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In a multiple regression, why is the estimated correlation between the coefficients beta 1 hat and...

In a multiple regression, why is the estimated correlation between the coefficients beta 1 hat and beta 2 hat positive when the correlation between the regressors is negative?

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Answer #1

The beta values, or b coefficients, are estimates of the parameters of the straight line equation underlying your data set. The absolute value of the correlation coefficient is a measure of the alignment of the points in your data set. The sign of the coefficient indicates whether the slope of the fitted line is positive or negative.

We take absolute value because of this the estimated correlation between the coefficients beta 1 hat and beta 2 hat positive when the correlation between the regressors is negative

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