Chapter 13, Problem 1FP

To determine

To discuss: The concept of correlation.

Explanation of Solution

Correlation is measure of linear association between two variables. The variables are said to be correlated when the change in one variable affects the other variable.

The correlation coefficient $\left(r_{xy}\right)$ is a numerical value of the correlation representing the relationship between the dependent and independent variables. The computed value of correlation coefficient must fall between $-1$ and $+1$ .

If two variables have a very strong positive relation, then the correlation value lies between .8 and 1. If two variables have a strong correlation, then correlation falls between .6 and .8. If two variables have a moderate positive relation, then the correlation value lies between .4 and .6. If two variables have a weak positive relation, then the correlation value lies between .2 and .4. And, if two variables have a very weak positive relation, then the correlation value lies between .0 and .2.

Similarly, if two variables have a very strong negative relation, then the correlation value lies between $-.8$ and $-1$ . If two variables have a strong correlation, then correlation falls between $-.6$ and $-.8$ . If two variables have a moderate negative relation, then the correlation value lies between $-.4$ and $-.6$ . If two variables have a weak negative relation, then the correlation value lies between $-.2$ and $-.4$ . And, if two variables have a very weak negative relation, then the correlation value lies between $-.0$ and $-.2$