g. intercept or custom weight). For more information, see this OriginLab blog post.

Errors as Weight

Use error bars values for weighting. A designated error bar column (yEr±) must be selected:

No Weighting:

Do not apply weighting.

Direct Weighting: $w_i$ = values from the $i^{th}$ row of yEr± column and

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

Instrumental Weighting: $w_i=\frac 1{\sigma_i ^2}$ , where $\sigma _i$ = values from the $i^{th}$ row of yEr± column

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

Fix Intercept

Fix the Y intercept.

Fix Intercept at

Intercept value.

Scale Error with sqrt(Reduced Chi-Sqr)

Available only when Direct Weighting or Instrumental is selected for Error as Weight. Use reduced chi-square to calculate the errors of the parameters. This option does not affect the fitting process or the fitted curve. This is checked by default and the covariance matrix is calculated by: $\sigma (x'x)^{-1}\,\!$ , otherwise, $(x'x)^{-1}\,\!$ .

When it is checked, it uses reduced Chi-Sqr to estimate error variance, and parameter's standard error is scaled by it, otherwise error variance is specified with 1, and parameter's standard error is not scaled.

This option is checked by default to keep parameter's standard error and related results compatible with other software. It is recommended to uncheck this option when fitting data with instrumental weight, so that parameter's standard error can reflect the magnitude of weight.

Invalid Weight Data Treatment

Treat as Invalid

If there is invalid value in weight data, Origin will throw an error.

Replace with Custom Value

Replace the Invalid Weight data with Custom Value

Custom Weight

Set the value of Custom Weight. This option is available when Replace with Custom Value is selected.

Quantities

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. Cl Half-Width Half-width of the confidence interval. For more information, see: Parameters.
Fit Statistics	Number of Points Total number of fitted points. Degrees of Freedom Model degrees of freedom. R Value The R value, equal to square root of $R^2$ . 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) Residual standard deviation (square root of MSE). Norm of Residuals Norm of residuals (square root of RSS). For more information, see Statistics.
Fit Summary	Select to output the fit summary table. This table organizes all the selected fit parameters by row for each curve (dependent data).
ANOVA	Output the analysis of variance table. For more information, see: ANOVA Table
Lack of Fit Test	Output the Lack of Fit results for fitting replicate data, which is used to measure the adequacy of the specified model. For more information, see: Lack of Fit Table
Covariance matrix	Output the covariance matrix.
Correlation matrix	Output the correlation matrix.
Fitted Values	Output the fitted values to result worksheet.

Residual Analysis

For more information, see Graphic Residual Analysis.

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

Output

Dataset Identifier	Identifier Determine how to identify the source data in your output. Range Use the range syntax. Book Name Use the workbook long name. Sheet Name Use the worksheet name. Name Use the long name of the corresponding column if there is a long name, otherwise use the short name of column. Short Name Use the short name of the corresponding column. Long Name Use the long name of the corresponding column. Units Use the unit of the corresponding column. Comments Use the comment of corresponding column. <Custom> Use custom formats to define a data identifier. Custom Identifier Enter your custom identifier. For a complete list of options, please refer to Text Label Options.
Report Tables	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. Results Log Use this check box to Specify whether to output the report to Results Log. Script Window Use this check box 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	Destination workbooks and worksheet for the fitted values. 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	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.
Partial Leverage Values	Destination workbook and worksheet for partial leverage 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.
Optional Report Tables	Notes Notes table. Input Data Table for input data. Masked Data Table for masked data. Missing Data Table for missing data.

Plots

For more information on residuals, see Graphic Residual Analysis.

Predicted vs. the Order of the Data Plot	Specify whether to show the predicted vs. the order of the data plot.
Stack with Residual Plot	Specify whether to show the residual plots stacked with the Predicted vs. the order of the data plot.
Partial Leverage Plots	Specify whether to show the partial leverage 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