Orthogonal Projection in Teaching Regression and<br>Financial Mathematic


Authors: 
Farida Kachapova and Ilias Kachapov
Volume: 
18(1)
Pages: 
online
Year: 
2010
Publisher: 
Journal of Statistics education
URL: 
http://www.amstat.org/publications/jse/v18n1/kachapova.pdf
Abstract: 

Two improvements in teaching linear regression are suggested. The first is to include the<br><br>population regression model at the beginning of the topic. The second is to use a geometric<br><br>approach: to interpret the regression estimate as an orthogonal projection and the estimation<br><br>error as the distance (which is minimized by the projection). Linear regression in finance is<br><br>described as an example of practical applications of the population regression model.<br><br>The paper also describes a geometric approach to teaching the topic of finding an optimal<br><br>portfolio in financial mathematics. The approach is to express the optimal portfolio through<br><br>an orthogonal projection in Euclidean space. This allows replacing the traditional solution of<br><br>the problem with a geometric solution, so the proof of the result is merely a reference to the<br><br>basic properties of orthogonal projection. This method improves the teaching of the topic by<br><br>avoiding tedious technical details of the traditional solution such as Lagrange multipliers and<br><br>partial derivatives. The described method is illustrated by two numerical examples

The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education