I have a dataset containing weights and heights of 1000 people. I used simple linear regression to arrive at an equation. I wonder why cannot I try to fit an ellipse or a parabola or some curve. Is there is a theory which helps to decide whether a curve or a straight line fits a data.
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Well, an ellipse is not a function, and we try and fit data to functions. – siegehalver Jun 14 '17 at 02:33
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This question doesn't make a lot of sense unless you define clearly what is meant by "best-fit" for the data. – user160738 Jun 14 '17 at 03:31
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This arguably is the domain of statistics, but of course there is some math involved. – Matt Samuel Jun 14 '17 at 03:32
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@John Ruby : Nothing prevents you from fitting another kind of curve than a straight line. It is up to you to chose a convenient equation to model the phenomena that you are studying. And it's important as well to clearly define the criteria of fitting, i.e. the mathematical definition of what you call "best fit" convenient for your model. The theory to decide whether a curve or a straight line depends on the context, physical-, modeling-, statistical-,... theories. – JJacquelin Jun 14 '17 at 05:03
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It depends on whether you have a model that the data should fit.
In your case, for example, if the bodies are all of similar shape, you might expect that $weight \sim a\ height^3 $ for some $a$.
Therefore $\log weight \sim \log a +3\,\log height $ so a linear plot of log weight vs. log height might be informative. In particular, if this does not show a linear relationship, it might indicate that the proposed relationship does not hold.
marty cohen
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