# Do residuals vs fitted plot have to be concentrated around the x-axis?

Since the residuals and the fitted values are independent, we would expect the residuals to be distributed evenly around some horizontal line, if the model is linear. But does this horizontal line have to be the x-axis? I think in the cases when the expected value of the residuals is not zero, we can have that the fitted values are distribued evenly around some lines above or below the x-axis?

Here is an example to illustrate. The x-axis is the residuals and the y-axis is the fitted values. All the points are above the x-axis, but they seem to be evenly distributed around some horizontal line. Can we claim that the model is linear?

• It is more usual to plot $\hat y$ horizontally and residuals vertically. The residuals having a mean of $0$ is what you would expect from ordinary least squares linear regression (otherwise you can reduce the sum of squares by shifting all the $\hat y$s by the same amount), and something similar to that often happens in other modelling Commented Dec 9, 2021 at 9:21
• @ Henry Thanks for your clarification. To summarize, we generally put residuals on the y-axis so that if the model is linear, the data points should fluctuate around the x-axis?
– XXX
Commented Dec 9, 2021 at 9:31