# Solved – Hellwig’s method of selection of variables

Hellwig's method is a method of selection of variables in linear model. It is widely used in Poland, probably only in Poland because it is really hard to find it in any scientific paper written in English.

Description of method:

\$m_{k}\$ – set of variables in k'th combination (there are \$2^{p}-1\$ combinations, where p is number of variables)
\$r_{j}\$ – correlation between \$Y\$ and \$X_{j}\$
\$r_{ij}\$ – correlation between \$X_{i}\$ and \$X_{j}\$
\$H_{k}=sumlimits_{j in m_{k}}frac{r_{j}^2}{sumlimits_{i in m_{k}}|r_{ij}|}\$

Choose the combination of variables with the highest \$H_{k}\$

Question
Is this method used anywhere outside the Poland?
Does it have any scientific background? It seems that it based only on intuition that variables in a model should by highly correlated with \$Y\$ and poorly correlated with eachoter.

Contents

#### Best Answer

After spending too long on web research, I'm pretty sure the source of 'Hellwig's method' is:

Hellwig, Zdzisław. On the optimal choice of predictors. Study VI in Z. Gostkowski (ed.): Toward a system of quantitative indicators of components of human resources development; Paris: UNESCO, 1968; 23 pages. [pdf]

Google Scholar finds 3 papers that have cited it. None of them appear particularly noteworthy. So I think the answer to your first question is 'No'. As for your second question, I'll leave you to study the paper as i've spent far too long on this already. But from a skim, it appears the motivation behind his method was to avoid calculations that were very tedious without an electronic computer:
"… generally speaking one has to compute \$2^n-1\$ times the inverse matrices, which is of course an extremely dull perspective. The method we are going to present in this paper does not require finding inverse matrices." (p3-4).

Biographical note:
A little further googling reveals Zdzisław Hellwig was born on 26 May 1925 in Dobrzyca, Poland, and was for many years professor of statistics at the Wrocław University of Economics. There was a scientific meeting to honor his 85th birthday in November 2010.

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