Variance: regression, clustering, residual and variance – Liyun Chen ’11

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Liyun ChenLiyun Chen ’11 (Economics) is Senior Analyst for Data Science at eBay in Shanghai, China. The following post originally appeared on her economics blog in English and in Chinese. Follow her on Twitter @cloudlychen


Variance is an interesting word. When we use it in statistics, it is defined as the “deviation from the center”, which corresponds to the formula  sum (x- bar{x})^2 / (n-1), or in the matrix form Var(X) = E(X^2)- E(X)^2=X'X/N-(X'1/N)^2(1 is a column vector with N*1 ones). From its definition it is the second (order) central moment, i.e. sum of the squared distance to the central. It measures how much the distribution deviates from its center — the larger the sparser; the smaller the denser. This is how it works in the 1-dimension world. Many of you should be familiar with these.

Variance has a close relative called standard deviation, which is essentially the square root of variance, denoted by sigma// . There is…

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About Damian Merciar
Damian Merciar is Managing Director of Merciar Business Consulting, http://www.merciar.com, a niche business economics consultancy founded in 1998. He has over twenty years experience in the areas of commercial Business Strategy. He is experienced in the transition environments of nationalized to private sector state utilities and the senior practice of commercial management, advisorial consultancy, and implementation. He has carried out policy advisory work for government ministries and been an adviser to institutional bodies proposing changes to government. He holds an MSc Economics from the University of Surrey’s leading Economics department and an MBA from the University of Kent. Also attending the leading University in the Middle East, studying International Relations and Language, for which he won a competitive international scholarship, and has a BA (Hons) in Economic History and Political Economy from the University of Portsmouth. He is currently based in London.

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