Simple linear regression

The aim in this chapter is to extend the analysis of the relationship between two variables to cover the topic of regression. In this introductory discussion we will deal only with linear (straight-line) relationships between two variables ( bivariate regression ). In chapter 8 this analysis will be extended to include more than two variables ( multiple or multivariate regression ), and non-linear relationships will be discussed in chapter 12. As with the discussion of correlation, problems arising from the use of sample data are deferred until the issues of confidence intervals and hypothesis testing are covered in chapters 5 and 6. The concept of regression In the discussion of correlation in chapter 3 we emphasized that no distinction was made between the two variables, X and Y, and that interchanging them would have no effect on the correlation coefficient. In the present chapter we change procedure and introduce a fundamental distinction between the two variables. Explanatory and dependent variables It will often be the case that we have some theoretical reason to think that movements in one of the variables are influenced by movements in the other. In that case, the convention is to use X for the variable that is having the influence , and Y for the variable that is influenced .