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Why equation y on x minimises the vertical distances in scatter diagram and equation x on y minimises the horizontal distances in scatter diagram?
Answers (1)
Nice point, its conceptual. Trying to simplify below: When we say Regression line of y on x , what we are trying to do is find the line of best fit that is used to calculate value of y for a given value of x. Now, on a graph we have, x on horizontal axis, y on vertical axis. There are all scattered points on graph. For a given x, there will be y. But, what we are trying is to put that into an equation i.e. finding a line, where we shall have for given x, some y which is very close to actual y. We obtain this through the method of least squares where we are actuallly minimisng the vertical distances between observed data points and line i.e. trying to reduce that vertical distance of actual y and y as given by line. Same logic applies for x on y. For given y, we have x and are minimising horizontal distance between observed data points and line i.e. trying to reduce that horizontal distance of actual x and x as given by line. (Remember x is on horizontal axis)