A three median regression line is an alternative and graphical approach to the least squares regression line, to find a relationship between two variables. A three median regression line can be fitted if the variables are numerical and the relationship is linear. This method is especially useful when there are outliers as it is not easily affected by them.

To find the regression line using the three median method:

1. Divide the data into three groups.
• Note: The number of data points in the outside groups must always be the same. If there is one left over, put that one in the middle group. If there are two points left over, divide them evenly between the side groups.
2. Locate the median of each group of points.
3. Place your ruler or any straight surface on the right and left median points.
4. Move one-third of the way towards the middle median point
5. Find the gradient. $m = \dfrac{y_u-y_l}{x_u-x_l}$. u = upper value, l = lower value.
6. Find or calculate the y-intercept.

Example:

y = the amount of fertilizer (gm) and x = crop yields.

The data is divided into three groups as represented by the double line separating the cells in the graph. The median for the first group is (2.5, 3.7), the second group is (6.5, 8) and the third group is (10.5, 11.3). Below are the three points when they are plotted, as well as the line when it is moved 1/3 towards the middle median point.

From this graph, it can be estimated that the gradient is approximately 1.8. the value of c (y-intercept) is approximately 1.75, and thus the equation is:

$y = 1.8x + 1.75$