Currently the Regression Learner App only supports having a single response variable.
There are several workarounds that allow you to include all of your response variables:
1) You can use either "mvregress" or "plsregress", depending on your specific data. Both regression functions support multiple response variables.
2) If your data fits better as a classification problem, for example if your response variables are binary values, you can use a classification algorithm instead of regression. To use a classification approach, you can ignore correlations between response variables and fit one response variable at a time. The Statistics and Machine Learning Toolbox contains various functions that begin "fitc...", for example "fitctree" and "fitclinear". The following documentation page discusses using a classification approach, and gives examples using several of these functions:
The function "fitglm" would also be a good fit for this approach; see the following documentation page for more information:
Hope it helps!