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?
The equation relating the angle of a line to the slope (angle = arctan(m)) seems 'oversimplified' because it doesn't take into account the dimensions of the axes. If you zscore a set of datapoints and plot the original data points in one graph and the zscore data points in another graph (in Matlab or Excel), the geometric angle of the two graphs will LOOK identical even though the slope of the line (the b from the regression) is different. According to the equation above (angle = arctan(m)), the angle should be different since the slope of the lines is different, but it's not. Clearly, excel or matlab is changing something about the scales to accommodate and make the angles appear the same, when in fact they should not be.
Thank you for your help.