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Q: What does in mean to bring variables up to a power? ( Answered ,   2 Comments )
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 Subject: What does in mean to bring variables up to a power? Category: Science > Social Sciences Asked by: gareth981-ga List Price: \$5.00 Posted: 26 Dec 2002 08:08 PST Expires: 25 Jan 2003 08:08 PST Question ID: 133495
 `e.g. In the context of multiple regression.` Clarification of Question by gareth981-ga on 28 Dec 2002 05:49 PST ```I don't understand what it means to say "variables brought/raised up to a power". What is "power"? What is "raising"?```
 Subject: Re: What does in mean to bring variables up to a power? Answered By: mcfly-ga on 28 Dec 2002 10:29 PST Rated:
 ```Hi gareth, To illustrate my answer I will use the simplified example of 'x to the power n'. This can also be written as x^n or x followed by a superscript n. The letters x and n represent numbers which must be known to solve the equation. If x is 'raised to the power n', then x is multiplied by itself n times. For example, '2 raised up to the power 3' means 2^3 = 2*2*2 = 8. Therefore, the term 'power' means the number of times a variable is mulitplied by itself. 'Raising' is the verb which describes the process of multiplying a variable by itself a certain number of times. In the context of multiple regression, a regression model is obtained through minimising the sum of the squared errors between the model and a sample data set. Therefore a likely application of raising a variable's power is squaring the error between a data point and the predicted value. In this case, squaring the error is synonymous with raising the error to the power 2. A full description of the use of powers and indices is available from the University of Loughborough at http://learn.lboro.ac.uk/olmp/chap1/1_2.pdf The above explanation holds for instances where the 'power' is a positive whole number. To avoid complicating my answer I will not cover negative or non-integer powers unless you ask for it through the 'Request Answer Clarification' option. Additional links: University of Exeter: Introduction to the multiple regression component http://www.ex.ac.uk/~SEGLea/psy2005/introduction.html Queens University at Kingdom: Multiple Regression http://qed.econ.queensu.ca/walras/custom/300/351B/notes/multiple.htm I hope you find this answer useful and informative; please do not hesitate to ask should you require any clarification. mcfly-ga :-)``` Clarification of Answer by mcfly-ga on 28 Dec 2002 10:30 PST ```Search strategy: power raising indices "multiple regression"```
 gareth981-ga rated this answer: and gave an additional tip of: \$1.00 ```Excellently explained, and I like that further resources were suggested and web site links.```

 ```hi gareth! please rephrase your question so that it is a bit clearer I Eradicator```
 ```Do you mean: y = (b1) + (b2)*x + (b3)*x^2 + (b4)*x^4 + ... + (bn)*x^n where n is the power that the independent variable is raised to?```