# Example of Positive Correlation (And How to Calculate It)

By Indeed Editorial Team

Updated November 6, 2022

Published September 29, 2021

The Indeed Editorial Team comprises a diverse and talented team of writers, researchers and subject matter experts equipped with Indeed's data and insights to deliver useful tips to help guide your career journey.

In statistics, correlations indicate the presence of a relationship between two variables. While a correlation doesn't always mean causation, you can gain valuable insight into how the variables influence one another. Calculating the correlation coefficient can tell you more about how strong the relationship is between the variables and help you think more critically in your career. In this article, we explore what positive correlations are, discuss what correlation coefficients are, explain what types of correlation coefficients there are, and cover how to calculate correlation coefficients with an example of positive correlation to guide you.

## What is a positive correlation?

A positive correlation occurs when two variables share a relationship in which they move in similar directions on a graph. Sometimes, a positive correlation occurs because one variable causes an effect on the other. In other cases, the two variables are independent of each other, and only experience changes when another variable influences their movement.

It's also important to note that observing a positive correlation doesn't always indicate a causal relationship between the variables. Correlations can provide valuable insight into how variables change in relation to one another, which is essential in applications like financial analysis, sales and marketing, medical studies, and technical developments.

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## What is an example of positive correlation?

In an ideal example of a positive correlation, variables move at the same rate of change and in the same direction as each other all the time. While this isn't always the case, there are several instances when a positive correlation displays this behaviour. Consider the following examples of positive correlations for more insight:

### Example 1: Sales analysis

In a sales analysis, team members might look for positive correlations between customer demand and product prices. In competitive markets, customer demand can influence product prices to increase. If sales teams observe this trend, they might identify a positive correlation. In this case, a positive correlation exists between the team's increase in customer demand and the recent increase in product prices.

### Example 2: Financial analysis

Stock investors often look for positive correlations when trading in the stock market. A stock trader, for instance, may notice the rise in stock prices for a specific company that has recently introduced new products. A positive correlation, in this case, can occur between the company's stock prices and its profitability. As the company's profitability increases, the stock prices increase too. This means the stock trader may consider investing in this company's shares as a way to earn a substantial return.

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### Example 3: Healthcare

The healthcare field relies on statistical research for many applications, including medical studies for new pharmaceuticals. For example, a pharmaceutical company conducts clinical trials with participants to understand the effects of a new drug for treating arthritis. During the study, clinical researchers note patient symptoms when administering the new arthritis medication. If the researchers notice that the patient's mobility and dexterity increase with regular doses of the medication, they can assume a positive correlation. With further study, they may even find a causal relationship, making their new medication a viable treatment for patients with arthritis.

### Example 5: Economics

A census surveyor may use correlative indicators to understand how different changes in the community affect individuals. When surveying community members, for instance, they might find that an increase in the open areas, parks, and recreational areas in the city seems to relate to an increase in community members' use of these locations. The surveyor might consider this a positive correlation, as both variables (the number of recreational areas and the number of community members) appear to move in the same direction.

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You can observe other types of correlations besides positive relationships. When analyzing data, if you notice two variables moving in opposite directions from one another, this becomes a negative correlation. For instance, when a vehicle's age increases, its value decreases. Depreciation is one example of a negative correlation.

Zero or no correlation shows that there is no relationship between the two variables. This can show as one variable moving in an identifiable direction while the other shows no related movement. You can also see a zero correlation when one variable exhibits no change. One example of a zero correlation is an unrelated increase in native bird populations and gas prices.

## What is a correlation coefficient?

While correlation studies how two entities relate to one another, a correlation coefficient measures the strength of the two variables' relationship. Knowing your variables is helpful in determining which correlation coefficient type you need to use. Applying the right correlation equation will help you better understand the relationship between the datasets you're analyzing. In statistics, there are three different types of correlation coefficients:

• Pearson correlation: The Pearson correlation is the most common correlation measurement for linear relationships between a set of two variables. The stronger the correlation between these two datasets, the closer to +1 or -1 the coefficient should be.

• Spearman correlation: This type of correlation helps determine the association (monotonic relationship) between two datasets. Unlike the Pearson correlation coefficient, it's based on ranked values within each dataset and uses ordinal or skewed variables instead of normally distributed ones.

• Kendall correlation: This type of correlation is effective for measuring how strong the dependency is between two variables.

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## Correlation coefficient equation

You can use the following equation and variable representations to calculate correlation:

∑ (x(i) - x̅)(y(i) - ȳ) / √ ∑(x(i) - x̅) ^2 ∑(y(i) - ȳ)^2

• x(i) = the value of x

• y(i) = the value of y

• x̅ = the mean of the x-value

• ȳ = the mean of the y-value

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## Example of positive correlation coefficients calculations

Follow these steps to calculate the correlation coefficient:

At the beginning of your calculation, determine what your variables are going to be. You can organize them in a chart and in ascending order if it helps you visualize them better. Separate each variable with a comma and create a separate line for your x and y variables. As an example, use the following dataset:

x: (1, 2, 3, 4) and y: (2, 3, 4, 5)

### 2. Calculate the mean of the x and y variables

To calculate the mean or average of each dataset, add the values of the x variables and the y variables and then divide by the number of values in the datasets. With the example datasets for x and y, determine the mean of x by adding one, two, three, and four together. Divide this sum by four, as four is the number of values you have for x. Do the same for the y variables. Using the example dataset above, add together two, three, four, and five and divide by four. This results in:

x: (1 + 2 + 3 + 4 = 10) / 4 = 2.5

y: (2 + 3 + 4 + 5 = 14) / 4 = 3.5

### 3. Subtract the mean

For the x-variable, subtract the mean from each value of x-variable and call it "a." For the y-variable, subtract the mean from each value of the y-variable and call it "b." This gives you:

a: -1.5, -0.5, 0.5, 1.5

b: -1.5, -0.5, 0.5, 1.5

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### 4. Multiply and find the sum

Multiply each a-value by the corresponding b-value. After you've done this, find the sum, which will end up being the formula's numerator. Here's what the previous example data values result in:

[(-1.5) x (-1.5)] + [(-0.5)(-0.5) + (0.5)(0.5) + (1.5)(1.5)] =

(2.25) + (0.25) + (2.25) + (0.25) = 5

### 5. Take the square root

At this point, you can square every a-value and then determine the sum of the results. After you've done this, calculate the square root of the value you've just determined. This gives you the denominator in the coefficient formula. Use the previous example values to get:

a-values: -1.5, -0.5, 0.5, 1.5 =

(-1.5)2 + (-0.5)2 + (0.5)2 + (1.5)2 =

1.75 + 0.25 + 0.25 + 1.75 = 4

### 6. Divide

Divide the numerator from step four by the denominator from step five. This result gives you the correlation coefficient. If you prefer to calculate digitally, there are correlation calculators online. This method is more efficient when you have larger datasets. With the example dataset, the correlation coefficient is:

5 / 4 = 1.25

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