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

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

Similarly, we see a decrease in the correlation coefficients when we add a variable. What is the reason for this relationship as well?

Expert Solution

milcah answered 1 year ago

what does it mean when Correlation Coefficient: .500 and the Coefficient of Determination: .25

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