Linear Regression

Simple Linear Regression

Simple linear regression examines the relationship between two variables, one of which is referred to as the predictor variable (i.e., the variable that usually precedes the other), and the other of which is referred to as the criterion variable (i.e., the variable that the researcher is interested in explaining, predicting, or better understanding). Because simple regression results provide an understanding of the patterns of relationships between the two variables of interest in a given context, we often use the term prediction in describing the relationship. The procedure is called “simple” because it includes only one predictor variable.

As in studies employing Pearson product-moment correlation (r), the linear relationship between the predictor (X) and the criterion (Y) variables can be shown on a two-way scatterplot. A line of best fit drawn through the scatterplot is called the regression line, and the statistic representing the relationship between the two sets of points is called multiple R. In Pearson product-moment correlation, the coefficient r is used to show the strength and directionality of a relationship between two variables. A value of r close to zero indicates a low or negligible correlation between two variables, whereas a value closer to |1| indicates a more appreciable amount of correlation between the variables. Negative r values depict inverse relationships between variables, whereas positive r values depict direct relationships. Multiple R is very similar to the Pearson r with the exception that it is always positive in value (0 ≤ R ≤ 1) because of a set of variable weights developed as part of the analysis. Because there is only one predictor in simple linear regression, R will be equivalent to the absolute value of the Pearson correlation coefficient (|r|) between the two variables.

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