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## 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.

## 17. A Guide to Multivariate Analysis

This chapter extends the principles of bivariate analysis to multivariate analysis, which takes into account more than one independent variable and the dependent variable. With multivariate analysis, it is possible to investigate the impact of multiple factors on a dependent variable of interest, and to compare the explanatory power of rival hypotheses. Multivariate analysis can also be used to develop and test multi-causal explanations of political phenomena. After providing an overview of the principles of multivariate analysis, and the different types of analytical question to which they can be applied, the chapter shows how multivariate analysis is carried out for statistical control purposes. More specifically, it explains the use of ordinary least squares (OLS) regression and logistic regression, the latter of which builds on cross-tabulation, to carry out multivariate analysis. It also discusses the use of multivariate analysis to debunk spurious relationships and to illustrate indirect causality.

## 16. Patterns of Association: Bivariate Analysis

This chapter discusses the principles of bivariate analysis as a tool for helping researchers get to know their data and identify patterns of association between two variables. Bivariate analysis offers a way of establishing whether or not there is a relationship between two variables, a dependent variable and an independent variable. With bivariate analysis, theoretical expectations can be compared against evidence from the real world to see if the theory is supported by what is observed. The chapter examines the pattern of association between dependent and independent variables, with particular emphasis on hypothesis testing and significance tests. It discusses ordinary least squares (OLS) regression and cross-tabulation, two of the most widely used statistical analysis techniques in political research. Finally, it explains how to state the null hypothesis, calculate the chi square, and establishing the correlation between the dependent and independent variables.