Regression Coefficients from Correlation


Instructions: This regression coefficient calculator will show you, step-by-step how to calculate the slope and intercept of a regression line from the correlation coefficient, sample means and standard deviations. Please type the correlation (rr), sample means and the sample standard deviations (sxs_x and sys_y) to get the regression coefficients:

Sample Correlation (rr)
Sample Mean of X (Xˉ\bar{X})
Sample Mean of Y (Yˉ\bar{Y})
Sample Standard deviation of X (sxs_x)
Sample Standard deviation of Y (sys_y)

Learn more about this Regression coefficients Calculator from the Correlation Coefficient

Depending on whether your have the right pieces of information, there is shortcut to compute the estimated coefficients for a regression line.

As a matter of fact, when you know the correlation coefficient rr, the sample means Xˉ\bar{X}, Yˉ\bar{Y} and the standard deviations of both XX (sxs_x) and YY (sys_y), there is a very simple way to find the slope and intercept, without the need of computing the often times labor intensive formula that is usually the one used for getting those coefficients.

First, with this information we can compute the slope coefficient mm, which is obtained using the following formula

m=rsysxm = \displaystyle r \frac{s_y}{s_x}

where mm is the slope of the regression line y=mx+ny = mx + n.

Formula for the intercept

Now that you have the slope, you can compute the intercept nn using the following formula:

n=YˉmXˉn = \bar{Y} - m \bar{X}

Notice that here you use the mm you compute in the previous step.

Of course, if you don't have this specific pieces of information (correlation, sample means and sample standard deviations), you can always use the usual regression line calculator that uses sample data from the variables XX and YY.

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