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Individuals with dysarthria suffer from difficulties in speech production and consequent reductions in speech intelligibility, which is an important concept for diagnosing and assessing effectiveness of speech therapy. In the current study, we investigate which acoustic-phonetic features are most relevant and important in automatically assessing intelligibility and in classifying speech as healthy or dysarthric. After feature selection, we applied a stepwise linear regression to predict intelligibility ratings and a Linear Discriminant Analysis to classify healthy and dysarthric speech. We observed a very strong correlation between actual and predicted intelligibility ratings in the regression analysis. We also observed a high classification accuracy of 98.06% by using 17 features and a comparable, high accuracy of 96.11% with only two features. These results indicate the usefulness of the acoustic-phonetic features in automatic assessments of dysarthric speech