Beta coefficient of a linear regression in spss


So the way I understand linear regression is that you plot two variables against one another, one on the x-axis and one on the y-axis, this results in a pointcloud of all your observations. Then you draw the best fitting line through it and the direction coefficient (don’t know if that is the english word) of that line tells you in what way these variables correlate.
Now when I do this (creating such a graph and drawing the line) in spss the program gives me the formula for the line it draws including the direction coefficient. However when I directly perform a linear regression in spss the “beta” coefficient it gives me (which I think represents the same thing as the direction coefficient of the fitted line) is different. Not only that but it is sometimes higher and sometimes lower than the direction coefficient of the fitted line.
What am I missing / what do I not know?

In: Mathematics

Beta is usually used for the standardized slope. Meaning that it rescales both the x and y so each of their standard deviations is one, and expresses the slope in turns of those standardized variables. It will be different than the regression slope you find if you are using the original units of measurement of each variable.

So if you express your data as “kilograms” on one axis and “years” on the other, and then do it again but using “grams” and “days”, you will get the same beta, but different unstandardized slopes.