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Residuals randomness

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  • #42557

    gt
    Participant

    What does it mean when the residuals plot (residual vs fitted values) look like a funnel ? What can be the causes? Where should i look first?
    is there a way i can verify the error variance?
    thx

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    #134431

    Mr IAM
    Participant

    I “think” that a funnel shape in the residuals plot suggests that the data was not collected in a random order.  But, I could be wrong about this… See what some other posters have to say.

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    #134436

    G
    Participant

    My thought on this is a that if the residuals aren’t random then your data may not have had a normal distribution prior to the regression  analysis… (skewed data?)
    Did you validate your data was normally distributed prior to the regression?
    g~
     

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    #134438

    Ken Feldman
    Participant

    If you are trying to fit a linear line to the data and the data is not linear, then possibly the residuals might appear to be funneling or getting further away from the line.

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    #134443

    Robert Butler
    Participant

       If you are plotting the residuals against the predicted and you get a funnel shape  which looks either like a   where the vertical axis are the residual values, the horizontal axis are the predicted values and the 0 line for the residuals more or less bisects the < then the funnel is telling you that as your predicted values increase ( ) the variance is decreasing as the predicted values of the response increase.
      In the first case this means there is more error associated with the prediction of higher values of the response and in the second case there is more error associated with prediction of low values of the response.  In short, over the region of interest the variance is not constant and your residuals are not normally distributed.  Since the normal distribution of the residuals (not the X’s or the Y’s) is necessary for valid tests of regression term significance you will need toeither transform the Y’s or run a weighted least squares regression. 
      This coupling of mean and variance can occur for a variety of reasons.  One of the most common causes of this kind of coupling occurs when you exceed the ranges of a measuring device.  For example, you have a metering system that is calibrated for the range of 0-1 units but you suddenly find yourself measuring in the range of 1-2 units.  As you move away from 1 the uncertainty of the measurements increases and you get the funnel shape in the residual pattern.

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    #134450

    BTDT
    Participant

    GT:The variances should not be a function of the mean. The funnel usually indicates some kind of data transformation of the responding variable (Y) is required to stabilize the variances.Cheers, BTDT

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    #134733

    Chris Butterworth
    Participant

    The reason we experiment is to learn about our processes. The funneling is telling you something about your process that you didn’t know before. I would investigate this further to see if I can take advantage of this new knowledge e.g. reduce process variation.
    Chris
     
     

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    #134737

    Jonathon Andell
    Participant

    Best answer so far!

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