In correlations, we referred to a linear trend in the data. The concepts in the chapter are also related to ANOVA as the goal of regression is the same as the goal of ANOVA: to take what we know about one variable (X) and use it to explain our observed differences in another variable (Y) – we are just two continuous variables. So if sleep the night before is correlated with happiness the next day, this means that we should be able, to some extent, predict how happy a person will be the next day from knowing how much sleep the person got the night before. This is because if two variables are correlated it means that we can predict one from the other. Again, the concepts in this chapter are directly related to correlation. So we can think of this in terms of the predicted value of the criterion variable regressing, or going back, toward the mean of the criterion variable. We use the term regression here because the predicted score on the criterion variable is closer (in terms of standard deviation units) to the mean of the criterion variable compared to the distance from the value of the predictor variable to the mean of the predictor variable. Regression literally means going back or returning. Psychologists often call this kind of prediction regression. Regression is the most general and most flexible analysis covered in this book, and we will only scratch the surface.Ī major practical application of statistical methods is making predictions. Regression uses the technique of variance partitioning from ANOVA to more formally assess the types of relations looked at in correlations. In this chapter, we will combine these two techniques in an analysis called simple linear regression, or regression for short. In chapter 16, we learned about correlations, which analyze two continuous variables at the same time to see if they systematically relate in a linear fashion. In chapter 14, we learned about ANOVA, which involves a new way a looking at how our data are structured and the inferences we can draw from that.
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