What is a positive relationship between two variables?

Correlation analysis measures how two variables are related. Thecorrelation coefficient (r) is a statistic that tells you the strengthand direction of that relationship. It is expressed as a positive ornegative number between -1 and 1. The value of the number indicates the strengthof the relationship:

• r = 0 means there is no correlation
• r = 1 means there is perfect positive correlation
• r = -1 means there is a perfect negative correlation

The sign of the correlation coefficient indicates whether the direction ofthe relationship is positive (direct) or negative (inverse).

Variables whichhave a direct relationship (a positive correlation) increase together and decrease together.

In aninverse relationship (a negative correlation), one variable increases while the other decreases.

While the sign indivates how one variable changes with respect to anothervariable, the magnitude of the number indicates the strength of a relationship.

It is important to remember that while correlation coefficients can be usedfor prediction (i.e. if we know the value for one variable, and thecorrelation, we can predict what the value of the second variable will be) theymay NOT be used for causation (i.e. we cannot say that one variable causesanother).

Example

Suppose you are reading a study of Regents exams. The investigator wantedto know if performance in grade school was related to scores on the Regentsexams. He did a correlation analysis on grade school performance and Regentsexam score, and found that r = .75 in his study. This tells you two things:

1. r is positive, so grade school performance and Regents exam score tendto increase and decrease together.
2. r is fairly close to 1, so the direct relationship is fairly strong.

If a correlation exists between two variables, this does NOT imply that onevariable causes another. Causation and correlation are two very differentthings.

The two correlation coefficients that appear most often in the literatureare the Pearson-product moment and the Spearmanrank sum.

Table of contents

1. Understanding positive correlation
2. Positive and negative correlation coefficients
3. Why is positive correlation important?
4. Correlation vs. causation
5. How to calculate correlation
6. We can help

In finance, it’s important to understand the relationship between different variables. For example, with a prolonged heat wave in the forecast, are people more likely to buy plane tickets to cool-temperature northern destinations? If you’re investing in airlines, you’d want to know.

Looking at the positive correlation between variables can help you make more informed decisions. Here’s how it works.

Understanding positive correlation

The term correlation is used to define the relationship between variables. In statistics, a positive correlation shows that changes in one variable will relate to the same type of changes in a second variable. The data is usually displayed in a scatterplot, which shows the linear relationship between variables in a positive correlation graph. It can also be used as part of a

For example, consumers are more likely to purchase big-ticket electronics when the economy is doing well. This means there is a positive correlation between higher employment rates and electronics purchases. An investor might draw the conclusion that electronic company stocks will rise in tandem with employment rates.

Positive and negative correlation coefficients

Correlation is expressed with a coefficient, or value that indicates whether the correlation is positive or negative.

• +1: This is a perfect positive correlation. Variables will move in the same direction. When one increases, so does the other.

• 0: There is no correlation. In other words, no relationship is detected between the variables.

• -1: This is a perfect negative correlation. The variables are related, but they move in opposite directions from one another. As one increases, the other will decrease.

One way to calculate whether or not there’s a positive correlation is to run a regression analysis on the two variables, calculating their R2 figure. As the R2 increases, this indicates a strong positive correlation.

It’s important to note that most relationships between variables, if they exist, aren’t ‘perfect’ with a coefficient of exactly -1 or +1. It’s a sliding scale of relativity. For example, there might be a weak positive correlation between the money that a company spends on advertising and its related sales. While advertising might bear some influence on the customer’s decision to make a purchase, it won’t be the only factor involved.

Why is positive correlation important?

Both positive and negative correlation coefficients can be used to guide investors. A strong positive correlation can be used to analyse which way the wind is blowing with a certain stock in relation to the overall economy. Negative correlation is also useful. For example, it’s used in hedging with the idea that if one asset decreases in value, another rises.

Correlation vs. causation

One thing that investors must always keep in mind is that correlation doesn’t always mean causality. Two variables might be correlated, but it doesn’t mean that one is increasing solely as a result of the other. Correlation merely looks at the relationship, not what causes increases and decreases. There might be a third variable influencing both factors or even no direct causation at all.

For example, the number of consumers purchasing smartphones increased steadily throughout the 2000s, as did the price of oil. There might be a weak positive correlation between these two variables, but it’s highly doubtful that higher oil prices influenced more people to purchase a smartphone or vice versa.

How to calculate correlation

To calculate the coefficient and chart a negative or positive correlation graph, you must chart the values of an x-variable and y-variable over time. To do this, you’ll need to obtain a wide data sample for each variable, calculate mean values, and enter them into your formula. One easy way to get around doing this manually is to use the CORREL function in Excel, which quickly tabulates the correlation.

What is an example of a positive relationship between two variables?

What does a positive relationship mean between two variables?

What is a negative relationship between two variables?

What is a positive and negative relationship between variables?