linear correlation and prediction

Publisher Summary This chapter describes three main topics: the description of the relationship between two variables for a set of observations; making inferences about the strength of the relationship between two variables in a population given the data of a sample; and the prediction or estimation of values on one variable from observations on another variable with which it is paired. The chapter discusses the principles of linear regression, computation of the equations for predicting y from x and x from y, and how to measure prediction error, the standard error of estimate. Correlation refers to the co-relationship between two variables. The Pearson r coefficient is a useful measure of linear correlation; the sign of r indicates the direction of the relationship and the size of the numerical value of r indicates the strength of the relationship. The maximum values of the Pearson r are: –1 (perfect negative linear relationship) and +1 (perfect positive linear relationship). The Pearson r can be tested for statistical significance; however, it cannot be interpreted as a percent. Linear regression is used to predict scores on one variable given scores on the other. The standard error of estimate is a measure of error in the prediction process.