Login or register (free and only takes a few minutes) to participate in this question.
You will also have access to many other tools and opportunities designed for those who have language-related jobs
(or are passionate about them). Participation is free and the site has a strict confidentiality policy.
|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.
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
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:
R. A. Stegemann
Local time: 13:42
|Thank you for your help!|
3 KudoZ points were awarded for this answer
9 mins confidence:
Ungar, GE Dict. of Physics and Related Sciences
This dictionary also gives the following for "Zerlegung": decomposition, breakup, breakdown, dissection, analysis and disassembly
|Login to enter a peer comment (or grade)|
Return to KudoZ list
KudoZ™ translation help
The KudoZ network provides a framework for translators and others to assist each other with translations or explanations of terms and short phrases.
Search millions of term translations