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In this section, we will use R to conduct a regression analysis of the relationship between variables, in which the outcome variable is continuous and the other variables can be continuous or discrete. A continuous variable can take an infinite number of possible values within an interval such as economic growth or height; in contrast, a discrete variable only takes a countable number of values, such as the income group variable.

For illustration, we will address the following substantive question: Does trade promote economic growth? While the correlation coefficient between trade and growth provided useful information about their relationship in the previous section, it does not tell us the size of the effect of trade on growth. More importantly, it does not take into consideration that some other variables might affect both trade and growth, confounding their bivariate correlation. A regression model is a useful way to address both issues.

We will first provide a brief but important introduction to regression modeling in terms of conceptualization, identification, and estimation technique. We will discuss how to specify a statistical model from a theoretical argument, prepare data, estimate a regression model in both theory and practice, and interpret the estimated coefficients. Next, we will use the estimated regression model to conduct statistical inferences including hypothesis testing and confidence interval construction to answer the question of interest. In addition, we will discuss how to understand the notion of sum of squares regarding the outcome variable and interpret overall model fit. Finally, we will demonstrate how to report our regression model results.

Our objectives in this section are as follows:

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