I know that you can adjust the scale of the x and y axes to change the geometric angle of a regression line. For example, if you plotted a regression line with slope of b=0.3, perhaps the default settings of axes length etc. would create a regression angle of 35 degrees.
If you adjust the axes, you will change the angle the regression line makes with the x-axis so that it is greater or less than 35 degrees-WITHOUT changing the mathematical value of the slope--it will still stay as b=0.3.
What systematic equation/set of equations is there that allows me to know how the geometric angle of the regression line will be changed as I change the axes of the graph itself?
I have spent a lot of time on the internet looking for the answer to this and have not yet succeeded. For some reason statistics and geometry do not overlap much.
Refer to this web page: http://www.mathworks.in/help/matlab/ref/axis.html
Based on the data you have, set the same ranges for all the axes in your plot. Then the regression line would have the same angle for both the datasets.
Hope this helps!