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.

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...).

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

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 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 Output the fit summary table. This table organizes fit parameters by row for each curve (dependent data). Output the analysis of variance table. For more information, see: ANOVA Table 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 Output the covariance matrix. For more information, see: Covariance and Correlation Matrix Output the correlation matrix. For more information, see: Covariance and Correlation Matrix Output outliers list. Intercept of the fitted curve with line Y = 0.

Residual Analysis

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

Regular Output the regular residuals. Output the standardized residuals. Output the studentized (internally studentized ) residuals. 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. 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. 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. 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. 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 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. Specifies the destination of report tables. Book Specify the destination workbook. Do not output report worksheet tables. The workbook that is automatically picked by the program. The source data workbook. A new workbook. A specified existing workbook. BookName The name of the destination workbook. Sheet The destination worksheet, always . 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: Do not output to any Notes window. Output to a new Notes window. You can enter the desired name of the Note window here. Specifies the destination workbooks and worksheet for the fitted values. Book Specify the destination workbook. The workbook that is automatically picked by the program. The source data workbook. The workbook containing the report tables. A new workbook. A specified existing workbook. BookName The name of the destination workbook. Sheet Specify the destination worksheet. Source data worksheet. A new worksheet A specified existing worksheet. SheetName The name of the destination worksheet. Book Specify the destination workbook. The workbook has the fitted values. The source data workbook. A new workbook. A specified existing workbook. BookName The name of the destination workbook. Sheet Specify the destination worksheet. The worksheet has the fitted values. A new worksheet. A specified existing worksheet. SheetName The name of the destination worksheet. 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. The workbook has the fitted values. The workbook has the source data. A new workbook. A specified existing workbook. BookName The name of the destination workbook. Sheet Specify the destination worksheet. The worksheet that has the fitted values. A new worksheet. A specified existing worksheet. FindX SheetName The name of the destination Find X worksheet. FindY SheetName The name of the destination Find Y worksheet. 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. 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 the fitted curve with the Residual vs. Independents Plot. Specify whether to update legend on the source graph. Specify whether to use color settings of source graph to color multiple fitted curves. 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. 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 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 Specify the confidence level for confidence bands and prediction bands. 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.