Prediction and Correlation
PREDICTION AND CORRELATION
Correlation coefficients not only describe the relationship between variables; they also allow us to make predictions from one variable to another. Correlations between variables indicate that when one variable is present at a certain level, the other also tends to be present at a certain level. Notice the wording used. The statement is qualified by the use of the phrase “tends to.” We are not saying that a prediction is guaranteed, nor that the relationship is causal—but simply that the variables seem to occur together at specific levels. Height and weight are positively correlated. One is not causing the other, nor can we predict exactly what an individual’s weight will be based on height (or vice versa). But because the two variables are correlated, we can predict with a certain degree of accuracy what an individual’s approximate weight might be if we know the person’s height.
Let’s take an example. Think about what the purpose of the SAT is. College admissions committees use the test as part of the admissions procedure. Why? They use it because there is a positive correlation between SAT scores and college GPAs. Individuals who score high on the SAT tend to have higher college freshman GPAs; those who score lower on the SAT tend to have lower college freshman GPAs. This means that knowing students’ SAT scores can help predict, with a certain degree of accuracy, their freshman GPA and thus their potential for success in college. At this point, some of you are probably saying, “But that isn’t true for me—I scored poorly (or very well) on the SAT and my GPA is great (or not so good).” Statistics only tell us what the trend is for most people in the population or sample. There will always be outliers—the few individuals who do not fit the trend. Most people, however, are going to fit the pattern. Think about another example. We know there is a strong positive correlation between smoking and cancer, but you may know someone who has
Correlation coefficients not only describe the relationship between variables; they also allow us to make predictions from one variable to another. Correlations between variables indicate that when one variable is present at a certain level, the other also tends to be present at a certain level. Notice the wording used. The statement is qualified by the use of the phrase “tends to.” We are not saying that a prediction is guaranteed, nor that the relationship is causal—but simply that the variables seem to occur together at specific levels. Height and weight are positively correlated. One is not causing the other, nor can we predict exactly what an individual’s weight will be based on height (or vice versa). But because the two variables are correlated, we can predict with a certain degree of accuracy what an individual’s approximate weight might be if we know the person’s height.
Let’s take an example. Think about what the purpose of the SAT is. College admissions committees use the test as part of the admissions procedure. Why? They use it because there is a positive correlation between SAT scores and college GPAs. Individuals who score high on the SAT tend to have higher college freshman GPAs; those who score lower on the SAT tend to have lower college freshman GPAs. This means that knowing students’ SAT scores can help predict, with a certain degree of accuracy, their freshman GPA and thus their potential for success in college. At this point, some of you are probably saying, “But that isn’t true for me—I scored poorly (or very well) on the SAT and my GPA is great (or not so good).” Statistics only tell us what the trend is for most people in the population or sample. There will always be outliers—the few individuals who do not fit the trend. Most people, however, are going to fit the pattern. Think about another example. We know there is a strong positive correlation between smoking and cancer, but you may know someone who has