Which model is better(Occam's Razor)?

Question

If there is a bunch of data that follows a linear pattern, is it better to have a theory with more parameters to account for the data or a simpler theory to account for the data? Is it better to have a model with a bunch of parameters in which we can vary the value of the parameters to fit the data or is it better to have a simple model with fewer parameters? For example:

x^2 + 2x + 9 = y
2x +9 = y

why is occam's razor accepted? Isn't it to extreme. Shouldn't there be a theory which is not too simple and not to complex?

Answer 1

Ditto what ron971 said. Occam's razor only comes into play when comparing two theories with equally good accuracy and explanatory powers. For a linear pattern, having an x^2 term makes that formula inherently less accurate than the truly linear 2x+9 one, thus Occam's razor can not be applied to your above example.

When you introduce extra, unnecessary factors or explanations into a theory, those extra terms must then also be accounted for. Since they are by definition unneeded (because the simpler explanation can explain just as accurately without them), there is then no data that can account for the extra factors, and their inclusion amounts to an unfounded assumption. Having unfounded assumptions in a theory, in turn, knocks it down from being a theory to a hypothesis or even merely a conjecture.

Answer 2

Keep in mind that Occam's Razor favors the simplest explanation (the one with the fewest constructs or terms) that accounts for all relevant data. There is no advantage to decorating a theory with pretty but unnecessary and cumbersome constructs.