Regression analysis is the statistical method you use when both the response variable and the explanatory variable are continuous variables (i.e. real numbers with decimal places – things like heights, weights, volumes, or temperatures). Perhaps the easiest way of knowing when regression is the appropriate analysis is to see that a scatterplot is the appropriate graphic (in contrast to analysis of variance, say, where it would have been a box-and-whisker plot or a bar chart). We cover seven important kinds of regression analysis in this book:
- linear regression (the simplest, and much the most frequently used);
- polynomial regression (often used to test for non-linearity in a relationship);
- piecewise regression (two or more adjacent straight lines);
- robust regression (models that are less sensitive to outliers);
- multiple regression (where there are numerous explanatory variables);
- non-linear regression (to fit a specified non-linear model to data);
- non-parametric regression (used when there is no obvious functional form).
The first five cases are covered here, non-linear regression in Chapter 20 and non-parametric regression in Chapter 18 (where we deal with generalized additive models and non-parametric smoothing).
The essence of regression analysis is using sample data to estimate parameter values and their standard errors. First, however, we need to select a model which describes the relationship between the response variable and the explanatory variable(s). ...