# Zerlebungsformel

## English translation: reduced expression

GLOSSARY ENTRY (DERIVED FROM QUESTION BELOW)
 German term or phrase: Zerlebungsformel English translation: reduced expression Entered by:

 03:21 Jan 5, 2003
German to English translations [PRO]
Science / statistic
 German term or phrase: Zerlebungsformel Closely related to Verschiebungssatz: Besonders einfach gestaltet sich die Berechnung (von Kovarianz) bei Anwendung der Zerlegungsformel Sxy=XY-X Y(lies:s-x-y gleich x-y-quer minus x-quer mal y-quer).Um die Formel anwenden zu koennen, ergaenzen wir die Tabelle um eine Hilfsspalte, welche die Produkte der Werte xi und yi ausweist. Um die Mittelwerte fuer die drei Spalten zu erhalten, werden die Elemente jeder Spalte zu naechst addiert. Dannach ist nur noch durch die Anzahl der Werte pro Spalte zu dividieren, wobei wir auf drei Dezimalstellen runden. Einsetzen der berechneten Spaltenmittelwerte in die Zerlegungsformel liefert dann die gesuchte Kovarianz.
 Local time: 02:32
 reduced expression Explanation:The formula that you have provided is simply a rearrangement of the standard formula for the calculation of covariance. The standard measure of the covariation of two variables is E[(Xi - X)(Yi - Y)] . Expanding this expression obtains E[XiYi - XYi - XiY + XY] In the case where E(Xi) = E(Yi) = 0 the expanded form reduces to E[XiYi + XY]. This is very close to the expression described by your author. In the above expression E is the expected value operator, Xi and Yi are the values of the variables X and Y for the ith observation, and X and Y are the mean values for the variables X and Y. Please forgive the double meaning of the symbols X and Y in the above explanation. It is difficult to write X-bar and Y-bar in ASCII script. You could also use the terms reduced expression reordered expression rearranged expression Depending on the overall context of your text good substitutes for the word "expression" might also include "term", "equation", and "formula". As more than just factoring takes place in the above reduction, I would shy away from the term "factor". Covariance is very basic to statistical analysis, and can be found in any book on elementary statistics. Source: my own brain and many hours of training in statistics and econometrics. Credits: several very patient, perhaps even brilliant instructors and authors of excellent textbooks.
Selected response from:

Roddy Stegemann
United States
Local time: 09:32
 Thank you for your help!3 KudoZ points were awarded for this answer

4reduced expression
 Roddy Stegemann
4factorization formula
 Dr. Fred Thomson

9 mins   confidence:
factorization formula

Explanation:
Ungar, GE Dict. of Physics and Related Sciences
This dictionary also gives the following for "Zerlegung": decomposition, breakup, breakdown, dissection, analysis and disassembly

 Dr. Fred ThomsonUnited StatesLocal time: 10:32Native speaker of: EnglishPRO pts in pair: 5861

neutral  Roddy Stegemann: Although no one could be led to far astray by your suggestion, please see my own entry for what I believe to be a much better rendering of Zerlegung in this particular instance. By the way Happy New Year!
 1 hr

1 hr   confidence:
reduced expression

Explanation:
The formula that you have provided is simply a rearrangement of the standard formula for the calculation of covariance.

The standard measure of the covariation of two variables is E[(Xi - X)(Yi - Y)] .

Expanding this expression obtains
E[XiYi - XYi - XiY + XY]
In the case where E(Xi) = E(Yi) = 0 the expanded form reduces to
E[XiYi + XY]. This is very close to the expression described by your author.

In the above expression E is the expected value operator, Xi and Yi are the values of the variables X and Y for the ith observation, and X and Y are the mean values for the variables X and Y. Please forgive the double meaning of the symbols X and Y in the above explanation. It is difficult to write X-bar and Y-bar in ASCII script.

You could also use the terms

reduced expression
reordered expression
rearranged expression

Depending on the overall context of your text good substitutes for the word "expression" might also include "term", "equation", and "formula".

As more than just factoring takes place in the above reduction, I would shy away from the term "factor".

Covariance is very basic to statistical analysis, and can be found in any book on elementary statistics.

Source: my own brain and many hours of training in statistics and econometrics.

Credits: several very patient, perhaps even brilliant instructors and authors of excellent textbooks.

 Roddy StegemannUnited StatesLocal time: 09:32Native speaker of: EnglishPRO pts in pair: 285

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