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From what I understand, the Pearson Coefficient determines if there is a linear relationship between some data. However, doesn't the error from a least squares regression line also do basically the same thing?

I have some points that have around r~=0.90 with error~=15. I also have some other points around r~=0.85 with error~=45. Is there a big difference in meaning between the two? Why is the error rate 3x for only a 0.05 difference in the Pearson Coefficient?

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I suppose you are talking about a univariate linear regression (right?). In a univariate linear regression $y=a+bx+e$ the correlation between y and x is the square root of the $R^2$ of the regression (i.e. the percentage of the total sum of squares of the dependent variable which is explained by the model, or, if you prefer, the complement to 1 of the percentage explained by the residuals). For more help check this

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