# R Correlation: How to Find the Relationship between Variables

Many times people will think of programming, and consider languages such as C, Python, and Perl, but there are other languages out there that have vastly different purposes. One such language is R, and it is quickly becoming popular. R isn’t used for creating video games or making webpages though, but instead it is designed for people to do complex statistics easily.

In statistical analysis, you will be using the letter r quite a bit. Finding the r correlation is one of the fundamental principles in statistics, and there is even an entire programming language that revolves around it.

When finding the correlation coefficient of two variables, you will first get the data sample and then find the covariance divided by the product of each variables standard deviation.

Although the concept of finding the r correlation can seem difficult to understand, it’s not all that complicated. There are people who can easily find the r correlation between variables. If you really want to get a better understanding of r correlation and other statistical concepts of r, then you should check out the Udemy courses Learn R by Doing It and Introduction to R.

**Calculating the R Correlation**** **

Before learning how to find the r correlation through the language, it’s best to understand how to calculate the correlation yourself. Understanding the concept will make it easier for you to program. In addition to this, if you understand how the r correlation works beyond just the program you can identify mistakes much easier.

With that being said, finding the r correlation involves very lengthy calculations, and without a calculator or r programming, you can expect to spend a lot of time doing it.

Before you begin to find the r correlation, you must first do preliminary calculations with your paired data. The pairs will be called (x_{i,}y_{i)}. When you’re doing basic arithmetic, it’s a lot easier to make a mistake, which means that you should always check your answers before continuing.

The first thing you want to do is calculate the mean of all of the first coordinates of data on the x plane, the result of this mean will be called x^{–}.

Next you want to do the same for your second coordinates or the coordinates on the y plane, and call the result y^{–}.

The following step is to calculate the s_{x} or the sample standard deviation for the first coordinates of x_{i} and do the same thing for s_{y} for the second set of coordinates of all the data in y_{i}.

The next steps will help you work your way towards finding the correlation coefficient. If things are getting a little too complicated, you can go back and try to do the first set of calculations again until you’re comfortable moving on. You can try to use a program to help you as well, such as Microsoft Excel, which is great for finding the relationship between variables through linear correlation coefficients.

Following the previous steps, you will use a few formulas to help you find the correlation coefficient. To start, you will use the formula *(z _{x})_{i}* = (

*x*– x̄) /

_{i}*s*which will allow you to calculate the standardized value of every x

_{ x, }_{i}. You will use a similar formula to find the standardized value for every y

_{i}by switching out every x in the previous formula with y.

The final steps are much simpler. First, you will multiply the corresponding values of Z_{x }and Z_{y} together. Add the products the problems you did before. The final step is to divide the sum you just got from adding the values by the last step n – 1. In this situation, n is all of the points, both on the x and y plane that are in the data. The final result is called the correlation coefficient r.

As you can see, each individual step is rather simple, and you only need knowledge of basic addition and multiplication to do it, but they are all deeply involved and making a mistake on one step could completely ruin the problem altogether. Because of this, it can be difficult to accurately find the r correlation in problems.

**Examples of Finding the Correlation Coefficient**** **

Now that you’ve seen the correlation coefficient, let’s look at an example of how you would do the problem yourself. You can start with a simple set of pairs. In this particular situation, you can use (1, 1), (2, 3), (4, 5), and (5, 7).

Following the first step, you would find the mean value of numbers on the x and y coordinates, which in this case is 3 for x and 4 for y. Next, you will have to find the standard deviation of both x and y. Try to use the formulas that were shown above, and you should get 1.83 for x and 2.58 for y. After this you will have to do a list of calculations. Remember to add the products when you’re done doing your calculations divide everything by n – 1. Remember that n is the number of pairs that you have for the problem, which means that you would divide everything by 4 – 1 or 3. Your correlation coefficient should be 0.9899

**Using Statistical Software**** **

Thanks to the r programming language, you don’t have to worry about doing all of the calculations above by hand. If you have statistical software, you can have a computer do everything for you and greatly reduce the chance of you making a mistake.

For the r language, you can use the correlation function, cor () to find the r correlation. A simple version of this function is cor (x, use=, method= )

In this function, x is the matrix or data frame that you will be using to find your correlations. Use is for handling all of your missing data, you can state that there is no missing data, that the program should do listwise deletion, or that it should do pairwise deletion.

The final part of the function is the most important since it is the method of correlation that the program is going to decide to use. You can choose the pearson, spearman, or kendall correlation, but for this situation, you will be using the pearson method.

Statistical software is not only good for doing quick calculations, but you can do it for larger sets of data. This type of software is important for anyone who is serious about doing statistical analysis, and you should consider growing accustomed to it so that you can better understand r. If you want to try your hand at doing different types of statistics with r, then you should check out the Udemy course Data analysis with R. This course is designed to help beginners with understanding the way r works, and how it is used. Of course r correlation is also covered, which makes it a great resource to review what you’ve learned.

**The Importance of R**** **

Through statistics, people are able to find out a lot about their business. It’s possible to see how much money a company could potentially make or what the customers prefer in a store. There are several models that use data analysis to help with decision making. If you want to see an example of how data analysis is used in real life applications, check out the Customer Choice Modeling with R course in Udemy. This course gives a detailed explanation on how you can predict what customers want.

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