# Correlation: What It Means in Finance and the Formula for Calculating It

To learn more about Matplotlib in-depth, check out Python Plotting With Matplotlib (Guide). You can also take a look at the official documentation and Anatomy of Matplotlib. However, if you provide only one two-dimensional array as an argument, then kendalltau() will raise a TypeError.

The value of the off-diagonal elements of r, which represents the correlation coefficient between X and Y, is low. Likewise, the value of the off-diagonal elements of p, which represents the p-value, is much higher than the significance level of 0.05. This value indicates that not enough evidence exists to reject the hypothesis of no correlation between X and Y. For example, a correlation of -0.97 is a strong negative correlation, whereas a correlation of 0.10 indicates a weak positive correlation. A correlation of +0.10 is weaker than -0.74, and a correlation of -0.98 is stronger than +0.79. When the correlation is weak (r is close to zero), the line is hard to distinguish.

## Relationship between correlation coefficient and scatterplots using statistical simulations

We performed feature selection using the training data set in order to discover which of the bioreactor features were most influential on the cardiomyocyte content. The set of features considered consists of all the collected bioreactor features measured up until the seventh day of differentiation (dd7). And sx and sy are the standard deviation of X and Y, respectively. For example, the Pearson correlation of two data points X (1,2,3,4,5) and Y (10,15,35,40,55) is 0.98.

• As the number of pizza slices eaten increases, so does the amount of soda consumed.
• Correlations tell us that there is a relationship between variables, but this does not necessarily mean that one variable causes the other to change.
• If not, the estimated full length reliability for Spearman–Brown will be greater than obtained by other measures of internal consistency.
• For example, imagine that you are looking at a dataset of campsites in a mountain park.
• The Pearson correlation coefficient can’t be used to assess nonlinear associations or those arising from sampled data not subject to a normal distribution.
• Pearson’s correlation coefficient is the test statistics that measures the statistical relationship, or association, between two continuous variables.

This significant negative correlation suggests that countries with more specific search queries (i.e. high SoS index) will usually also display a lower variety of search topics (low VoU index) and vice versa. In other words, there is a certain trade-off between the variety and the specificity of searches. This assumption gets further support in a Spearman25 single-tailed correlation test that indicates a strong positive correlation between the SoS values and the percentage of entertainment-related searches in each country.

## Visualizing correlations with scatterplots

In this example, there is a causal relationship, because extreme weather causes people to use more electricity for heating or cooling. However, in general, the presence of a correlation is not sufficient to infer the presence of a causal relationship (i.e., correlation does not imply causation). For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox). For example, suppose someone holds the mistaken belief that all people from small towns are extremely kind.

When they meet a very kind person, their immediate assumption might be that the person is from a small town, despite the fact that kindness is not related to city population. While most countries with high SoS values tend to have a greater concentration of entertainment-related searches and thus less variety, findings also indicate that it is possible to maximise the two. A combination of the VoU and the SoS indices in one graph reveals the differences between countries in terms of the specificity and the variety of searches. Here, you use plt.style.use(‘ggplot’) to set the style of the plots. You’ll learn how to prepare data and get certain visual representations, but you won’t cover many other explanations.

## Example 2: Exam Results and TV Viewing Time

The horizontal axis represents one variable, and the vertical axis represents the other. In theory, very high scores EPV index mean that most search queries are concentrated in economic and political-related categories. Similarly, very low EPV index scores mean that most search queries are concentrated in entertainment-related categories. In both extreme cases (of very high and low EPV scores) the VoU index is supposed to be low, as the spread of search queries is not even among the different categories.

You now know that correlation coefficients are statistics that measure the association between variables or features of datasets. Depending on the sign of our Pearson’s correlation coefficient, we can end up with either a negative or positive correlation if there is any sort of relationship between the variables of our data set. Correlation coefficients are used in science and in finance to assess the degree of association between two variables, factors, or data sets.

## Correlation and independence

If you look back at Image 5, you can see that this number also references a strong positive correlation. A correlation coefficient formula describes the statistical and mathematical relationship between variables x and y. Essentially, the formula serves as a quantitative measure of the correlation. There are several types of correlation coefficients, and therefore different formulas. Pearson’s coefficient measures linear correlation, while the Spearman and Kendall coefficients compare the ranks of data. There are several NumPy, SciPy, and pandas correlation functions and methods that you can use to calculate these coefficients.

• The correlation coefficient can never be less than -1 or higher than 1.
• Correlation is often dictated and related to other statistical considerations.
• Linear regression is the process of finding the linear function that is as close as possible to the actual relationship between features.
• Image 7 shows some data you gathered on your friends and a scatterplot of that data.
• The Spearman correlation coefficient between two features is the Pearson correlation coefficient between their rank values.
• In other words, there is a certain trade-off between the variety and the specificity of searches.

The interpretation for the Spearman’s Correlation remains the same before and after excluding outliers with a correlation coefficient of 0.3. The difference in the change between Spearman’s and Pearson’s coefficients when outliers are excluded raises an important point in choosing the appropriate statistic. Non-normally distributed data may include outlier values that necessitate usage of Spearman’s correlation coefficient. Pearson’s correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a “product moment”, that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.

## More meanings of correlation

A combination of the two correlated indices in one graph provides a vivid presentation of the differences between countries in terms of the content and the variety of searches (Figure 4.4). Let’s look at the Pearson correlation for another set of paired list attributes. Mirko has a Ph.D. in Mechanical Engineering and works as a university professor. He is a Pythonista who applies hybrid optimization and machine learning methods to support decision making in the energy sector.

The Pearson correlation coefficient can’t be used to assess nonlinear associations or those arising from sampled data not subject to a normal distribution. It can also be distorted by outliers—data points far outside the scatterplot of a distribution. Those relationships can be analyzed using nonparametric methods, such as Spearman’s correlation coefficient, the Kendall rank correlation coefficient, or a polychoric correlation coefficient. A perfect positive correlation means that the correlation coefficient is exactly 1. This implies that as one security moves, either up or down, the other security moves in lockstep, in the same direction.

The Pearson correlation for two objects, with paired attributes, sums the product of their differences from their object means and divides the sum by the product of the squared differences from the object means (Fig. 11.3). In this case, the Pearson correlation is intermediate between 0 and 1, indicating some correlation. How does the Pearson correlation help us to simplify and reduce data? If two lists of data have a Pearson correlation of 1 or of − 1, this implies that one set of the data is redundant.