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 \(r\), the sample means \(\bar{X}\), \(\bar{Y}\) and the standard deviations of both \(X\) (\(s_x\)) and \(Y\) (\(s_y\)), 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 \(m\), which is obtained using the following formula

\[m = \displaystyle r \frac{s_y}{s_x}\]

where \(m\) is the slope of the regression line \(y = mx + n\).

Formula for the intercept

Now that you have the slope, you can compute the intercept \(n\) using the following formula:

\[n = \bar{Y} - m \bar{X}\]

Notice that here you use the \(m\) 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 \(X\) and \(Y\).