[Commerce Class Notes] on Correlation in a Whole Pdf for Exam

Students of Commerce or Economics must be aware of the term correlation in Economics. The literal meaning of correlation is association. In the fields of Statistics, correlation is the measure of the strength of the relationship between two different parameters or variables. These are linear relationships like height, weight, etc.

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Introduction of Correlation in a Whole 

As per correlation, variables are associated if the change in the value of one is followed by a change in the other variable too. For example, if the demand for a product decreases, it leads to an increase in its price.  

The correlation coefficient, denoted by ρ, signifies the degree of correlation, i.e. the degree to which the movement of the various variables is associated. Pearson product-moment correlation can measure the correlation of linear variables. For non-linear variables, it does not prove to be a suitable measure of dependence.

The value of the Correlation coefficient can lie between -1.0 and +1.0. The values cannot be less than -1 or more than +1. A value of zero denotes no relationship between the variables.

Correlation does not necessarily imply that change in one variable causes the change in another (causation), there could be other reasons involved too.

Here, we will know about different kinds of correlations, with positive correlation examples and negative correlation examples for clarity. 

What is a Positive Correlation?

A positive correlation between two variables is characterized by the movement of both the variables in the same direction. It refers to that if one variable increases, the other one increases too and vice versa. One of the positive correlation examples is if you exercise more, you burn more calories. The values of the correlation coefficient,  ρ,  in case of a positive correlation are greater than 0. A perfect positive correlation happens when the correlation coefficient is equal to +1.0. An entirely positive correlation would mean that both the variables are 100% in tandem concerning the direction of movement and the percentage of movement. Few examples of perfect positive correlation are:

• If supply is constant, then demand and price both increases in a perfect positive correlation.

• As a person grows in height, the shoe size increases.

• If you spend less time in marketing and advertising, you will get fewer customers. 

• Gains or losses in one market segment will cause gains and losses in another segment. For example, with an increase in the price of fuel, airline tickets also become costlier.

A positive correlation does not always guarantee growth or benefit. At times the causation of movement of two variables in the same direction is not known. As an example, ice cream sales and sunglasses sales both increase at the same time during summer. But the sale of ice cream does not correlate with the sale of sunglasses.

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Negative Correlation Meaning

In a negative correlation, the value of one variable decreases when the value of the other increases, and vice versa. The negative correlation is also called inverse correlation, and its value is less than 0 and goes till -1.0.

A perfect negative correlation is when the relationship between two variables is negative at all times, consistently. One variable decreases with a predictable and comparable increase in the other in a  perfect negative correlation.

A negative correlation is denoted by the value -1.0. Few negative correlation examples are:

• As the height above sea level increases, atmospheric temperature decreases.

• If you sleep more, you will feel less tired.

• If the temperature goes low, you will wear more clothes.

• An increase in spending habits will decrease bank balance.

• If there is an increase in average driving speed, there is a decrease in gas mileage.

In the world of statistics, a negative correlation holds special meaning concerning stocks and bonds. As stock prices rise, the bond market begins to decline. The opposite is also true, i.e. the bond market performs better if the stock market underperforms.

So, the difference between positive and negative correlation is that in positive correlation, both variables move in the same direction but negative correlation, they move in opposite directions.

Zero Correlation

When two variables share absolutely no relationship, then they are said to have zero correlation. In other words, the direction in which a variable moves has no relation with the direction of movement of the other variable. Zero correlations examples could be:

• You sing more when you exercise more.

• You cook more and you get smarter.

• More the temperature in a room, the longer you would stay there.

• If you sleep less, you drink more soda.

What are Scattergrams?

You can show correlation visually utilizing scattergrams. Other names of scattergrams are scatterplot, scatter diagram, scatter graph, and scatter chart. Two numerical values or co-variables are displayed graphically in a scatter diagram as points or dots. Using the scattergram one can determine the strength and direction of the correlation between variables.

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Strong and Weak Correlations 

• Strong Correlation – If you can predict the values of one variable given the value of another with a high level of accuracy, then the two variables share a strong correlation.

• Weak Correlation – A weak correlation exists between variables when on average there is a correlation, but exceptions might be there.

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