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A manipulated variable is not changed on purpose.
There is no answer to a manipulated variable because "a manipulated variable" is not a question!
The independent variable is the value being manipulated or changed, while the dependent variable is the observed result of the independent variable being manipulated. "IF" you change the independent variable, "THEN" what happens to the dependent variable?
operational definition of a manipulated variable
X3 + a3 = (X + a)(X2- aX + a2)Just a formula so that when you see an expression of any value that is additive cubes ( on the left ) then you can factor it. Works in any direction and some expressions can be manipulated into this form for factoring.