Question

Calculate the value of the sample correlation coefficient. Based on this value, how would you describe the nature of the relationship between the two variables

Answer 1

Explained below.

Explanation:

The correlation coefficient is a statistical degree that computes the strength of the linear relationship amid the relative movements of the two variables (i.e. dependent and independent).It ranges from -1 to +1.

The formula to compute correlation coefficient is:

`r(X,Y)=(Cov(X,Y))/(√(V(X)\cdot V (Y)))`

`=\frac{n\cdot \sum XY-\sum X\cdot \sum Y}{\sqrt{[n\cdot\sum X^(2)-(\sum X)^(2)][n\cdot\sum Y^(2)-(\sum Y)^(2)]}}`

Positive correlation is an association amid two variables in which both variables change in the same direction.

A positive correlation occurs when one variable declines as the other variable declines, or one variable escalates while the other escalates.

Negative correlation is a relationship amid two variables in which one variable rises as the other falls, and vice versa.

In statistics, a perfect positive correlation is represented by +1 and -1 indicates a perfect negative correlation.