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Q: What does in mean to bring variables up to a power? ( Answered 4 out of 5 stars,   2 Comments )
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:4 out of 5 stars
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

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

Queens University at Kingdom: Multiple Regression 

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:4 out of 5 stars and gave an additional tip of: $1.00
Excellently explained, and I like that further resources were
suggested and web site links.

Subject: Re: What does in mean to bring variables up to a power?
From: ieradicator-ga on 26 Dec 2002 10:15 PST
hi gareth!

please rephrase your question so that it is a bit clearer

I Eradicator
Subject: Re: What does in mean to bring variables up to a power?
From: zhiwenchong-ga on 26 Dec 2002 14:08 PST
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?

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