# Large coefficients and std. errors

I run a fixed effect model with Stata and because my dependent variable is a large number (max of 12 million and min of - 4 million), I got large coefficients for all independent variables, although most variables are significant

for example

coefficients

• 122896.2
22478.689
• 21096.348
412.539

is it a problem thanks in advance

• I edited your title and article; I hope this reflects your true question. If not, please edit again. May 31 '14 at 13:13
• You say "is it a problem" but it's not clear what "it" is. Is what a problem? Jun 1 '14 at 1:17

This is not a statistical problem; it's fine. However, interpretation may be easier if you scale your dependent variable. You didn't say what it is, but, for example, if it is income in Italian Lira, you could change it to income in millions of lira by dividing the DV by 1,000,000. The meaning is the same, but there will be fewer digits to deal with before the decimal.

• thanks, I tried that and it looks normal afterword and also the results still the same only the coef. and std error, but how can I justify that, do you have any source. thanks again
– Ben
May 31 '14 at 13:26
• You don't really need a source. You can say, if you need to, "for ease of interpretation, 'income' was expressed in millions of lira". May 31 '14 at 13:32
• thank you dear @peter ..... I will try to find an article that did that
– Ben
Jun 2 '14 at 5:19
• @Ben you can look at Gelman and Hill, Data Analysis Using Regression and Multilevel/Hierarchical Models, §4.1 "Linear transformations" and §4.2 "Centering and standardizing, espacially for models with interactions". Jun 2 '14 at 21:43

Many apologies if I have misunderstood your question. I believe your question is: "Is it OK that the regression coefficients are unusually large in magnitude". The answer is, yes it's OK, because the MLEs for the regression coefficients depend on the scale of your data.

However, just because the MLEs look large in magnitude, it doesn't necessarily mean that they are significant (that's what hypothesis tests do!). It can simply be the scale of your real data which mess things up.

One way to get around this problem is to standardise your data so it's centred around, say zero, and has variance covariance matrix as the identity matrix.