# Real Statistics Release 4.4

The spreadsheets for all the examples used on the Real Statistics website, including those related to the new Release 4.4 features) are available for free download (Download Examples Workbooks). These are contained in three Excel files (i.e. workbooks): Examples Workbook Part 1, Examples Workbook Part 2 and Multivariate Examples. See Workbook Examples for a description of which examples are contained in which files.

The Real Statistics website is in the process of being updated to reflect the new features. These changes will be made over the next several days.

Release 4.4 contains the following new features:

Multiple Linear Regression without Intercept

There is a new option for the Linear Regression data analysis tool which performs Multiple Linear Regression where the intercept is assumed to be zero.

To access this data analysis tool, press Ctrl-m (or choose Real Statistics Data Analysis Tools from the Add-Ins ribbon), double-click on the Regression option and then select Multiple Linear Regression. On the dialog box that appears, uncheck the Include constant (intercept) option.

There is a new array function Reg0Coeff, which is similar to the existing RegCoeff function, except that it outputs the regression coefficients and their standard errors for regression without an intercept coefficient.

The following existing functions now take a new argument con: HAT, DIAGHAT, LEVERAGEAdjRSquare, RegAIC, RegAICc, SSReg, SSRes, SSRegTot, dfRes, dfRegTot, MSReg, MSRes, MSTot, RegF, RegTest, RSquare, AdjRSquare, MultipleR, RegE, RegY. When the con argument is TRUE (default) then the regression is assumed to have an intercept, while when this argument is FALSE the regression is done assuming that the intercept is zero.

Weighted Multiple Linear Regression

There is a new data analysis tool which performs Weighted Multiple Linear Regression. This is especially useful when the homogeneous variance assumption for least squares method is not met.

To access this data analysis tool, press Ctrl-m (or choose Real Statistics Data Analysis Tools from the Add-Ins ribbon), double-click on the Regression option and then choose the Weighted Linear Regression option.

There is a new array function WRegCoeff, which is similar to the existing RegCoeff function, except that it outputs the regression coefficients and their standard errors where there are weights.

Huber-White Robust Standard Errors

The Linear Regression data analysis tool has been modified to allow you to choose a robust standard errors option. This is especially useful when the homogeneous variance assumption for least squares method is not met, and there is not enough information to use weighted linear regression.

To use this capability, press Ctrl-m (or choose Real Statistics Data Analysis Tools from the Add-Ins ribbon), double-click on the Regression option and then choose the Multiple Linear Regression option. You are presented with a choice of the following options No, HC0, HC1, HC2, HC3 and HC4.

No is the ordinary least squares option (default), which assumes that the variances are equal (called homoscedasticity). This is how we calculated the standard errors of the regression coefficients in all previous releases of the software. HC0 modifies the OLS approach in large samples to provide better estimates of the standard errors of the regression coefficients when the variances are not equal (called heteroscedasticity). The other options are used in place of HC0 with smaller samples.

There is a new array function RRegCoeff, which is similar to the existing RegCoeff function, except that it outputs the regression coefficients and their standard errors when robust standard errors are employed.

Both the Multiple Linear Regression data analysis tool and RRegCoeff function also support regression without an intercept.

Schwarz Baysean Criterion (BSC)

There is a new RegSBC function which computes the SBC for multiple linear regression. SBC is also called Schwarz Information Criterion (SIC). This function takes the form:

RegBSC(Rx, Ry, con, aug)

where Rx is a range containing the X data and Ry is a range containing the Y data. If con = TRUE (default) regression with an intercept is used and if con = FALSE regression without an intercept is used. If aug = TRUE an extra constant term n(1+LN(2π)), where n is the sample size, is added to the output (default for aug is FALSE).

The RegAIC and RegAICc functions have now been revised so that they too take con and aug arguments.

Gage R&R

There is a new Gage R&R data analysis tool which generates a Gage Repeatability and Reproducibility report that can be used to assess a measurement system using ANOVA.

To access this data analysis tool, press Ctrl-m (or choose Real Statistics Data Analysis Tools from the Add-Ins ribbon), double-click on the Analysis of Variance option and then choose Two Factor Anova which contains the Gage R&R option.

Jenks Natural Breaks

There is a new data analysis tool which performs the Jenks Natural Breaks algorithm. This is a cluster analysis method which breaks a range of values into natural categories, typically used to color maps.

To access this data analysis tool, press Ctrl-m (or choose Real Statistics Data Analysis Tools from the Add-Ins ribbon), double-click on the Multivariate Analyses option and then choose the Jenks Natural Breaks option.

Option to Disable Ctrl-m

For those of you who use the keyboard shortcut Ctrl-m for some other purpose, you can disable Crtl-m from being used as a way to display the dialog box for Real Statistics data analysis tools. In this case you will need to use choose Real Statistics Data Analysis Tools from the Add-Ins ribbon to display this dialog box.

To disable Ctrl-m, press Alt-F8 (or select View > Macros|Macros). Next insert the macro name DisableToolsShortcut in the Macro dialog box that appears and press the Run button. To enable Ctrl-m, repeat the same sequence of steps except that you need to insert EnableToolsShortcut as the macro name.

Bug Fixes

The ATEST(R1, b) function computes the p-value for one-way ANOVA where the groups are arranged in columns when b = TRUE (default) and in rows when b = FALSE. A bug has been fixed which gave the wrong p-value when b = FALSE.

When the input entries for Kaplan-Meier’s Survival Analysis which are latest in time all have a dead status, then the standard error for these entries result in division by zero. This has now been corrected.

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### 2 Responses to Real Statistics Release 4.4

1. Laurent says:

Dear Charles,
this looks amazing. I simply noted a small typo in your presentation (page http://www.real-statistics.com/blogs/). As far as I know, the R-square decomposition is from Shapley-Owen instead of Shapely-Owen.

Best regards,
Laurent DEVILLE

• Charles says:

Laurent,
Yes, you are correct. I have already corrected this in a number of places. The name of the function will be changed in the next software release.
Charles