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Issue with residual analysis of a linear regression
Disclamer 2 : My statistic skills are pretty low so I may be way off the mark.
Tl;Dr : Applied a linear regression on some data but during the residual analysis I found out that the scatterplot of PredictedValuesVSResiduals is oddly shaped, wich does not respect the postulate of homoscedasticity, and I can't figure out why. What should I do?
Hello, The Tl;Dr tells it all but I guess you may need more info to understand where I'm coming from so I'll detail what I did. The instructions are in french so they may be some weird named things (like groupe instead of group) or stuff I don't know how to translate in english, sorry :<
This assignment consist of a database about an experiment where they research the link betwin substance abuse and how much people recall important events in their life where they asked 14 drug addicts and 14 non-addicted people (control group) to list the life events they remember.
DV : nb.ev wich is the number of reported events. IV : age given in years IV : groupe dummy variable where 1=DrugAddict 0=NonAddict
The hypothesis are that :
- Age predicts the number of significant events reported.
- The number of significant events reported is greater among drug addicts than among non-addicts.
- The effect of drug addiction on the number of significant events reported changes with age.
I thought that by answering the third hypothesis I'll have the data to answer the others and sice it is a Continuous Variable (nb.ev) predicted by the interaction betwin a Dummy Variable (groupe) and Continuous Variable (age) I used a Multiple Linear Regression.
The groupe variable is allready coded in 0 and 1 in the data set. Since there's an interaction betwin groupe and age I centered age to avoid multicollinearity, giving me age_c and the interaction of interest being groupeXage_c.
Descriptive statistics of all variables, where mean age_c=0
Redudnacy test, all R2 < 0.90 so no multicollinearity
Then I began the residual analysis and allready the Histogram of Raw Residuals doesn't completely fit a normal distribution, but not by much so I thought it was okay. The Normal Plot of Residuals fits (except maybe for that first value). Raw Residuals VS age_c, Raw Residuals VS groupe and Raw Residuals VS groupeXage_c seems to show homogeneous distributions.
And then I got this Predicted Values VS Residual Scores scatterplot that clearly shows a structure in the distribution. Wich it shouldn't. And I have no idea why. I guess I did a mistake somewhere but I just donit get it.
I thgout it might be because of an extreme value and there is one with a high Cook's distance but from what I know if it's < 1 it should be allright?
I went thourgh the Regression anyway and from what I can tell:
- age doesn't predict nb.ev
- the effects of groupe on nb.ev doesn't change with age
(I didn't figure out yet how to answer the 2nd hypothesis)
- Edit: I'm an idiot, nb.ev is actually greater among non-addicts since bgroupe is significative and negative and groupe1=DrugAddict
I hope this wall of text isn't too confusing and thanks for your time!