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If I get Pearson correlation coefficient as 0.5 for a variable 'y' with relation to 'x'. Then how can I derive the relation between two ?

I know that if this coefficient comes as +1 then it mean x is directly proportional to y and if it is -1 then x is inversely proportional to y.

But if the correlation coefficient is 0.5 then does it mean with linear increase in x there is 50% (0.5) increase in y ? Or we cannot derive any linear relation between these two variables ?

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The correlation does not lead to the equation between the two variables. It is a measure of how well a linear fit ($y = m x$) explains the data, without giving the value of $m$.

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