# Correlation coefficient between X and Y, linear regression.

The formula that I know for correlation coefficient
$\frac{\sum \left({x}_{i}-\overline{x}\right)\left({Y}_{i}-\overline{Y}\right)}{\sqrt{\sum \left({x}_{i}-\overline{x}{\right)}^{2}\sum \left({Y}_{i}-\overline{Y}{\right)}^{2}}}$
If the only given values I have are $\sum {x}_{i},\sum {x}_{i}^{2},\sum {y}_{i},\sum {x}_{i}{y}_{i}$ is it even possible to compute the correlation coefficient?
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Nathalie Rivers
Step 1
Apparently you are referring Pearson's sample correlation coefficient. In that case, one of the known alternative formulas is
${r}_{xy}=\frac{\sum {x}_{i}{y}_{i}-\sum xi\sum yi}{\sqrt{n\sum {x}_{i}^{2}-{\left(\sum {x}_{i}\right)}^{2}}\sqrt{n\sum {y}_{i}^{2}-{\left(\sum {y}_{i}\right)}^{2}}}$
So I believe that you would still need to have at least ∑y2i and n to compute it.