The personnel director of a firm has developed two tests to help determine whether potential employees would perform successfully in a particular position. To help estimate the usefulness of the tests, the director gives both tests to 43 employees who currently hold the position. Table 14.15 gives the scores of each employee on both tests and indicates whether the employee is currently performing successfully or unsuccessfully in the position. If the employee is performing successfully, we say that the employee is in group 1; if the employee is performing unsuccessfully, we say that the employee is in group 0. We can use discriminant analysis to classify a potential employee into group 0 or group 1. In discriminant analysis we develop a discriminant function
d = b0 + b1x1 + b2x2
that is used to discriminate between employees in group 0 and employees in group 1. One way to determine the discriminant coefficients b0, b1, and b2 is to calculate the least squares point estimates of the parameters of the regression model y = β0 + βlxl + β2x2 + ε. Here, we set the dependent variable y equal to 1 if an employee is in group 1 and equal to 0 if an employee is in group 0. If we use the data in Table 14.15, we find that b0 = -5.9291, b1 = .05858, and b2 = .015322. It follows that the discriminant function is
d= -5.9291 + .05858x1 + .015322x2
To use the discriminant function to classify future potential employees, we calculate d for each observed employee in Table 14.15. We next calculate the average of the d values for the n0 = 20 employees in group 0, which is 0 = .2475, and the average of the d values for the n1 = 23 employees in group I. which is 1 = .7848. We then compute the cutoff value

It can be proven that we minimize the probability of misclassification if we classify a prospective employee into group 1 if and only if d for the prospective employee is greater than the cutoff value c. For example, consider a prospective employee who scores a 93 on test 1 and an 84 on test 2. For this prospective employee
d = -5.9291 + .05858(93) + .015322(84) = .805888
Since d = .805888 is greater than c = .5349, the employee is classified into group 1.
a. Calculate d for a prospective employee who scores an 85 on test 1 and an 82 on test 2. Then, classify this employee into group 0 or group 1.
b. Statistical software packages do not use regression analysis to determine the discriminant function. They use a somewhat more sophisticated technique that produces either equivalent

Transcribed Image Text:

nodo nd 202475) 23(.7848) not ni 20 23 5349