I was hoping to get some input on people's thought process when looking at residual plots of a linear regression to assess the fit / whether assumptions are met. I included a plot of a model I'm currently working on as an example. I was always taught when looking at such a plot, it's best not to be so picky i.e. we're looking for serious deviations. Generally the first thing I usually look for is any apparent trend (i.e. what I want is a shapeless cloud of points centered around 0), and then look for evidence of uneven vertical spread, and then check qq plot for normality. Upon initial inspection of my plots, I thought the qq plot looked "normal enough" and there was no apparent trend in my residuals vs. fitted plot. However, it did look like there was evidence of uneven vertical spread (i.e. heteroskedasticity). Now it seems to me like what I thought was uneven vertical spread was really just a downward sloping trend. What do you guys think?
The residual plot shows that you have a lower-bound on your response variable, which is contrary to the assumptions of the standard Gaussian linear regression (I am assuming that this is the model you fit). Your description of the data does not disclose the variables and their allowable values, but presumably you have a response variable that gives only positive values.
In such cases you often get a better model fit using a log-linear model, where you take the logarithm of the response variable before fitting the regression. If you are using a response variable with a known lower-bound (e.g., zero), I would suggest you fit this alternative model. That is likely to conform far better to the regression assumptions than your present model.