The candidate writes: "We choose this model because it produces the optimal solution – a maximized R² and a minimized count of variables.  Under the four-variable model, only 29.46% of the variance in violent crime rate can be explained by the X’s.  Therefore, although the four-variable model is the most parsimonious of those that we have observed, it may not be used to accurately explain violent crime rates." Actually, 29.46% is quite good for a regression explaining crime rates. The analysis is done properly, and one would not expect a much higher correlation.