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Why does the correlation coefficient of a predictor increase when we remove a relevant predictor in...

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Basic Math

Why does the correlation coefficient of a predictor increasewhen we remove a relevant predictor in a multilinear regression?For example, if we are regressing income on education, gpa, andcollege rank and then remove college rank from the regression wewould see an increase on the correlation coefficient of educationand gpa. What is the intuitive explanation for this?

Similarly, we see a decrease in the correlation coefficientswhen we add a variable. What is the reason for this relationship aswell?

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