I'm constructing a model to predict the weight of a species of insect given a set of other variables. The plot below shows the performance of my model using a set of test data where the true weight of the insects is known. The x-axis is the true weight of the insect and the y-value is the associated error of my model—the absolute value of the predicted weight - true weight:
From this visual, you can see that I have many insects with relatively low weights. In these cases, my model has a relatively lower predictive error. In contrast, I have relatively few insects which are heavy and the error associated with these predictions displays much more variance along with higher error.
Given this model and the test data, I'd like to find a way to construct confidence intervals for new predictions. For example, if my model predicts a given insect is relatively heavy, the confidence intervals around this prediction would be large. My questions is, how can I do this? A linear model seems inappropriate for this data since most of the points are clustered near the origin. I'm at a loss for how I can construct confidence intervals for my predictions.