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What observations could i do?

Is it ok to artificially weight observations in a range of the independent variable when running a non-linear regression?

  • When I run the regression, the line fit great through the range of the independent variable where I have a high density of observations but not very well in the range with a low density of observations.  However, I want the line to also fit the data points that are in the area with low density because I want to manage to the data points that I do have.  Do I somehow decrease the integrity of the resulting curve by artificially weighing the observations in the low density range of the independent variable when running the non-linear regression?  What other considerations should I be exploring?

  • Answer:

    With a non-linear regression of the form y = b1x1 + b2x2^2 the form of the equation can sometimes be determined by an area of high density, which means that you are wildly wrong in the extremes.  I would consider some sort of non-parametric regression (a loess, for example), or perhaps a spline regression.  Can you post a scatterplot?  Or tell us more about your data?

Jeremy Miles at Quora Visit the source

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This suggests that what you have is a non-linear relationship so modelling with a linear regression might not be appropriate at all.  A transformation or alternative regression approach might be better.

George Savva

IMO in most cases I think altering the data for no other reason than to fit a model is self deception pure and simple and you should rather change your model. Perhaps separate models for the high-density & low density regions would be appropriate in your situation.

Paavo Suhonen

Just throwing another idea out there, but could you remove datapoints from the high-density area?  Seems like another way to achieve a similar goal?

Murthy Mathiprakasam

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