Consider using LDA for a binary classification problem. Suppose we have p-dimensional predictors x Rp , and the response variable y {1, +1}. The numbers of data points in class 1 and class 2 are N1 and N2, respectively.

1) If N1 = N2, show the LDA classification rule.

2) If N1 not equal N2, show the LDA classification rule.

3) Use linear regression, describe the condition under which the linear regression results in the same classification rule as in LDA.

4) If we use a different coding scheme, e.g., y {0, 1}, how does this affect your conclusion in 3)?