In general, if p is the number of predictor variables and k is the number of groups

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In general, if p is the number of predictor variables and k is the number of groups for the outcome variable in a DA, how many different discriminant functions can be obtained to differentiate among groups? (This question assumes that the X predictor variables have a determinant that is non zero, that is, no individual Xi predictor variable can be perfectly predicted from scores on one or more other X predictor variables.)
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