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:
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:
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