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I've been having some troubles interpreting my residual plot to check the assumptions for multiple linear regression. I've checked for independence by calculating Durbin Watson and I've checked for collinearity, both okay. However, my residual plot looks very strange to me, and I think it's because my dependent variable (and independent variables as well) is job satisfaction, measured with only 1 question where the respondents had to indicate their satisfaction with 1, 2, 3, 4 or 5, ranging from very satisfied to not satisfied. So there are only 5 different values for my dependent variable. I think that is why my residual plot has these strange parallel lines.

However, I have no idea how to check for a linear curve and normal distribution. I think homoscedasticity is okay, right? But I think it's not a good sign that the parallel lines aren't all distributed around zero.

Can anyone help? enter image description here

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    $\begingroup$ The lines in residuals vs $y$ shouldn't be scattered about $0$; it's the plot of residuals vs fitted ($\hat{y}$) that should have that. $\endgroup$
    – Glen_b
    May 7, 2017 at 10:47

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I believe you'd have to provide more details on your problem/code so we can address the residuals not being around zero. But yes, it probably means some extreme specification mistake; one which could also be causing the upward trend, maybe for the lack of another relevant variable.

Still, the vertical lines are to be expected when modelling categorical data using linear models, after all you don't have observations for classes with values in between. But unless such approach is being explicitly required, I'd say Logit/Probit models better suited for such data.

In any case, you should take a look at:

How to perform residual analysis for binary/dichotomous independent predictors in linear regression?

The discussion on residual analysis for such models is quite insightful.

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