# What is Positive Correlation?

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Definition:

A positive correlation indicates that two variables have a relationship with each other and move in the same direction — when one rises or falls, so does the other.

## 🤔 Understanding positive correlation

When two variables have a positive correlation, they move in the same direction. The relationship means that when one variable increases or decreases in value, the other does as well. The strength of a positive correlation is determined by the Pearson correlation coefficient. The higher the correlation coefficient, the stronger the positive relationship — greater than zero indicates a fair to moderate positive association, all the way up to one, indicating a perfect positive correlation. But a positive correlation doesn’t imply causation. The changes in one variable are associated with those of another but aren’t necessarily the cause. Testing for correlation, including positive correlation, is useful for managing the diversification of an investment portfolio — choosing a range of assets that behave differently to optimize the level of acceptable risk.

Example

Let’s say you wanted to see whether Facebook stock prices tended to move in line with the broader stock market. You could check whether they have a positive correlation by inputting the average daily prices of the S&P 500 and Facebook for the last five years into an Excel spreadsheet:

ABC
1YearAverage Daily Price S&P 500Average Daily Price Facebook
22015\$2,061.07\$88.77
32016\$2,095.30\$117.04
42017\$2,449.84\$156.74
52018\$2,746.21\$171.51
62019\$2,912.09\$181.54

Using the CORREL function, you can calculate the Pearson correlation coefficient as follows: =CORREL(B2:B6,C2:C6)

The result is 0.95. A Pearson correlation coefficient of 0.95 (very close to a perfect correlation of 1) indicates that there is a robust positive correlation between the average daily prices of the S&P 500 and Facebook for the last six years. So when the price of the S&P 500 increases, the price of Facebook shares is very likely to increase as well.

However, this positive association isn’t causation — a rise in the price S&P 500 likely doesn’t cause the increase in the price of the Facebook stock.

## Takeaway

A positive correlation is like going on vacation in the summer…

Suppose you gather data on vacations and seasons, and determine there is a strong relationship between how warm it is and how many people travel. So, when the temperature rises, you can predict more people will travel. While they are closely related, keep in mind the weather may not be driving the travel — it could be related to outside factors, such as when students are out of school. Similarly, two things that have a positive correlation move in the same direction, but one doesn’t necessarily cause the other to move.

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## What is a positive correlation?

A positive correlation indicates that there is a direct relationship between two variables, with both variables moving in the same direction (e.g., when one variable increases, the other does as well).

Correlation measures how closely the movements of the two variables are connected, and this relationship can be observed by plotting the data on a graph.

• Positive correlation: the data of both variables align along a rising line.
• Negative correlation: the data of both variables gather around a decreasing line.
• No correlation: the data of both variables doesn’t indicate a relationship.

The closer that the points are to the trend line on the graph, the stronger the degree of correlation.

While a positive correlation indicates that two variables move in the same direction, the movement may follow patterns other than a line. The three main patterns are:

• Linear correlation: the data sets align along a straight line.
• Nonlinear correlation: the data sets align in a nonlinear pattern, such as a parabola or hyperbola (think of a U or V shape on a graph)
• Monotonic correlation: the data sets appear to move in the same direction but not at the same rate.

### Example of positive correlation using a graph

Let’s plot the daily prices of the S&P 500 and Facebook stock from Jan. 2, 2015 ( markets are closed on New Year’s Day) to Dec. 31, 2019, to check what type of pattern appears, if any.

The Facebook stock price is on the horizontal axis, and the S&P 500 price is on the vertical axis (e.g., the first point indicates that Facebook was \$78.45 and the S&P 500 was \$2,058.20).

The graph indicates that the daily prices of the S&P 500 and Facebook shares appear to aggregate along a rising line. When the price of the Facebook stock increased, the level of the S&P 500 did as well. Because the data points are close to the line, you can assume that there is a positive linear correlation between the two variables for that period.

### Example of positive correlation using Excel

Let’s gather the average daily prices of Starbucks and Dunkin’ shares from Jan. 2, 2015 to Dec. 31, 2019, and input them into an Excel spreadsheet:

ABC
1YearAverage Daily Price StarbucksAverage Daily Price Dunkin’
22015\$53.25\$47.99
32016\$56.58\$46.96
42017\$57.28\$55.26
52018\$57.50\$67.45
62019\$81.42\$75.77

Using the CORREL function, you can calculate the Pearson correlation coefficient as follows: =CORREL(B2:B6,C2:C6)

The result is 0.81. A Pearson correlation coefficient of 0.81 indicates that there is a positive correlation between the average daily price of Starbucks and Dunkin’ shares for the period.

When the price of Starbucks stock increased, the price of Dunkin’ stock did as well. However, this positive correlation doesn’t indicate causation. Some other factor could be responsible for driving up both stock prices.

## How does positive correlation work?

Positive correlation points out that two data sets maintain a positive relationship and move in line with each other. When one variable rises, so does the other. Likewise, when one variable decreases, so does the other.

Some financial analysts and investors believe that the price-to-earnings ratio (P/E ratio), which compares a company’s stock price to its earnings per share, has a positive correlation with future earnings growth. High P/E ratios are often considered a sign that investors expect higher future earnings, while low P/E ratios often signal that investors expect lower future earnings.

So if you know the change in the P/E ratio over time, you can make assumptions about changes in future earnings. For example, the 2020 estimated P/E ratio for Tesla stock was over 300 as of March 4, 2020, meaning that investors expected Tesla’s earnings to grow in 2020. On the other hand, the estimated 2022 P/E ratio for Tesla was under 40, indicating that investors expect Tesla’s earnings to slow down in 2022 if the assumptions prove correct.

## What is indicated by a positive value for a correlation?

The Pearson correlation coefficient determines the strength of positive correlation — greater than zero indicates a fair to moderate positive correlation. A coefficient of one indicates a perfect positive correlation.

The higher the Pearson correlation coefficient, the stronger the positive correlation. For example, a Pearson correlation coefficient of 0.78 indicates a stronger positive correlation between two variables than a Pearson correlation coefficient of 0.15.

## How are positive correlation and inverse correlation different?

The main difference between a positive correlation and an inverse correlation is that the first indicates a positive relationship, and the latter indicates a negative relationship. In an inverse correlation, the two variables move in opposite directions — when one variable increases, the other decreases.

Another difference is the sign of the Pearson correlation coefficient. While a positive correlation coefficient is greater than zero, an inverse correlation coefficient is less than zero. Therefore, an inverse correlation coefficient has a negative sign in front of the statistic (e.g., -0.20 or -0.85). Due to its negative sign, an inverse correlation is also referred to as a negative correlation.

A third difference is in the shape of the graphs made by a positive correlation versus an inverse correlation. If you were to draw a line through the points in the graph of two variables with a positive correlation, the line would be rising. However, the line through the points of two variables with an inverse relationship would be trending downward.

### How to interpret an inverse correlation coefficient

Negative correlation coefficients don’t work the same way as negative numbers. While the number -0.2 is greater than -0.9, a negative correlation coefficient of -0.2 signals a weaker inverse relationship than one of -0.9. An inverse correlation coefficient of -1 indicates a perfect contrary relation, meaning that both variables always move in opposite directions.

## How are correlations used in psychology research?

Psychology researchers use correlations to perform preliminary studies to assemble data about a topic, situation, or issue when running an experiment isn’t possible, cost-efficient, or ethical.

These types of studies, referred to as correlational studies, seek to understand the relationship between two variables (e.g., playing chess and improving memory retention).

While correlations are useful in understanding the level of association between two data sets, these measures don’t explain a cause-effect relationship.

Let’s assume that playing chess and showing an improvement in memory retention have a positive correlation coefficient of 0.75, meaning that there is a direct relationship between the two variables. The more hours you spend playing chess, the better your memory retention tends to get. However, the 0.75 correlation coefficient doesn’t necessarily mean that playing chess is the cause of improved memory retention.

The free stock offer is available to new users only, subject to the terms and conditions at rbnhd.co/freestock. Free stock chosen randomly from the program’s inventory. Securities trading is offered through Robinhood Financial LLC.

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