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## Covariance

### A First Step in the Analysis of the Relationship between Two Variables

This chapter examines the covariance, which is either a comprehensive qualitative approach or the first step of a quantitative approach to the analysis of the relationship between two variables. On the one hand, in qualitative studies, and in particular in case study methods, covariation is an analytical approach used alongside causal process-tracing and congruence analysis. In the co-variational approach, causal inferences are drawn based on observed covariation between causal factors (independent variables) and causal effects (dependent variables). On the other hand, when the type of data allows a quantitative approach, looking at the covariance constitutes a first step in the statistical analysis. The covariance is then a measure of linear association between two variables.

## Regression Analysis

This chapter evaluates regression analysis, which uses quantitative and sometimes also qualitative independent variables to explain or predict change in a quantitative dependent variable. To attain this goal, it relies on the principles of covariance and correlation. Its most basic form is linear regression, also known as ordinary least squares (OLS) regression. In addition, there are many other varieties of regression methods for different research questions and data characteristics, such as time-oriented questions or data with a limited range of values. Researchers use regression analysis especially to analyse complex patterns of correlation in situations with more than one explanatory variable. Often such patterns are interpreted in the context of causal theories. The concept of regression goes back to Francis Galton’s study on human height.