It is important to understand the difference among r Multipl

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)

Solution

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: