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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?

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