Scaling of data

[Patrick Mauder]

Hi,

I am using Stata 14.2.

I have a data set with several indepvar (number of members) which range from two digit numbers to 7 digit numbers. When I run a regression my coefficients are tiny e.g. (-1.04e-06) see below which means when I include them in my paper I would have to show 0.000. Now I have some other data which is the total assets of each company. Could I scale my indedvars by dividing them by the total asset number?

VARIABLES	Y
X1	-1.04e-06
	(7.67e-07)
X2	-1.67e-05
	(1.56e-05)
X3	4.42e-08
	(3.29e-06)
Control	-0.000431
	(0.00203)
Constant	0.353***
	(0.0991)
Observations	1,255
Number of sec	74

Standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1

Thanks,

Patrick

[Clyde Schechter]

You could. The question is whether X1/total assets, etc. would make sense to whoever the audience for your analysis is. Or, it might make sense to simply acale them by a factor of 1,000,000 or something like that. (If X1 is, for example, in units of dollars, this would change it to units of $1,000,000, which would bring the coefficient for X1 up to an order of magnitude of 10.)

Note that there is a 2 order of magnitude difference between the coordinates of x2 and x3, While a scale factor about 1,000,000 will work nicely for X1 and X2, for X3 it will still leave your coefficient with an order of magnitude of 0.01. If that's OK, fine. If not, you could apply a larger scale factor to that one.

Alternatively, you could scale your outcome variable Y down by a similarly large factor.

There is no substantive or statistical difference between these approaches. Any inferences or predictions you make will come out the same regardless. It is a matter of what your audience will most easily understand.

[Patrick Mauder]

Thank you Clyde! That makes sense

[Nick Cox]

Your results however imply that the model is not doing anything useful, so re-scaling won't change that. Perhaps you need to work on transformed scales or try something quite different.