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CORRELATION & CO-EFFICIENT

Till the previous chapter we have been mainly concerned with univariate data. In this chapter we study bivariate and multivariate populations. According to Ya-lun Chou, “There are two related but distinct aspects of the study of association between variables. Correlation analysis and regression analysis. Correlation analysis has the objective of determining the degree or strength of the relationship between variables. Regression analysis attempts to establish the nature of the relationship between variables – that is, to study the functional relationship between the variables and thereby provide a mechanism of prediction, or forecasting.”

Meaning

In our daily lives we notice that the bigger the house the higher are its upkeep charges, the higher rate of interest the greater is the amount of saving, the rise in prices bring about a decrease in demand and the devaluation of country’s currency makes export cheaper or import dearer. The above example clearly shows that there exists some kind of relationship between the two variables. Croxton and Cowden rightly said, “when relationship between two variables is of quantitative nature the appropriate statistical tool for measuring and expressing it in formula is known as correlation. Thus correlation is a statistical device which helps in analyzing the relationship and also the covariation of two or more variables. According to Simpson and Kafta “correlation analysis deals with the association between two or more variables.” If two variables vary in such a way that movements in one are accompanied by movements in the other, then these quantities are said to be correlated.

 

Importance of Correlation
A car owner knows that there is a definite relationship between petrol consumed and distance travelled. Thus on the basis of this relationship the car owner can predict the value of one on the basis of other. Similarly if he finds that there is some distortions of relationship, he can set it right.
Correlation helps in the following ways
1. It helps to predict event and the events in which there is time gap i.e. it helps in planning
2. It helps in controlling events.

Types of Correlation
Correlation can be classified under the following heads
1. Positive and negative correlation
2. Simple multiple and partial correlation
3. Linear and non-linear correlation

Positive and Negative Correlation
Two variables are said to be positively correlated when both the variables move in the same direction. The correlation is said to be positive (directly related) when the increase in the value of one variable is accompanied by an increase in the value of the other variable and vice versa.

Two variables are said to be negatively correlated when both the variables move in the opposite direction. The correlation is said to be negative (inversely related) when the increase in the value of one variable is accompanied by a decrease in the value of the other variable and vice versa.

 

Simple, Multiple and Partial Correlation
Correlation is said to be simple when only two variables are studied. In multiple correlation three or more variables are studied simultaneously. In partial correlation though more than two variables are recognised, but only two are considered to be influencing each other; and the effect of other influencing variables are kept constant.

Linear and Non-linear Correlation
If the amount of change in one variable tends to bear a constant ratio to the amount of change in the other variable, then the correlation is said to be linear. The correlation is said to be non-linear if the amount of change in one variable does not bear a constant ratio to the amount of change in the other related variable.

Measurement of Correlation
 The correlation can be measured by any of the following methods
1. Scatter Diagram
2. Karl Pearson’s coefficient of correlation
3. Rank correlation coefficient

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FAQs on Correlation & Co-Efficient, Business Mathematics & Statistics - Business Mathematics and Statistics - B Com

1. What is correlation and coefficient in business mathematics and statistics?
Ans. Correlation refers to the statistical relationship between two or more variables. It measures the strength and direction of the linear relationship between the variables. Coefficient, on the other hand, is a numerical value that quantifies the strength and direction of the correlation. It ranges from -1 to +1, where -1 represents a perfect negative correlation, +1 represents a perfect positive correlation, and 0 represents no correlation at all.
2. How can correlation and coefficient be useful in business decision-making?
Ans. Correlation and coefficient can be highly useful in business decision-making as they provide insights into the relationship between different variables. By analyzing the correlation and coefficient values, businesses can determine the extent to which changes in one variable may affect another. This information enables businesses to make informed decisions, such as identifying key drivers of sales, understanding customer behavior, predicting market trends, and optimizing resource allocation.
3. How can correlation and coefficient be calculated?
Ans. Correlation and coefficient can be calculated using statistical techniques such as the Pearson correlation coefficient formula. To calculate the correlation, you need to have pairs of values for the two variables of interest. The formula involves calculating the covariance of the two variables and dividing it by the product of their standard deviations. The resulting value is the correlation coefficient.
4. What does a correlation coefficient of 0.5 indicate?
Ans. A correlation coefficient of 0.5 indicates a moderate positive correlation between two variables. It suggests that there is a tendency for the variables to move together in the same direction, but not as strongly as a correlation coefficient of 1. This value indicates a reasonably strong relationship, but not a perfect one. It is important to consider the context and the specific variables being analyzed to interpret the meaning and significance of the correlation coefficient accurately.
5. Can correlation and coefficient be used to establish causation between variables?
Ans. No, correlation and coefficient alone cannot establish causation between variables. They only measure the strength and direction of the relationship between variables. Correlation does not imply causation, as there may be other factors or variables at play that influence the observed relationship. To establish causation, additional research and analysis are required, such as experimental design, control groups, and statistical tests.
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