# When using linear regression analysis to get the fitted values of an outcome, why do the more extreme values tend to be predicted closer to the mean?

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 residuals and outcome.

Samples with lower values of outcome tend to have negative values for residuals, and vice versa for samples with high outcome values.

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 residuals and outcome is 0.58, and the $R^2$ between fitted and 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?