Question

In your own words, explain the concept of “correlation.” Please use technical language and formulas where appropriate. In your explanation, discuss how correlation relates to causation and how a relationship can be used for prediction.

Answer 1

Answer:

The simple meaning of the word correlation is "a mutual relationship or connection between two or more things."

Correlation is a statistical technique that can show whether and how strongly pairs of variables are related. For example, height and weight are related; taller people tend to be heavier than shorter people.

Types of correlation:

1)  Positive Correlation

A correlation in the same direction is called a positive correlation. If one variable increases the other also increases and when one variable decreases the other also decreases. For example, the length of an iron bar will increase as the temperature increases.

2)  Negative Correlation

Correlation in the opposite direction is called a negative correlation. Here if one variable increases the other decreases and vice versa. For example, the volume of gas will decrease as the pressure increases, or the demand for a particular commodity increases as the price of such commodity decreases.

3)  No Correlation or Zero Correlation

If there is no relationship between the two variables such that the value of one variable changes and the other variable remains constant, it is called no or zero correlation.

Methods of Computing Coefficient of Correlation:

In ease of ungrouped data of bivariate distribution, the following three methods are used to compute the value of coefficient of correlation:

1. Scatter diagram method.

2. Pearson’s Coefficient of Correlation.

3. Spearman’s Rank Order Coefficient of Correlation.

1. Scatter Diagram Method:

Scatter diagram or dot diagram is a graphic device for drawing certain conclusions about the correlation between two variables.

In preparing a scatter diagram, the observed pairs of observations are plotted by dots on a graph paper in a two dimensional space by taking the measurements on variable X along the horizontal axis and that on variable Y along the vertical axis.

2. Pearson’s Coefficient of Correlation.

for bivariate data (x,y) with n observations the Coefficient of Correlation is given as

3. Spearman’s Rank Order Coefficient of Correlation.

When data is in ordinal type the rank correlation is

Note : All Coefficient of Correlation lies in -1 to +1

This relationship can be used for prediction. By using simple linear regression we can make predictions.

Y= b0+ b1X, where b0 and b1 are coefficients and can determined by least square method.