Abstract: The linear regression has been studied particularly with respect to its identical relationship to the Fisher's Discriminant Analysis (FDA). In this paper, we prove that the coefficient vector of the least squares regression is identical to the vector of coefficients of the Fisher's Discriminant Analysis. We therefore refer to the classification procedure using the least squares regression as Regression Discriminant Analysis (RDA). We further carry out empirical investigations using both real world and simulated datasets, to show that a classification procedure based on both RDA and FDA are identical.