Understanding Residual Plots: Impact on Model Relationships and Homoscedasticity

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Discussion Overview

The discussion revolves around the interpretation of residual plots in the context of statistical modeling, specifically regarding the implications for linearity and homoscedasticity. Participants explore how residual plots can indicate the nature of relationships in models and the presence of equal variances.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether residual plots can indicate the type of relationship in a model or if they solely assess homoscedasticity.
  • Another participant suggests that residuals plotted against an independent variable can reveal non-linearity, proposing that a parabolic shape in the residuals indicates a quadratic relationship.
  • A participant raises a scenario where residuals plotted against fitted values show a fanning pattern, questioning whether this indicates a violation of linearity assumptions.
  • It is noted that increasing scatter in residuals for larger fitted values suggests potential issues with homoscedasticity.
  • One participant expresses uncertainty about concluding the implications of their residual plot, seeking clarity on linearity and homoscedasticity assumptions.
  • A participant references external resources to compare their residual plot with known patterns, suggesting a logical connection to linear dependence but acknowledging that interpretations can vary.
  • Another participant proposes that while homoscedasticity may not be assumed, the linearity assumption could still hold, albeit with potential inaccuracies at higher dependent variable values.
  • There is a mention of behavior in linear models related to the slope and its effect on relative errors in the dependent variable.

Areas of Agreement / Disagreement

Participants express differing views on the implications of residual plots for linearity and homoscedasticity, with no consensus reached on the interpretations or conclusions regarding the assumptions of the model.

Contextual Notes

Participants refer to specific characteristics of residual plots and their implications, but there are limitations in the discussion regarding the clarity of assumptions and the specific context of the models being analyzed.

stats_student
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hey guys, just wondering if the residual plot can tell one anything about the type of relationship in a model i.e is it linear or not?

Or does it just tell one if homoscedasticity (i.e equal variances) is observed?

thanks
 
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Hi there,

If I were a computer, I'd print "not enough input" ...

residuals can help you for what you describe, e.g.: if the residuals for some calculated variable (that was assumed to depend linearly on some independent variable) are plotted against that independent variable, you should get something looking like a parabola if the actual dependence is quadratic. Whether you can recognize it from the plot depends on the amount of scatter (noise)
 
what if i just had residuals against fitted values, and the pattern began to fan out towards the right of the residual plot. Does this tell me anything about linearity? i.e can i assume linearity is appropriate for my model? Or should i assume non linearity instead?
 
It means the scatter increases for bigger values of the fitted value. If the errors are only due to the noise, the 'trumpet' should appear to be 'horizontal'.

If I were a computer, I'd now ask to see the plot and a short description of the model .. .:wink:
 
the question that I'm asked is based solely on what the residual plot looks like which is in the file attached. It asks if there are any issues with the assumption of linearity and/or homoscedasticity.

not really sure what to conclude...
 

Attachments

  • residual.jpg
    residual.jpg
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Googling heteroscedasticity and homo idem (I have a lot of experience with fitting, never needed the words, though -- so I learn from this too) I'd say you picture resembles the picture in the first link more than the one in the other.
To me that's logical in a linear dependence relationship (*), but apparently it can be considered separately.

(*) with a correlation coefficient > 1 Especially for residual versus fitted variable. (In this link they have a plot of residual versus prediciting variable.
 
Ah, so i think homoscedasiticty cannot be assumed but the assumption of linearity may still be good however there will be a lot of inaccuracy in the model at higher DV values?
 
By now you're the expert ! Usually for a linear model you have this kind of behaviour when the slope is > 1 ( y = b x with a given b > 1 means same relative error in y as in x )
 
Thanks BvU.
 

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