What you show us is *pairwise* plots and you have multivariate data. It does not have to be the case that any of the variables individually let you to do accurate predictions, but nevertheless it *does not* mean that the combinations of variables would not let you to do so.

Check [this example][1], where the corelation changes from positive to groupwise negative when introducing another variable. 

In fact, if you look at the paper by [Erdogdu et al (2013)][2] that is provided as a reference for this dataset, you'll learn that the authors actually were able to make predictions that were better then random guessing using this data.

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Erdogdu Sakar, B., Isenkul, M., Sakar, C.O., Sertbas, A., Gurgen, F., Delil, S., Apaydin, H., Kursun, O. (2013). [Collection and Analysis of a Parkinson Speech Dataset with Multiple Types of Sound Recordings.][2]' IEEE Journal of Biomedical and Health Informatics, 17(4), 828-834. 


  [1]: https://stats.stackexchange.com/questions/125683/pearson-correlation-has-quizzy-results/125686#125686
  [2]: https://www.researchgate.net/profile/Hulya_Apaydin/publication/260662600_Collection_and_Analysis_of_a_Parkinson_Speech_Dataset_With_Multiple_Types_of_Sound_Recordings/links/552658a60cf24b822b408142.pdf