What is an isolated variable?

Answer 1

In a mathematical equation, the expressions on either or both sides of the equality sign (=) may involve one or more symbols standing for unknown quantities: the "variables." A standard method of solving an equation is by transforming it into another that has the same set of solutions. When all occurrences of a variable appear on just one side of the equality, that variable has been "isolated." Some people might apply a stricter criterion in which one side of the equation must consist only of that variable.

For example, in the equation

x + 3 = 2x + 1

there is one variable "x" but it is not isolated. It can be isolated by subtracting x+1 from both sides to produce the equivalent equation

(x + 3) - (x + 1) = (2x + 1) - (x + 1)

Rules of arithmetic permit the left hand side to be rewritten as "2" and the right hand side to be rewritten as "x", giving

2 = x.

Now x is an isolated variable.

See the Wikipedia article on "Elementary algebra" for details.

The term "isolated variable" is also used in statistics in many slightly different ways. It appears to be used by investigators to refer to an experiment in which exactly one of many factors under experimental control is varied to determine its effect on the experimental outcome. This factor is called the "isolated variable."

Another related meaning is in a multiple regression context where, as part of the analysis, all but one of the explanatory variables is left out: the remaining one is the "isolated variable." See Walter et al., "Creatinine clearance versus serum creatinine as a risk factor in cardiac surgery," BMC Surgery 2003, 3:4 at http://www.biomedcentral.com/1471-2482/3/4 for an example.

Yet another related meaning is that a statistical variable 'X' is "isolated" when there is no direct causal relationship between 'X' and any of the other variables in the statistical model. For an example of this usage, see the "final review questions" page for the "Quantitative Research in Public Administration" course at NC State University at http://www2.chass.ncsu.edu/garson/PA765/ch15qanda.htm.