# Report coefficients of a factor in a GLM

I have a GLM and my explanatory variables are a factor of 9 levels (X1) and a numeric variable (X2).

If I have to report the formula:

$Y = B_0 + B_1X_1 + B_2X_2$

I have 1 coefficient for the intercept and 1 coefficient for the numeric variable, that's ok, but I have 8 coefficients for the factor, how do I report them? I mean, Bo is one number, B2 is one number, but B1? do I sum the eight numbers? or I report the mean of the 8 numbers, or I have to report the formula with the eight numbers?

Thank you.

• When you have a factor with 9 levels, you need 8 coefficients. Each compares one level to others. You need to report them all, but you first need to figure out whether they are are dummy coded, effect coded or some other parameterization. What software are you using? Different software has different defaults. – Peter Flom - Reinstate Monica Oct 19 '12 at 10:23
• I am using R, my question is, do I have to report a formula like this: Y = -0.041 + -2.17X1L2 + -18.58X1L3 + ... + -0.4X1L8 + -0.75X1L9 + -0.6X2 ?? Or there is a way to resume the coefficients in just one coefficient for the X1 explanatory variable? – Juan Oct 19 '12 at 10:27
• No, you cannot use just one coefficient. There is no meaningful way to do this. You need to look at summary() of your model. You might also want to look at the xlevels. – Peter Flom - Reinstate Monica Oct 19 '12 at 10:45
• Sorry for the ignorance, what do you mean for "look at the xlevels"? what can I look at the nine levels of the factor? – Juan Oct 19 '12 at 10:56
• Type ?lm inside R to see a lot more about them. xlevels tell you how the categorical variable was parameterized; this will be important for interpretation. You might also want to consult a book on regression - one that uses R would be ideal. I liked the first edition of Fox. – Peter Flom - Reinstate Monica Oct 19 '12 at 11:09