**Multiple linear regression**

We use the barley QTL mapping data to illustrate this function. After deleting unwanted traits and removing irrelevant markers, we are ready to conduct multiple linear regression. (**Note**: these previous steps are not mandatory, although they simplifies the analysis.)

Under the main menu of *Association*, click *Multiple Linear Regression*, and select *Conduct Regression*. A dependent variable selector will appear on the top of the biplot.

Select the variable that you want to use as the dependent variable, here KW in this example, and click the *Regress *button. If the number of variables (testers) plus 2 is greater than the number of observations (entries), you will get the following message:

In our case, we had 145 observations, many more than the number of variables. So this was not a problem and multiple regression was conducted as requested. The regression results were printed to the log file, and the biplot was changed to the following:

There is much to say about this "biplot" (actually, the above image is not a biplot; it is just a "plot" of the testers, because the genotypes are hidden so that a better view about the "testers" can be achieved).

- The testers include the target trait KW (framed and with a big font) and the markers that are associated with it at the selected 0.05 probability level.

- All the markers together explained 72% of the total KW variation.

- On the background, the regression results are printed. These results are also printed to the log file. They can be cleared from the biplot by clicking
*Refresh*under the main menu*View*.

- Groups of markers suggest independent QTL for KW.

**In Depth:**

GGEbiplot has a function to remove markers that are only remotely related to the QTL.