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This provides a more conservative test of the model. Thus, a set of cases should, if possible, be saved for this purpose. Having completed the analysis, the results can be used to predict the work potential of job candidates and hopefully serve to improve the selection process. There are more complicated cases, in which the dependent variable has more than two categories. For example, workers might have been divided into three groups: high performers, average performers, low performers. Discriminant analysis allows for such a case, as well as many more categories.

The interpretation, however, of the discriminant function scores and coefficients becomes more complex.

## The Benefits of Performing Discriminant Analysis on Survey Data

The books included in the "Further Reading" section below explain in detail how to perform discriminant analysis with multiple categories and provide in-depth technical discussions. Lawler ]. Huberty, Carl J. Applied Discriminant Analysis. New York: Wiley, Klecka, William R. Discriminant Analysis for Social Sciences.

Lachenbruch, Peter A. Discriminant Analysis. New York: Hafner Press, McLachlan, Geoffrey J.

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E-mail: Show my email publicly. In this case there are of each group and so an equal chance an input belongs to each one. As well, group 1 has a mean of Calculating an estimate for standard deviation we get. Plugging these values into the discriminant function for group 1 we get. We would just need to evaluate the discriminant function K times instead of twice. If we relax the constraint that Var X is constant throughout the K classes however we arrive at a slightly different technique called Quadratic Discriminant Analysis or QDA. But that is a topic for another post. Thanks for reading and leave any comments or questions below! Sign in. Get started.

## ML | Linear Discriminant Analysis

Ryan Gotesman Follow. Towards Data Science Sharing concepts, ideas, and codes. The regression coefficients are b 0 , b 1 , and b 2. On the right side of the equation, the only unknowns are the regression coefficients; so to specify the equation, we need to assign values to the coefficients. To assign values to regression coefficients, we consult the regression coefficients table produced by Excel:.

Here, we see that the regression intercept b 0 is So the least-squares regression equation is:. This is the discriminant function that we can use to classify incoming students as likely graduates or non-graduates. The fact that our discriminant function satisfies a least-squares criterion does not guarantee that it fits the data well or that it will classify students accurately.

The coefficient of multiple determination measures the proportion of variation in the dependent variable that can be predicted from the set of independent variables in the regression equation. When the regression equation fits the data well, R 2 will be large i. The coefficient of multiple determination is a standard output of Excel and most other analysis packages , as shown below. A quick glance at the output suggests that the regression equation fits the data pretty well.

## Discover Which Variables Discriminate Between Groups, Discriminant Function Analysis

The coefficient of muliple determination is 0. Another way to evaluate the discriminant function would be to assess the statistical significance of the regression sum of squares.

This table tests the statistical significance of the independent variables as predictors of the dependent variable. The last column of the table shows the results of an overall F test. The p value 0.

### What is Discriminant Analysis?

Like the coefficient of multiple correlation, the overall F test found in the ANOVA table suggests that the regression equation fits the data well. In the real world, we are probably most interested in how well we can classify observations, based on outputs from the discriminant function.

StatQuest: Linear Discriminant Analysis (LDA) clearly explained.

Recall that the discriminant function was designed to predict 0's and 1's. The incorrect classifications are highlighted in gray. One student who did not graduate was incorrectly assigned to the "graduating" group, and one student who actually graduated was incorrectly assigned to the "not graduating" group.