curve fitting is a very difficult and time wasting method while regrresion is more to use as compare to curve fitting
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of, pertaining to, or determined by regression analysis: regression curve; regression equation. dictionary.com
Regression techniques are used to find the best relationship between two or more variables. Here, best is defined according to some statistical criteria. The regression line is the straight line or curve based on this relationship. The relationship need not be a straight line - it could be a curve. For example, the regression between many common variables in physics will follow the "inverse square law".
a linear curve does not represent x^2
About $50.
well a polygon has angles and a curve has none.