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If i know the means and standard deviations of 2 sets of data, and i know the slope of the regression line, how can I find the correlation?


Sample 1

SD: 12.37

Sample 2

SD: 7.00

Slope of regression line: 0.789

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There is actually a Statistics Stack Overflow -- – Justin L. Dec 9 '10 at 0:42
up vote 3 down vote accepted

The formula is $$r = b_1 \frac{s_x}{s_y},$$ where $r$ is the correlation, $b_1$ is the slope, and $s_x$ and $s_y$ are the standard deviations of the independent $(x)$ and dependent $(y)$ variables, respectively.

A reference is Wikipedia's page on simple linear regression. See the formula for $\hat{\beta}$.

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so the means don't matter if i already know the standard deviations? – Sev Dec 8 '10 at 22:07
also i'm getting a value > 1 when I use that formula...must be something wrong ? – Sev Dec 8 '10 at 22:08
@Sev: The means are part of the slope calculation. So all the information you need from the means to find the correlation is already contained in the slope. – Mike Spivey Dec 8 '10 at 22:10
@Sev: What are your numbers for the standard deviations and the slope? (Edit them in to your original question.) – Mike Spivey Dec 8 '10 at 22:11
@Mike: done.... – Sev Dec 8 '10 at 22:13

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