c2 - Chapter 2 Linear Models for Continuous Data The...

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Unformatted text preview: Chapter 2 Linear Models for Continuous Data The starting point in our exploration of statistical models in social research will be the classical linear model. Stops along the way include multiple linear regression, analysis of variance, and analysis of covariance. We will also discuss regression diagnostics and remedies. 2.1 Introduction to Linear Models Linear models are used to study how a quantitative variable depends on one or more predictors or explanatory variables. The predictors themselves may be quantitative or qualitative. 2.1.1 The Program Effort Data We will illustrate the use of linear models for continuous data using a small dataset extracted from Mauldin and Berelson (1978) and reproduced in Table 2.1. The data include an index of social setting, an index of family planning effort, and the percent decline in the crude birth rate (CBR)—the number of births per thousand population—between 1965 and 1975, for 20 countries in Latin America and the Caribbean. The index of social setting combines seven social indicators, namely lit- eracy, school enrollment, life expectancy, infant mortality, percent of males aged 15–64 in the non-agricultural labor force, gross national product per capita and percent of population living in urban areas. Higher scores repre- sent higher socio-economic levels. G. Rodr´ ıguez. Revised September 2007 2 CHAPTER 2. LINEAR MODELS FOR CONTINUOUS DATA Table 2.1 : The Program Effort Data Setting Effort CBR Decline Bolivia 46 1 Brazil 74 10 Chile 89 16 29 Colombia 77 16 25 CostaRica 84 21 29 Cuba 89 15 40 Dominican Rep 68 14 21 Ecuador 70 6 El Salvador 60 13 13 Guatemala 55 9 4 Haiti 35 3 Honduras 51 7 7 Jamaica 87 23 21 Mexico 83 4 9 Nicaragua 68 7 Panama 84 19 22 Paraguay 74 3 6 Peru 73 2 Trinidad-Tobago 84 15 29 Venezuela 91 7 11 The index of family planning effort combines 15 different program indi- cators, including such aspects as the existence of an official family planning policy, the availability of contraceptive methods, and the structure of the family planning program. An index of 0 denotes the absence of a program, 1–9 indicates weak programs, 10–19 represents moderate efforts and 20 or more denotes fairly strong programs. Figure 2.1 shows scatterplots for all pairs of variables. Note that CBR decline is positively associated with both social setting and family planning effort. Note also that countries with higher socio-economic levels tend to have stronger family planning programs. In our analysis of these data we will treat the percent decline in the CBR as a continuous response and the indices of social setting and family planning effort as predictors. In a first approach to the data we will treat the predictors as continuous covariates with linear effects. Later we will group 2.1. INTRODUCTION TO LINEAR MODELS 3 change 40 60 80 • • • • • • • • • • • • • • • • • • • • 20 40 • • • • • • • • • • • • • • • • • • • •...
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This note was uploaded on 11/20/2011 for the course STATISTICS ST3241 taught by Professor Manwai's during the Spring '11 term at National University of Singapore.

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c2 - Chapter 2 Linear Models for Continuous Data The...

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