Suppose you want to investigate the relationship between a dependent variable Y and two potential explanatory variables X1 and X2.
Is the R 2 value for the equation with both X variables included necessarily at least as large as the R 2 value from each equation with only a single X?
Explain why or why not. Could the R 2 value for the equation with both X variables included be larger than the sum of the R 2 values from the separate equations, each with only a single X included?
Is there any intuitive explanation for this?