How to Teach the Solution of the Problem of Linear Regression, Direct Approach in a Closed Form

The paper refers to the situation teaching basic statistics to students with little background in mathematics, especially no knowledge in differential calculus. Goal of the paper is to show that knowledge of basic linear algebra is sufficient to explain the problem and the solution of linear regression, and this in a closed form. This approach avoids black box teaching where students learn how to get results and don’t learn why, and it replaces the so-called Gaussian normal equations which use partial derivatives. Starting point is the so-called residual variance of the dependent variable. The paper presents a decomposition of this variance in three non-negative terms, hence the solution of the problem of linear regression is obvious. Besides, this decomposition may be used to explain properties of the correlation coefficient and the coefficient of determination.