Understanding Residual Plots: Impact on Model Relationships and Homoscedasticity

  • Thread starter stats_student
  • Start date
  • Tags
    Plot
In summary, the residual plot can help you determine if a model is linear or not, and can also help you determine if homoscedasticity (i.e. equal variances) is observed.
  • #1
stats_student
41
0
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
 
Last edited:
Physics news on Phys.org
  • #2
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)
 
  • #3
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?
 
  • #4
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:
 
  • #5
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
    11.8 KB · Views: 379
  • #6
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.
 
  • #7
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?
 
  • #8
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 )
 
  • #9
Thanks BvU.
 

FAQ: Understanding Residual Plots: Impact on Model Relationships and Homoscedasticity

What is a residual plot?

A residual plot is a graphical representation of the difference between the observed values and the predicted values in a regression analysis. It is used to check the assumptions of a linear regression model, such as the linearity and homoscedasticity of the data.

How do you interpret a residual plot?

In a residual plot, the vertical axis represents the residuals (the difference between the observed and predicted values) and the horizontal axis represents the independent variable. A good residual plot should have no clear pattern or trend, indicating that the regression model is a good fit for the data. Patterns or trends in the residual plot may suggest that the model is not appropriate for the data.

What does a positive/negative residual mean?

A positive residual means that the observed value is higher than the predicted value, while a negative residual means that the observed value is lower than the predicted value. Positive and negative residuals should balance out in a good residual plot, indicating that the model is making equally good predictions for both high and low values of the independent variable.

Can a residual plot help identify outliers in the data?

Yes, a residual plot can help identify outliers in the data. Outliers are data points that fall far from the overall trend of the data. In a residual plot, outliers will appear as points that are far from the horizontal line at y=0, indicating that they have large residuals. These outliers may need to be further investigated and potentially removed from the data set.

Is a residual plot necessary for all regression analyses?

Yes, a residual plot should be used for all regression analyses. It is an important tool for checking the assumptions of the model and identifying potential problems. Without a residual plot, it is difficult to determine if the regression model is a good fit for the data and if the results can be trusted.

Similar threads

I Normality of errors and residuals in ordinary linear regression
Replies
3
Views
2K
I What are the commonly used estimators in regression models?
Replies
23
Views
3K
I Time Series Models vs Models Used for Cross-sectional Data
Replies
14
Views
1K
I Nonlinear Least Squares or OLS for Nonlinear Models?
Replies
7
Views
2K
I Linear Model with independent categorical variable
Replies
5
Views
1K
Understanding Overlay Plots in Linear Regression
Replies
2
Views
10K
I Fitting two models in sequence with parameters in common
Replies
12
Views
2K
MATLAB To what extent is the fit to experimental data good?
Replies
12
Views
3K
I Linear regression, feature scaling, and regression coefficients
Replies
8
Views
2K
Time Series: Residuals of ARMA model
Replies
5
Views
8K

Hot Threads

Recent Insights

Back
Top