# Residual plots (against y vs y hat)

#### Value Ninja

##### New Member
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

#### TheEcologist

##### R purist
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.

#### Value Ninja

##### New Member
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.

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#### TheEcologist

##### R purist
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?