I'm quite new at linear regression. I get the following Residuals vs Fitted plot with parallel straight lines:
I do not understand why there are two parallel lines. Is there a problem with my data?
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Your original data consist of a pair of parallel lines!
Something like this:
The red line indicates the least squares linear fit for this one-predictor case.
You then subtract the linear fit in red from the data laying on that pair of parallel lines to get a downsloping pair of lines in the residuals (calculating residuals from fitted is a skew transformation of the plot vs x, and making it vs fitted simply rescales the x-axis:
If you have multiple predictors the plot would not look "neat" like this (with two clean lines), though. Are you certain you fitted multiple regression in your display?
A linear fit is generally not suitable for such data since the fitted line goes outside 0-1 (see where with my data the line crosses to above the data at about x=4?). More commonly a model that predicts the probability that the response is 1 would be used, such as logistic regression.
You may find the discussion of the model you fitted with the one I just mentioned at this post of some additional value.