Simple Versus Multiple Regression

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The difference between simple and multiple regression is similar to the difference between one way and factorial ANOVA. Like one-way ANOVA, simple regression analysis involves a single independent, or predictor variable and a single dependent, or outcome variable. This is the same number of variables used in a simple correlation analysis. The difference between a Pearson correlation coefficient and a simple regression analysis is that whereas the correlation does not distinguish between independent and dependent variables, in a regression analysis there is always a designated predictor variable and a designated dependent variable. That is because the purpose of regression analysis is to make predictions about the value of the dependent variable given certain values of the predictor variable. This is a simple extension of a correlation analysis. If I am interested in the relationship between height and weight, for example, I could use simple regression analysis to answer this question: If I know a man’s height, what would I predict his weight to be? Of course, the accuracy of my prediction will only be as good as my correlation will allow, with stronger correlations leading to more accurate predictions. Therefore, simple linear regression is not really a more powerful tool than simple correlation analysis. But it does give me another way of conceptualizing the relation between two variables, a point I elaborate on shortly. The real power of regression analysis can be found in multiple regression. Like factorial ANOVA, multiple regression involves models that have two or more predictor variables and a single dependent variable. For example, suppose that, again, I am interested in predicting how much a person weighs (i.e., weight is the dependent variable). Now, suppose that in addition to height, I know how many minutes of exercise the person gets per day, and how many calories a day he consumes. Now I’ve got three predictor...
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