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Thread: Residual plots (against y vs y hat)

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    Residual plots (against y vs y hat)




    I'm reading up on residual analysis and am trying to apply to some data using multiple regression. The residual plot (std res vs the regression fits) looks good. I understand that this plot is conventionally used to test for constant variance. But there is a pattern in the plot of the residuals vs the y values. What is this telling me? If pattern in y, why not a pattern in y hat? For this data Y = Selling Price.

    See attached. Thank you
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    Re: Residual plots (against y vs y hat)

    Quote Originally Posted by Value Ninja View Post
    I'm reading up on residual analysis and am trying to apply to some data using multiple regression. The residual plot (std res vs the regression fits) looks good. I understand that this plot is conventionally used to test for constant variance. But there is a pattern in the plot of the residuals vs the y values. What is this telling me? If pattern in y, why not a pattern in y hat? For this data Y = Selling Price.

    See attached. Thank you
    Generally a pattern in a residual plots tells you that your models suffers from non-linearity in the data (see here for example).

    I don't think we can tell you why the one displays a trend and the other not, as you are not giving us enough information nor are the axis label informative.
    Reading this may help.
    The true ideals of great philosophies always seem to get lost somewhere along the road..

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    Re: Residual plots (against y vs y hat)

    Thanks for your reply. I guess my question is more general. What does a residual plot (vs y hat) actually tell you? Whats the interpretation of that chart? And how is that interpretation different from a residual chart (vs the Y values)? Back to my 2 charts.... I don't understand why the pattern in the res vs y chart wouldn't also manifest in someway in the residual vs y hat chart. I don't think it's important for my main questions, but I believe the pattern in my res vs Y chart is attributed to a relevant but omitted variable. For clarification... The first chart has std residuals on the X axis and fitted values of Sales Price on Y. The 2nd chart is has std residuals vs just the y value (Sales Price). Multiple regression model predicting real estate Sales Price with IV's: Age, Living Area, and Garage.
    Last edited by Value Ninja; 06-03-2015 at 07:33 PM.

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    Re: Residual plots (against y vs y hat)


    My interpretation is that you are seeing signs of non-linearity in for the std residual vs y plot. This would indicate that your model is systematically over and underestimating some values.

    Look at the original x vs y plat and include the trend line. Can you visually detect a trend in the residuals?
    The true ideals of great philosophies always seem to get lost somewhere along the road..

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