15.2.1 The Linear Regression Dialog Box

The Linear Regression dialog can be used to fit the simple linear model to your data:

y = β0 + β1x

where β0 is the intercept and β1 is the slope.

Linear Fit Confidence Band.png

Supporting Information

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

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


See Also:

Recalculate

Recalculate

Controls recalculation of analysis results

  • 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 a 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 text boxes to specify the range to be fitted.
  • All
Fit all rows of the dataset.
  • 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 a worksheet or a graph, you can use the Apply Row Range to All menu item to apply the same X row range to all input data. Specify a row range for the input column for Range 1, click the Button Select Data Right Triangle.png button to the right of Range 1, then click Apply Row Range to All.

For more information, see: Specifying Your Input Data

Fit Control

Errors as Weight

Use error bars as value for weights. Only available when a designated Error column is selected.

  • No Weighting
Do not use any data as weighting.
  • Direct Weighting
 w_i\,\! = values form the ith row of Error column and
\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\,\! = values form the ith row of Error column and
\chi ^2=\sum_{i=1}^n \frac 1{\sigma _i^2} (y_i-\hat y_i)^2

For more information, see: Weighted Fitting

Fix Intercept

Restrict the intercept to the value specified.

Fix Intercept at

Specify the intercept.

Fix Slope

Restrict the slope to the value specified.

Fix Slope at

Specify the slope.

Scale Error with sqrt(Reduced Chi-Sqr)

Available when fitting with weight. This check box only affects the error on the parameters reported from the fitting process, and does not affect the fitting process or the data in any way. By default, it is checked, and the covariance matrix is calculated by: \sigma^2 (x^{\prime }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.

Apparent Fit

Use the apparent values for fitting, according to the current axis scales. For example, select this box to fit exponentially decaying data with a straight line fit when data are plotted on a log scale. 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.

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.

Apparent Fit is useful when you are performing a fit on data in an active graph window and you have changed the plot axis type (e.g. from Linear to Log10). When you select this option, the fitter will first transform your raw data into a new data space as specified by the graph axis type, and then fit the curve of the new data. Otherwise, Origin always fits raw data directly, regardless of the axis type. An apparent fit is equivalent to a direct fit performed on transformed raw worksheet data. All items in Residual Analysis are available for Apparent Fit. Outliers identification is also supported in Apparent Fit.

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.

CI Half-Width

Half-width of the confidence interval.

For more information, see: Parameters

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 (equal to the residual sum of square divided by the degrees of freedom).

R Value

The R\,\! value (equal to to square root of R^2\,\!).

Residual Sum of Squares

Residual sum of squares (RSS); or sum of square error.

Pearson's r

Pearson correlation coefficient.

R-Square (COD)

Coefficient of determination.

Adj. R-Square

Adjusted coefficient of determination.

Root-MSE (SD)

Residual standard deviation; or square root of mean square error.

Norm of Residuals

Norm of residuals; equals to square root of RSS.

For more information, see Statistics

Fit Summary

Output the fit summary table. This table organizes 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.

For more information, see: Covariance and Correlation Matrix

Correlation matrix

Output the correlation matrix.

For more information, see: Covariance and Correlation Matrix

Outliers

Output outliers list.

X Intercept

Intercept of the fitted curve with X axis.

Residual Analysis

Select methods to calculate and output residuals. For more information, see Graphical Residual Analysis

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

Graph

Results Table

Specify whether to show the fitting results to the source/report graph.
  • None
No not add fitting result table to the graph.
  • Source Graph
Add fitting result table to the source graph. Make sense only when the input data is from graph.
  • Report Graph
Add fitting result table to the embedded graphs in the report sheet. When there are more than one graphs in the report sheet, the table will be added to the first one.
  • Source and Report Graphs
Add fitting result table to both the source graph and report sheet graph.
Table Style Template
Specify the Table Style Template used in the results graph.
Quantities in Table
Specify the quantities to display in table

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 check box is selected, plots of the same type will be arranged in one graph.

Arrange Residual Plots in One Graph

If this check box is selected, all residual plots will be arranged in one graph.
Fitted Results Sheet Arrangement

This drop-down list is only available when multiple datasets are input. Specify how to arrange the fitted result worksheets.

  • Combined
    All results are combined in a worksheet.
  • Separate
    The results are output to separate worksheets.
Dataset Identifier Specify how to label the source data in your output.
Identifier
Use the following to identify the source data. Note that when doing a linear fit on plotted data (i.e. a graph window is active) there is an extra Plot Legend option.
  • Range
Refer to the source data using range syntax.
  • Book Name
Use the workbook long name if it exists (even if not shown) otherwise use book short name.
  • Sheet Name
Use the worksheet short name.
  • Sheet Display Name
Use the displayed sheet name (See Name and Comments dialog for Sheet).
  • Name
Use the column long name if it exists, otherwise use the column short name.
  • Short Name
Use the column short name.
  • Long Name
Use the column long name.
  • Units
Use the column units.
  • Comments
Use the column comment.
  • Plot Legend
Available when the active window is a graph window. Uses the legend label for the plot being fitted.
  • <Custom>
Use custom notation to identify source data. This option adds a Custom Identifier box for entering your identifier. For help with identifier notation, please refer to these topics:
Designation
Specify using the X dataset, Y dataset etc. to provide the Identifier. Choosing <auto> uses the dependent variable (typically, the Y column). This control is not available for all identifiers.
Show Identifier in Flat Sheet
Many Origin analysis operations output data to a "flat" sheet in addition to the collapsible analysis report sheets. Use the Identifier in the flat sheet.
Report Tables

Specifies the destination of report tables.

Book
Specify the destination workbook.
  • <none>
Do not output report worksheet tables.
  • <auto>
The workbook that is automatically picked by the program.
  • <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
Specify whether to output the report to Result Log.
Script Window
Specify whether to output the report to Script Window.
Notes Window
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 values.

Book
Specify 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
Specify 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
Book
Specify 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
Specify 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

Specify the destination of Find Specific X/Y tables. This branch is only available when either the Find X from Y check box or the Find Y from X check box is selected.

See: Find Specific X/Y, below.
Book
Specify 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
Specify 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.

Equation in Notes
Specify the format of the equation on the report table.
  • Equation with Names
Output the equation with parameter names.
  • Equation with Values
Output the equation with the fitted values of parameter.
Notes
Notes table.
Input Data
Table for input data.
Masked Data
Table for masked data.
Missing Data
Table for missing data.

Fitted Curves Plot

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.
Stack with Residual vs. Independents Plot Stack the fitted curve with the Residual vs. Independents Plot.
Update Legend on Source Graph

Specify whether to update legend on the source graph.

Multiple Plots Use Source Graph Color

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 + Margin
  • Use Input Data Range + X Intercept + 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

If this is checked, confidence bands will be added to the fitted curve plot as two lines with filled area in between. You can turn the area fill off or customize the fill pattern on the Line tab of Plot Details dialog.

For more information, see Confidence and Prediction Bands

Prediction Bands

If this is checked, prediction bands will be added to the fitted curve plot as two lines with filled area in between. You can turn the area fill off or customize the fill pattern on the Line tab of Plot Details dialog.

For more information, see Confidence and Prediction Bands

Confidence Level for Curves (%)

Specify the confidence level for confidence bands and prediction bands.

Ellipse

Check this check box to add the confidence ellipse to the fitted curve plot based on the chosen confidence level.

Data Points
Specify the number of data points of the ellipse.
Mean
Check this check box to add the confidence ellipse for the population mean.
Confidence Level (%)
Specify the confidence level for the confidence ellipse.
Prediction
Check this check box to add the confidence ellipse for prediction.
Confidence Level (%)
Specify the confidence level for the confidence ellipse.

For more information, see: Confidence Ellipses.

Find X/Y

A Find Y from X table is used to obtain a dependent variable value that corresponds to a given independent variable value. A Find X from Y table is used to obtain an independent variable value for a given dependent variable value.

For more information, see: Finding Y/X from X/Y Standard Curves

Find X From Y

Generate a Find X From Y table.

Calculate 95% Confidence Interval
Calculate and output the 95% Confidence Interval. Note if the weighting is specified, or there is a fixed parameter, the confidence interval will not be calculated.
Find Y From X

Generate a Find Y From X table.

Calculate 95% Confidence Interval
Calculate and output the 95% Confidence Interval.

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

Residual Plots

Use the controls in this branch to customize the residual plots. For more information, see Graphical Residual Analysis

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 six 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
Normal Probability Plot of Residuals