What is the interpretation of a residual against fitted values plot?

Question

After performing a regression, you get the residuals and the fitted values for the dependent variable. Plotting them can yield insights over the violation of OLS-assumptions. I wonder If I correctly interpret this output as it seems that there is no proper explanation for it anywhere.

I heard you can draw following conclusions from this plot:

• distribution of the error (are the residuals i.i.d.?)
• homoskedasticity / heteroskedasticity
• autocorrelation between the residuals
• equality of the conditonal mean of u and the unconditional mean
• misspecification of the model

As an example I would like to present following plot which suggests a violation of an OLS-assumption.

Residuals against fitted values:

My interpretation:

• the error term is not i.i.d., it depends on the size of the fitted values and thus on the explanatory variables

• absence of homoskedasticity as the conditional variance is not equal to the unconditional variance

• presence of autocorrelation

• unconditional mean is not equal to conditional mean

• model is wrongly specified, non-linear might be better

Answer 1

This could help a bit:

Here are the characteristics of a well-behaved residual vs. fits plot and what they suggest about the appropriateness of the simple linear regression model:

• The residuals "bounce randomly" around the 0 line. This suggests that the assumption that the relationship is linear is reasonable.

• The residuals roughly form a "horizontal band" around the 0 line.
  This suggests that the variances of the error terms are equal.

• No one residual "stands out" from the basic random pattern of residuals. This suggests that there are no outliers.

Source: https://online.stat.psu.edu/stat462/node/117/#:~:text=The%20residuals%20%22bounce%20randomly%22%20around,the%20error%20terms%20are%20equal.

Regards.

FJ