The Effects Of Different Response Values In Linear Regression Model On Binary Classification

In this paper, we mainly investigate the effects of different response values and critical values in linear regression model on the classification problem of two populations. Firstly, we assign the mean and the midpoint of response values to the critical value in the discriminant criterion. In these two cases, we discuss the effects of different response values on classification for the balanced and unbalanced data respectively. Furthermore, we compare the discriminant method of assigning the mean of response values to the critical value with the classical discriminant methods such as the classical Mahalanobis distance discriminant and Bayes discriminant. We find the inner relation between these methods as well as the advantages and disadvantages of them. In addition, we make the response values fixed, and discuss three circumstances which the critical values in the discriminant criterion are unequal. We pick out the most appropriate critical value from these three critical values which can make the misclassification rate smallest.On the basis of the theoretical results, we use the r language and 5-fold Cross-Validation criteria to simulate the balanced data, unbalanced data and the real data WDBC respectively, the response values are different and the critical value is assigned to the mean of the response values. We get the simulation results being in conformity with the theoretical conclusions in this paper. Furthermore, we also assign the response variable three sets of values, and let the critical value be 0 or the mean of the response values or the midpoint of the response values. In these nine cases, we simulate their misclassification rate and get the simulation results consistent with theoretical results. We also find the relation between them and choose the most appropriate critical value which can make the misclassification rate smallest in order to have a better classification for the new data.