This article is concerned with the statistical modeling of children ever born (CEB) fertility data. It is shown that in a low fertility population, such as China, the use of linear regression approaches to model CEB is statistically inappropriate because the distribution of the CEB variable is often heavily skewed with a long right tail. For five sub-groups of Chinese women, their fertility is modeled using Poisson, negative binomial, and ordinary least squares (OLS) regression models. It is shown that in almost all instances there would have been major errors of statistical inference had the interpretations of the results been based only on the results of the linear regression models.