15.2.4 The Multiple Linear Regression Dialog Box

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

y = β0 + β1x1 + β2x2 + .. + βnxn

where βn are the coefficients.

Multiple Linear Regression.png

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:

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

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

Specifies the fitting options.

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