R: Interpreting high co-efficient with low p-value for a binary variable

Question

I am looking at baby weight data. Now a baby's gender is either male or female. A linear regression model to predict a baby's weight has a high coefficient (-0.38 for female and +0.38 for male). It also shows a very low p-value indicating that it is strongly correlated to the weight.

• I am unable to obtain both of these co-efficients at the same time using linear regression model where I have two columns each containing 0 or 1. One column is called gender_male and the other column is gender_female. Pearson regression model returns an NA for one or the other if I select both. Any suggestions on why that is the case or how to avoid it?

The other difficulty is about the utility of this finding? In what ways can I interpret this result so that it is useful?

Answer 1

So it is not necessary to have 2 columns for sex (gender applies to men and women, not male and female). The coefficient that you are getting is comparing one to the other. When you get a coefficient 0f -0.38 for female, that is saying that the baby's weight is likely to be approximately .38 units less than a male baby. This is why you get the exact opposite for your other column, males are likely to be 0.38 units more than females. Of course this is not a great method for predicting baby weights since your model hasn't included all of the confounding variables.

Answer 2

Yes, you don't need two dummy indicator variables (0,1) to denote a binary variable, just one. If you regress weight on only the female_gender(0,1) variable, and specify that no constant term or y-intercept is to be determined, you should obtain two coefficients, each of which will be the average weight of females and average weight of males. The typical approach used when regressing weight on the female_gender (only) variable will yield the constant term (equal to average weight of all subjects), and a coefficient represent the average difference (delta) in weight between females and males.