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I have just run both Pearson's correlation analysis and linear regression analysis, and both sets of correlations differ. Is this supposed to be the case and if so, could somebody please tell me why?

Thank you.

Vicky
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1 Answers1

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Normally, if you have just two variables, the Pearson correlation coefficient is the same as the standardized beta coefficient in the linear regression. However, if you have more than two variables you will normally not be able to reproduce the Pearson correlation coefficients in a linear regression where all variables entered the model.

Suppose you have three variables, x1, x2 and y and you get Pearson correlations between the three variables

1) r(x1,x2) > 0,
2) r(x1,y) > 0
3) r(x2,y) > 0

then you will not be able to reproduce the correlations 2) and 3) in a multiple linear regression where y is the dependent and x1 and x2 are the independent variables. This is because x1 and x2 do correlate themselves. The only case in which a reproduction of the correlation 2) and 3) in a multiple linear regression would be possible is when correlation 1) is equal to zero.

The term you may look for further information is multicollinearity

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