I am working on a project in which I am using several independent variables to "predict" the values of an outcome using linear regression.
In R this is done quite simply as
model <- lm(outcome ~ predictor1 + predictor2 + predictor3) fitted <- model$fitted.values
I am interested in the difference between the predicted values and the actual values - i.e. how accurate the predictors are.
residuals <- model$residuals
My question relates to the relationship between
Samples with lower values of
outcome tend to have negative values for
residuals, and vice versa for samples with high
Plotting the values against one another is the simplest way to see this:
The $R^2$ for the original LM (outcome ~ predictors) is 0.42, the $R^2$ between
outcome is 0.58, and the $R^2$ between
outcome is 0.39.
What could explain the phenomenon? Why would samples with high
outcome tend to be predicted lower than they actually are, and vice versa for lower values of
outcome? Or indeed, am I missing something conceptually here?
Many thanks for your input
Edited (13.08.20) to include an updated plots and terminology (now use "residuals" rather than "difference") - but in essence the questions remains the same. Thanks all for the input so far.