It is important to understand the difference among r, Multiple R, and R squared

Question

It is important to understand the difference among r, Multiple R, and R squared

Let's start with r.

Another name for r is the correlation coefficient

A few facts about r:

1. r measures the linear association between two variables

2. r ranges in value from -1 to +1

3. r tells both the direction and the strength of the relationship between the variables

4. correlations near -1 signify a strong negative relationship, meaning that as one variables increases, the other variable decreases

5. correlations near +1 signify a strong positive relationship, meaning that as one variables increases, so does the other one

6. We can predict future outcomes from r and the relationship. The stronger the relationship (how close r is to +1 or -1) the more accurate our prediction will be

What is Multiple R? (250 words)

Explanation / Answer

Another simple difference is interpretation. In multiple regression, the multiple R is the coefficient of multiple correlation, whereas its square is the coefficient of determination. R can be interpreted somewhat like a bivariate correlation coefficient, the main difference being that the multiple correlation is between the dependent variable and a linear combination of the predictors, not just any one of them, and not just the average of those bivariate correlations. R2 can be interpreted as the percentage of variance in the dependent variable that can be explained by the predictors; as above, this is also true if there is only one predictor.

R2 does not indicate whether:

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