Understanding Correlations

Afterward, a correlation coefficient can be calculated and interpreted, as discussed in the following sections. Correlation is a statistical measure that describes how two variables are related and indicates that as one variable changes in value, the other variable tends to change in a specific direction. We can therefore pinpoint some interpreting correlation coefficient real life correlations as income & expenditure, supply & demand, absence & grades decrease…etc. The linear correlation coefficient can be helpful in determining the relationship between an investment and the overall market or other securities. This statistical measurement is useful in many ways, particularly in the finance industry.

Pearson correlation (r) is used to measure strength and direction of a linear relationship between two variables. Mathematically this can be done by dividing the covariance of the two variables by the product of their standard deviations. The linear correlation coefficient is a number calculated from given data that measures the strength of the linear relationship between two variables. The linear correlation coefficient is a number calculated from given data that measures the strength of the linear relationship between two variables, x and y. The closer the value of ρ is to +1, the stronger the linear relationship.

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Scatterplots, and other data visualizations, are useful tools throughout the whole statistical process, not just before we perform our hypothesis tests. Remember, we are really looking at individual points in time, and each time has a value for both sales and temperature. We can also look at these data in a table, which is handy for helping us follow the coefficient calculation for each datapoint. When talking about bivariate data, it’s typical to call one variable X and the other Y (these also help us orient ourselves on a visual plane, such as the axes of a plot).

But correlation coefficients are used by real researchers to illuminate real connections all the time. Take for example recent research into the topic of “global warming,” also known as “climate change.” The theory goes that an increase in greenhouse gases in Earth’s atmosphere will cause the planet to heat up. One can interpret correlation coefficients by looking at the number itself, or by looking at a corresponding scatterplot, or both. For examples of how to interpret the correlation coefficient, please observe the graphs below. A correlation coefficient is defined as a numerical representation of the strength and direction of the relationship.

Scatterplots for several pairs of variables

The graph itself tells that there is no linear relation there and you don’t have to worry about still finding the correlation for it. In this section, we’re focusing on the Pearson product-moment correlation. This is one of the most common types of correlation measures used in practice, but there are others. One closely related variant is the Spearman correlation, which is similar in usage but applicable to ranked data. Because PEARSON and CORREL both compute the Pearson linear correlation coefficient, their results should agree, and they generally do in recent versions of Excel 2007 through Excel 2019. The numerical measure of the degree of association between two continuous variables is called the correlation coefficient (r).

The correlation coefficient can help investors diversify their portfolio by including a mix of investments that have a negative, or low, correlation to the stock market. In short, when reducing volatility risk in a portfolio, sometimes opposites do attract. Actually, a correlation coefficient different from 0 in the sample does not mean that the correlation is significantly different from 0 in the population. This needs to be tested with a hypothesis test—and known as the correlation test. Suppose that instead of visualizing the relationship between only 2 variables, we want to visualize the relationship for several pairs of variables.

Finish the calculation, and compare our result with the scatterplot

In this case, you’d be wise to use the Spearman rank correlation instead. In statistics, they measure several types of correlation depending on type of the data you are working with. You should now be able to calculate Pearson’s correlation coefficient within SPSS, and to interpret the result that you get. You may also be interested in our tutorials on (1) exporting SPSS output to another application such as Word, Excel, or PDF and (2) reporting Pearson’s correlation coefficient from SPSS in APA style. The first thing you might notice about the result is that it is a 2×2 matrix. In this quick SPSS tutorial, we’ll look at how to calculate the Pearson correlation coefficient in SPSS, and how to interpret the result.

You will only need to do this step once on your calculator. If you don’t do this, r (the correlation coefficient) will not show up when you run the linear regression function. In the financial markets, the correlation coefficient is used to measure the correlation between two securities. For example, when two stocks move in the same direction, the correlation coefficient is positive. Conversely, when two stocks move in opposite directions, the correlation coefficient is negative. When interpreting correlation, it’s important to remember that just because two variables are correlated, it does not mean that one causes the other.