Question

If you are modeling count data, explain why it is not sufficient to analyze ordinary raw residuals, (yi − μˆi), as you would for ordinary linear models.

Answer 1

The distribution of counts is discrete, not continuous, and is limited to non-negative values. There are two problems with applying an ordinary linear regression model to these data or consequently it is not sufficient to analyse ordinary raw residuals. The two problems are:

First, many distributions of count data are positively skewed with many observations in the data set having a value of 0. The high number of 0’s in the data set prevents the transformation of a skewed distribution into a normal one.

Second, it is quite likely that the regression model will produce negative predicted values, which are theoretically impossible.