Answer to Question #264381 in Statistics and Probability for Goldie

Question

Based on the concept on correlation and the learning exercises that you have done,

write your arguments or lessons learned below.

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Answer 1

Correlation means association. It is a measure of the level to which two variables are related. Correlation can be positive, negative, or zero correlation. 

A positive correlation shows a relationship between two variables in which both variables move in the same direction; an increase in one variable results in an increase of the other variable, and a decrease in one variable results in a decrease in the other variable. 

A negative correlation is an association between two variables in which an increase in one variable is associated with a decrease in the other variable.

Zero correlation exists when there is no relationship between two variables.

 Correlation is used to make predictions. One variable can be used to predict another variable.

The strength of association between two variables is measured using a correlation coefficient $(r)$ . $r$ lies between -1 and 1 inclusive. The value of $r$ close to -1 shows a strong negative relationship between two variables, and values of close to 1 show that there is a strong positive relationship between the two variables.

When the value of $r$ is zero, it implies that there is no relationship between the two variables. The values of $r$ close to zero show that the relationship between the two variables is weak.   

Assume we are given two variables $X$and $Y$ then, the value of $r$ can be calculated using the formula below,

$r=(n\sum(xy)-\sum(x)\sum(y))/\sqrt{(n\sum(x^2)-(\sum(x))^2)*(n\sum(y^2)-(\sum(y))^2)}$