Positive Correlation: Definition, Application and Examples
Last Updated :
16 Jul, 2024
Understanding the difference between inverse (correlations is essential for understanding how variables relate to each other. A positive correlation indicates that when one variable goes up the other also rises and when one goes down the other decreases well.
For instance, putting in study hours usually results in exam grades. On the other hand, an inverse correlation shows that as one increases the other decreases like spending more time on social media leading to poorer academic performance.
In this article, we will learn about, correlation definition, positive correlation, examples and others in detail.
What is Correlation?
Correlation is a statistical measure that describes the strength and direction of a relationship between two variables. It quantifies how changes in one variable are associated with changes in another variable.
Correlation between different variables may either,
- Positive Correlation
- Negative Correlation
What Is Positive Correlation?
When two variables move in the same direction, that is, when one increases, the other increases as well, and when one decreases, the other declines as well, there is a positive correlation.
For Example: If the price increases the supply will also increase, Suppose the Price is measured in Rupees on the other side supply will be measured in units. If the product price is ₹ 10 and the Supply is 50; Then if the price increases by ₹ 20 then the Supply will be 100. Therefore, It shows both the variables moving in the same direction. If Price (↑) is increasing then Supply (↑) is also growing.
Positive Correlation Examples in Real Life
Some real-life examples of positive correlations include:
- Number of study hours and test results: The more hours someone spends studying for an exam, the higher their test score is expected to be (better result).
- Exercise quantity and general fitness: An individual becomes more fit (health would improve) the more they exercise (more activity).
- Plant growth and sunlight: Compared to plants in the shade, those in greater sunshine typically grow taller and healthier.
Understanding Positive Correlation
A relationship in which both variables move in the same direction that is, when one rises, the other rises as well is referred to as a positive correlation. For Example: The more hours you spend studying the more you score in exams. This relationship shows that the two variables go hand in hand.
What Does a Correlation of 1.0 Mean?
A perfect correlation of 1.0 means two things always rise together. One moves up and the other moves up with a constant level and it is shown in a graph with a straight line. This is like the ideal and it will never happen again unless it somehow happens again and a super strong bond between each.
How Do You Know If a Correlation Is Strong or Weak?
The correlation coefficient, which ranges from 0 to 1, can be used to measure how strong the positive association is. A coefficient of near 1 indicates a very strong correlation, so both variables tend to increase together very uniformly The closer the coefficient is to 0, the weaker the correlation is (that is, the variables do not increase together as reliably. Positive Correlation ( r = 1 or near 1).
Applications of Positive Correlation
Some of the applications of positive correlation are given below:
- Commerce: Businesses may use their favourable relationships to employ marketing strategies. Example: If research shows a correlation between income level and the purchase of a particular product, an advertiser may use this information to target high-income consumers for its product.
- Educational: Teachers can use positive associations to pinpoint study habits that raise student achievement. If exam scores are not related and students learn more effectively in a different way, we as educators need to examine that and find out how to do it sooner rather than later.
- Science and Research: When scientists want to locate probable areas of further study they search for any rousing associations. If an association between breathing problems and air pollution were found, researchers could look into whether these breathing problems are a cause of air pollution.
How to Measure Positive Correlation?
A coefficient is a number that ranges from -1 to +1 that describes the intensity of a positive correlation. In this case, there is a positive correlation between the two variables always moving in the same direction but if the coefficient was +1 then the same variables would always move in the same proportion (positive perfect correlation). The coefficients can help to move the variables in the same direction, although not as reliable and to the same degree when the coefficient gets closer to 0. This is known as a weaker positive correlation.
Positive Correlation Vs Negative Correlation
When we talk about Inverse correlations we're referring to how two sets of data or variables are connected. By using a correlation coefficient you can figure out if the relationship, between these sets is either positive or Inverse. Sometimes you might come across the correlation coefficient being denoted as "p." It's crucial to keep in mind that the accuracy of the correlation coefficient is highest when the connection between your data points follows a line, rather than a curved one.
Positive and Inverse correlations simply indicate how numbers or variables are linked in a way that's easy to spot when you plot them on a graph. Let's delve deeper into what negative correlations mean;
Positive Correlation | Inverse Correlation |
|---|
Positive Correlation is a positive relationship between two variables such as if one variable goes up other also goes up. | Inverse Correlation is a negative relationship between two variables if one variable goes up then the other goes down. |
Value of correlation is between 0 and +1. | Value of correlation is between 0 and -1. |
Amount of a perfect positive correlation is +1. | Amount of a perfect negative correlation is -1. |
For Example: People typically buy more ice cream on hot days because they want something cool to eat. This tendency increases as the temperature rises. | For Example: When you go deeper underwater, you experience greater water pressure. If you change your position to go further underwater (one variable increases), you will also increase the water pressure (the other variable increases in the opposite direction). |
Conclusion
It is similar to comprehending how things change together to understand positive and inverse correlations. When two variables increase, they are said to be positively correlated.
For example, studying more can help you get better marks. When one thing increases, the other usually decreases, like in the case of higher social media usage and worse grades. Understanding these trends allows us to make more intelligent judgments in daily life, such as time management and financial decisions.
Numericals on Positive Correlation
Example 1: In this question, we will look at the study hours and after that exam scores of the students and Calculate the coefficient of correlation, given the following data.
Hours Studied (X) | Exam Score (Y) |
|---|
2 | 55 |
4 | 60 |
6 | 65 |
8 | 70 |
10 | 75 |
Solution:
X | Y | X = (X-Xˉ) | Y = (Y-Yˉ) | Xˉ2 | Yˉ2 | Xy |
|---|
2 | 55 | 2-6 = -4 | 55-65 = -10 | 16 | 100 | -4x-10 = 40 |
4 | 60 | 4-6 = -2 | 60-65 = -5 | 4 | 25 | -2x-5 = 10 |
6 | 65 | 6-6 = 0 | 65-65 = 0 | 0 | 0 | 0x0= 0 |
8 | 70 | 8-6 = 2 | 70-65 = 5 | 4 | 25 | 2x5 = 10 |
10 | 75 | 10-6 = 4 | 75-65 = 10 | 16 | 100 | 4x10 =40 |
ΣX/N= 30/5 = 6 | ΣY/N = 325/5 |
|
| ∑(X−Xˉ)2 = 40 | ∑(Y−Yˉ)2 = 250 | ∑Xy = 100 |
At last,
Correlation Coefficient (r) = ∑Xy/√∑ X2 - Y2
r = 100/√40 x 250
r = 100/√10000
r = 100/100 = 1.0
The exam scores and the amount of study hours have a perfect positive Correlation coefficient r = 1.0. This indicates that exam scores rise in a precisely linear fashion as the amount of study hours increases.
Example 2: Calculate coefficient correlation, given the following data:
Solution:
X | Y | X = (X-Xˉ) | Y = (Y-Yˉ) | Xˉ2 | Yˉ2 | Xy |
|---|
2 | 4 | 2-5 = -3 | 4-10 = -6 | 9 | 36 | 18 |
3 | 7 | 3-5 = -2 | 7-10 = -3 | 4 | 9 | 6 |
4 | 8 | 4-5 = -1 | 8-10 = -2 | 1 | 4 | 2 |
5 | 9 | 5-5 = 0 | 9-10 = -1 | 0 | 1 | 0 |
6 | 10 | 6-5 = 1 | 10-10 = 0 | 1 | 0 | 0 |
7 | 14 | 7-5 = 2 | 14-10 = 4 | 4 | 16 | 8 |
8 | 18 | 8-5 = 3 | 18 - 10 = 8 | 9 | 64 | 24 |
ΣX/N= 35/7 = 5 | ΣY/N= 70/7 = 10 |
|
| ∑(X−Xˉ)2 = 28 | ∑(Y−Yˉ)2 = 130 | ∑Xy = 58 |
At last the Correlation Coefficient (r) = ∑Xy/√∑ X2 - Y2
r = 58/√28 x 130
r = 58/√3640
r = 58/60.33 = + 0.96
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