The individual would be classified in group i

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, the individual would be classified in group I; otherwise the individual would be classified in group II. The linear discriminant function, given in equation, has the same from as that of a multiple regression equation. However, the discriminant coefficients, ' i l s are selected so to correctly classify the individual, whereas the regression coefficients are selected as to minimize the difference between the predicted score and the actual score. In a study to determine if certain tests could be used to predict whether a graduate of a management school is a successful manager or not, a discriminant analysis was carried out by a researcher. The estimation of the coefficients is carried out in such a way that the average score for group I is as far away as possible from the average score for group II. That is are chosen in such a way that they maximize the distance 1 2 D D , where (1) (1) (1) (1) 1 2 3 1 1 2 3 (2) (2) (2) (2) 1 2 3 2 1 2 3 ........ ........ k k k k D l X l X l X l X D l X l X l X l X Where (1) i X and (2) i X are the sample means of the i th predictor variable for group I and group II, respectively. This can be achieved by choosing which maximize the ratio of squared difference between the group means to the variance within the groups. This is expressed as 2 1 2 2 2 1 1 2 2 1 1 m n j j j j m D D G D D D D Where 1 k s is s D l X , 1, 1,2,3 ..... ; 2, 1, .... 1, ..... for i j m i j m n and s k The D score obtained from the discriminant function is used for identifying whether the new object (or individual) with a set of predictor values 1 2 3 , , , ..... k X X X X belongs to group I or group II. The critical score or cutoff score D , which lies between 1 D and 2 D , is chosen in such a way that if the new score (discriminant score) lies on the same side of D and 1 D , then the new individual belongs to group I. Otherwise, the new individual belongs to group II. Usually, we have 1 2 2 D D D
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230 Having developed a linear discriminant function, it is necessary to evaluate effectiveness. One such method used to test the efficiency of the estimated discriminant function is the confusion matrix. It summarizes the number of correct and incorrect classifications that are obtained by the use of the estimated discriminant function. Normally, a part of the observed sample data is used to estimate the linear discriminant function and, then using this function, the remaining individuals (sample data) are classified. The predicted classification is then compared with the actual classification in order to assess the efficiency of the discriminant function in classifying the individuals, when the discriminant function has a high probability of misclassification, either a different D (critical value) is chosen or some more predictor variables are included and a new discriminant function is developed.
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