# 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.

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...).

## 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

 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. 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. Select to output the fit summary table. This table organizes all the selected 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. Output the correlation matrix. Output the fitted values to result worksheet.