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Oct
1
comment Straight line through data by eye - least squares?
Figure 6-3 shows a comparison of least squares, least absolute and fit-by-eye for a set of 15 points, where the fit-by-eye is between the two others.
Oct
1
awarded  Scholar
Oct
1
accepted Straight line through data by eye - least squares?
Sep
30
comment Straight line through data by eye - least squares?
@GerryMyerson Thanks for the link! That pretty much is what I was looking for. And you're right. It's more a question for mathematical modelling and cognitive science. If you post that as an answer I'll accept.
Sep
30
revised Straight line through data by eye - least squares?
Limited scope to simple sum of exponent residuals.
Sep
30
comment Straight line through data by eye - least squares?
@joriki Ok, I see what you and Karolis are saying. But assuming we have realistic data, that situation won't arise. If the data is pre-filtered somewhat such that there exists a meaningful least sum of error^p, then I believe there will be a "natural" value for p that we tend to use when penalising residuals. It obviously requires that there is some (probably normally distributed) random noise on the data. Otherwise no "minimal error" fit makes sense.
Sep
30
awarded  Editor
Sep
30
revised Straight line through data by eye - least squares?
Added example plot
Sep
30
comment Straight line through data by eye - least squares?
@joriki Indeed. That's what I'm after. We humans live in a world that is very well described by mathematics. But no-one would suggest that we actively use mathematics to go about our daily lives. For example catching a ball involves some moderately complex ballistics - but of course we don't work out simultaneous equations. Assuming there exists a "typical" line that people draw given a set of data, and assuming there exists an exponent which would analytically produce the same line, we can say something about how our built-in error penalty function works.
Sep
30
comment Straight line through data by eye - least squares?
@KarolisJuodelÄ—, I think a plot of linear data with a bump would be a special case. Beside, what you describe is exactly what I'm saying: We would intuitively allow some points to be far away from the line in favour of getting most points close to the time (i.e. follow the linear data (many points) and ignore the bump (a few outliers). I know I could just ask a bunch of people - that's in fact exactly what I should do. But I know someone has already done that! I just don't remember where I saw it, nor what the answer was.
Sep
30
comment Straight line through data by eye - least squares?
@PatrickLi, I mean that if rather than finding the line of best fit given a chosen exponent, you find the exponent given the line of best fit.
Sep
29
awarded  Student
Sep
29
asked Straight line through data by eye - least squares?