variable whose random fluctuations are governed by the normal distribution (see Chapters 16 and

17).

Logistic regression is used when the outcome variable is a two-level or dichotomous variable

whose fluctuations are governed by the binomial distribution (see Chapter 18).

Poisson regression is used when the outcome variable is the number of occurrences of a sporadic

event whose fluctuations are governed by the Poisson distribution (see Chapter 19).

Survival regression when the outcome is a time to event, often called a survival time. Part 6

covers the entire topic of survival analysis, and Chapter 23 focuses on regression.

Figuring out what kind of function is being fitted

Another way to classify different types of regression analysis is according to whether the mathematical

formula for the model is linear or nonlinear in the parameters.

In a linear function, you multiply each predictor variable by a parameter and then add these products

to give the predicted value. You can also have one more parameter that isn’t multiplied by anything —

it’s called the constant term or the intercept. Here are some linear functions:

In these examples, Y is the dependent variable or the outcome, and X, W, and Z are the independent

variables or predictors. Also, a, b, c, and d are parameters.

The predictor variables can appear in a formula in nonlinear form, like squared or cubed, inside

functions like Log and Sin, and multiplied by each other. But as long as the coefficients appear only in

a linear way, the function is still considered linear in the parameters. By that, we mean each

coefficient is multiplied by a term involving predictor variables, with the terms added together in a

linear equation.

A nonlinear function is anything that’s not a linear function. For example:

is nonlinear in the parameters, because the parameter b is in the denominator of a fraction, and the

parameter c is in an exponent. The parameter a appears in a linear form, but if any of the parameters

appear in a nonlinear way, the function is said to be nonlinear in the parameters. Nonlinear regressions

are covered in Chapter 19.