Kinds of Correlations
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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FAQs on Correlation: Understanding the Whole Picture
1. What exactly does correlation mean in statistics?
In statistics, correlation refers to a mutual relationship or connection between two or more variables. It measures the extent to which these variables tend to change together. For example, if one variable increases as the other increases, they have a positive correlation. If one increases as the other decreases, they have a negative correlation. It's a key concept for understanding relationships in data.
2. How is the strength and direction of correlation determined?
The strength and direction of correlation are typically determined using a correlation coefficient, a numerical value that ranges from -1 to +1. A value close to +1 indicates a strong positive correlation, meaning variables move in the same direction. A value close to -1 indicates a strong negative correlation, meaning they move in opposite directions. A value near 0 suggests a very weak or no linear correlation.
3. What are the different types of correlation that students should know?
Students commonly encounter several types of correlation:
- Positive Correlation: As one variable increases, the other also increases (e.g., hours studied and exam scores).
- Negative Correlation: As one variable increases, the other decreases (e.g., price of a good and quantity demanded).
- Zero Correlation: No apparent linear relationship between variables.
- Linear Correlation: The relationship can be best represented by a straight line.
- Non-linear Correlation: The relationship follows a curve rather than a straight line.
4. How is the Pearson correlation coefficient calculated and what does its value signify?
The Pearson correlation coefficient (r) is a measure of the linear relationship between two quantitative variables. It is calculated by dividing the covariance of the two variables by the product of their standard deviations. Its value signifies both the strength and direction of the linear relationship. A positive 'r' indicates a positive linear relationship, a negative 'r' indicates a negative linear relationship, and the closer 'r' is to 1 or -1, the stronger the relationship.
5. How should one interpret a correlation plot or scatter diagram?
To interpret a correlation plot (or scatter diagram), observe the pattern of the points: If points cluster around an upward-sloping line, it suggests a positive correlation. If they cluster around a downward-sloping line, it's a negative correlation. If points are widely scattered with no clear pattern, there's little to no linear correlation. The closer the points are to forming a straight line, the stronger the relationship.
6. What is the process to effectively interpret correlation results in a table or dataset?
To effectively interpret correlation results in a table:
- Look at the correlation coefficient values for each pair of variables.
- Note the sign (+ or -) to determine the direction of the relationship.
- Examine the absolute value (magnitude) to assess the strength. Values closer to 1 (either positive or negative) indicate stronger relationships, while values near 0 suggest weak or no linear relationship.
- Always consider the context of the variables to make meaningful conclusions.
7. Can you provide a real-world example to illustrate the concept of correlation?
Certainly! A common real-world example of correlation is the relationship between the amount of rainfall and crop yield. In many regions, higher rainfall (up to a certain point) tends to be associated with higher crop yields, indicating a positive correlation. Conversely, if you consider the price of a popular video game and the number of copies sold, you'd likely see a negative correlation: as the price goes up, fewer copies are sold.
8. What are some key uses of correlation in areas like business or economics?
Correlation is highly useful in business and economics:
- Projection and Forecasting: Businesses can correlate advertising spend with sales to project future sales or consumer behavior.
- Risk Mitigation: Identifying negative correlations (e.g., between inflation and product sales) helps foresee and prepare for risks.
- Performance Measurement: Correlating employee bonuses with productivity can inform incentive structures.
- Market Analysis: Economists use it to understand relationships between economic indicators like GDP, interest rates, and employment, helping in policy-making.
9. What is a mediator variable and how does it relate to observed correlations?
A mediator variable explains the relationship between an independent variable and a dependent variable. It acts as an intermediary, where the independent variable influences the mediator, which then influences the dependent variable. For example, increased heat might correlate with increased ice cream sales; however, the mediator variable could be 'number of people sweating due to heat.' The heat causes more sweating, which then drives ice cream sales, offering a deeper understanding of the correlation.
10. What are the crucial differences between correlation and causation?
The crucial difference between correlation and causation is that correlation simply indicates that two variables move together, while causation means one variable directly causes a change in the other. For instance, increased umbrella sales and increased rain are correlated, but umbrellas don't cause rain. Understanding this distinction is vital: correlation does not imply causation.
11. Why is understanding the context important when interpreting a correlation?
Understanding the context is crucial when interpreting a correlation because a statistical relationship doesn't always imply a meaningful or practical one. Without context, one might misinterpret spurious correlations (relationships that appear to exist but are purely coincidental) or overlook lurking variables. Knowing the background of the data, how it was collected, and what it represents helps ensure accurate and relevant conclusions.
12. What are some common mistakes students make when trying to understand correlation?
Common mistakes students make when trying to understand correlation include:
- Confusing correlation with causation.
- Assuming a zero correlation means no relationship at all, when it only means no *linear* relationship.
- Misinterpreting the strength of correlation (e.g., thinking a correlation of 0.5 is 'strong' without context).
- Ignoring outliers, which can significantly skew the correlation coefficient.
- Failing to visualize the data with a scatter plot, which can reveal non-linear relationships not captured by the Pearson coefficient.
