Mark Thomas

Making History Count: The classical linear regression model

This chapter builds on our previous work and takes a succession of giant strides towards realistic quantitative analysis of relationships between two or more variables. After completing this material it will be possible to examine a large range of potential historical problems, and to read critically many of the studies in history and the social sciences that make use of regression and related quantitative techniques. We will begin in §9.1 with a brief discussion of the concept of a ‘model’ and of the associated methodology of quantitative research into the relationships between two or more variables. The basic technique of linear regression (discussed in chapters 4 and 8) is then extended in §9.2 to examine the reasons why the observed values of the dependent variable deviate from the regression line, and to consider the implications of these deviations. In §9.3 a new test statistic, the F -test, is introduced and used to test the significance of the multiple regression as a whole. Finally, §9.4 is devoted to a further useful summary statistic, the standard error of the estimate. Historical research and models of relationships between variables One of the principal features of quantitative research in the historical and social sciences is the attempt to analyse and explain the behaviour of some particular variable.

Making History Count: Multiple linear regression

Making History Count introduces the main quantitative methods used in historical research. The emphasis is on intuitive understanding and application of the concepts, rather than formal statistics; no knowledge of mathematics beyond simple arithmetic is required. The techniques are illustrated by applications in social, political, demographic and economic history. Students will learn to read and evaluate the application of the quantitative methods used in many books and articles, and to assess the historical conclusions drawn from them. They will also see how quantitative techniques can open up new aspects of an enquiry, and supplement and strengthen other methods of research. This textbook will encourage students to recognize the benefits of using quantitative methods in their own research projects. The text is clearly illustrated with tables, graphs and diagrams, leading the student through key topics. Additional support includes five specific historical data-sets, available from the Cambridge website.

Making History Count: Specifying and interpreting models: four case studies

Making History Count introduces the main quantitative methods used in historical research. The emphasis is on intuitive understanding and application of the concepts, rather than formal statistics; no knowledge of mathematics beyond simple arithmetic is required. The techniques are illustrated by applications in social, political, demographic and economic history. Students will learn to read and evaluate the application of the quantitative methods used in many books and articles, and to assess the historical conclusions drawn from them. They will also see how quantitative techniques can open up new aspects of an enquiry, and supplement and strengthen other methods of research. This textbook will encourage students to recognize the benefits of using quantitative methods in their own research projects. The text is clearly illustrated with tables, graphs and diagrams, leading the student through key topics. Additional support includes five specific historical data-sets, available from the Cambridge website.

Making History Count: Frontmatter

Making History Count introduces the main quantitative methods used in historical research. The emphasis is on intuitive understanding and application of the concepts, rather than formal statistics; no knowledge of mathematics beyond simple arithmetic is required. The techniques are illustrated by applications in social, political, demographic and economic history. Students will learn to read and evaluate the application of the quantitative methods used in many books and articles, and to assess the historical conclusions drawn from them. They will also see how quantitative techniques can open up new aspects of an enquiry, and supplement and strengthen other methods of research. This textbook will encourage students to recognize the benefits of using quantitative methods in their own research projects. The text is clearly illustrated with tables, graphs and diagrams, leading the student through key topics. Additional support includes five specific historical data-sets, available from the Cambridge website.

Making History Count: Samples and inductive statistics

Making History Count introduces the main quantitative methods used in historical research. The emphasis is on intuitive understanding and application of the concepts, rather than formal statistics; no knowledge of mathematics beyond simple arithmetic is required. The techniques are illustrated by applications in social, political, demographic and economic history. Students will learn to read and evaluate the application of the quantitative methods used in many books and articles, and to assess the historical conclusions drawn from them. They will also see how quantitative techniques can open up new aspects of an enquiry, and supplement and strengthen other methods of research. This textbook will encourage students to recognize the benefits of using quantitative methods in their own research projects. The text is clearly illustrated with tables, graphs and diagrams, leading the student through key topics. Additional support includes five specific historical data-sets, available from the Cambridge website.

Making History Count: Elementary statistical analysis

Making History Count introduces the main quantitative methods used in historical research. The emphasis is on intuitive understanding and application of the concepts, rather than formal statistics; no knowledge of mathematics beyond simple arithmetic is required. The techniques are illustrated by applications in social, political, demographic and economic history. Students will learn to read and evaluate the application of the quantitative methods used in many books and articles, and to assess the historical conclusions drawn from them. They will also see how quantitative techniques can open up new aspects of an enquiry, and supplement and strengthen other methods of research. This textbook will encourage students to recognize the benefits of using quantitative methods in their own research projects. The text is clearly illustrated with tables, graphs and diagrams, leading the student through key topics. Additional support includes five specific historical data-sets, available from the Cambridge website.

Making History Count: List of panels

Making History Count introduces the main quantitative methods used in historical research. The emphasis is on intuitive understanding and application of the concepts, rather than formal statistics; no knowledge of mathematics beyond simple arithmetic is required. The techniques are illustrated by applications in social, political, demographic and economic history. Students will learn to read and evaluate the application of the quantitative methods used in many books and articles, and to assess the historical conclusions drawn from them. They will also see how quantitative techniques can open up new aspects of an enquiry, and supplement and strengthen other methods of research. This textbook will encourage students to recognize the benefits of using quantitative methods in their own research projects. The text is clearly illustrated with tables, graphs and diagrams, leading the student through key topics. Additional support includes five specific historical data-sets, available from the Cambridge website.

Making History Count: Index of names

Making History Count introduces the main quantitative methods used in historical research. The emphasis is on intuitive understanding and application of the concepts, rather than formal statistics; no knowledge of mathematics beyond simple arithmetic is required. The techniques are illustrated by applications in social, political, demographic and economic history. Students will learn to read and evaluate the application of the quantitative methods used in many books and articles, and to assess the historical conclusions drawn from them. They will also see how quantitative techniques can open up new aspects of an enquiry, and supplement and strengthen other methods of research. This textbook will encourage students to recognize the benefits of using quantitative methods in their own research projects. The text is clearly illustrated with tables, graphs and diagrams, leading the student through key topics. Additional support includes five specific historical data-sets, available from the Cambridge website.

Making History Count: Dummy variables and lagged values

In chapter 8 the simple linear regression model was extended to cover the introduction of two or more explanatory variables, and in chapter 9 the model was given its essential stochastic form. In the present chapter two further extensions are described. First, §10.1 is devoted to the use of dummy variables . This is a procedure developed to enable us to include in a regression a variable that cannot be measured in the same way as a continuous numerical value (for example, income, or age at marriage) but is instead represented by two or more categories (for example, single, married, or widowed). This special form of a nominal (or categorical) scale is known as a dummy variable. Secondly, in §10.2 we develop the implications of the idea that it may be appropriate for one or more of the explanatory variables to refer to an earlier period than the one to which the dependent variable relates. Such lagged values recognize the fact that there may be a delay before the changes in the explanatory variable make their full impact. Dummy variables Dummy variables with two or more categories In historical research we often want to take account of factors in a regression that are not measurable in the usual way, but can be expressed as representing one of two (or more) categories. This is a special form of a nominal scale and is called a dummy variable .