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"?

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"

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?