Hướng dẫn python covariance to correlation
IntroductionWorking with variables in data analysis always drives the question: How are the variables dependent, linked, and varying against each other? Covariance and Correlation measures aid in establishing this. Show
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In this article, we'll learn how to calculate the covariance and correlation in Python. Covariance and Correlation - In Simple TermsBoth covariance and correlation are about the relationship between the variables. Covariance defines the directional association between the variables. Covariance values range from -inf to +inf where a positive value denotes that both the variables move in the same direction and a negative value denotes that both the variables move in opposite directions. Correlation is a standardized statistical measure that expresses the extent to which two variables are linearly related (meaning how much they change together at a constant rate). The strength and directional association of the relationship between two variables are defined by correlation and it ranges from -1 to +1. Similar to covariance, a positive value denotes that both variables move in the same direction whereas a negative value tells us that they move in opposite directions. Both covariance and correlation are vital tools used in data exploration for feature selection and multivariate analyses. For example, an investor looking to spread the risk of a portfolio might look for stocks with a high covariance, as it suggests that their prices move up at the same time. However, a similar movement is not enough on its own. The investor would then use the correlation metric to determine how strongly linked those stock prices are to each other. Setup for Python Code - Retrieving Sample DataWith the basics learned from the previous section, let's move ahead to calculate covariance in python. For this example, we
will be working on the well-known Iris dataset. We're only working with the Let's have a look at the dataset, on which we will be performing the analysis: We are about to pick two columns, for our analysis - In a new Python file (you can name it
In data science, it always helps to visualize the data you're working on. Here's a Seaborn regression plot (Scatter Plot + linear regression fit) of these setosa properties on different axes: Visually the data points seem to be having a high correlation close to the regression line. Let's see if our observations match up to their covariance and correlation values. Calculating Covariance in PythonThe following formula computes the covariance: In the above formula,
The denominator is With the math formula mentioned above as our reference, let's create this function in pure Python:
We first find the mean values of our datasets. We then use a list comprehension to iterate over every element in our two series' of data and subtract their values from the mean. A for loop could have been used a well if that's your preference. We then use those intermediate values of the two series' and multiply them with each other in another list comprehension. We sum the result of that list and store it as the Check out our hands-on, practical guide to learning Git, with best-practices, industry-accepted standards, and included cheat sheet. Stop Googling Git commands and actually learn it! We then return the value when the Running our script would give us this output:
The positive value denotes that both the variables move in the same direction. Calculating Correlation in PythonThe most widely used formula to compute correlation coefficient is Pearson's 'r': In the above formula,
Seems like we've discussed everything we need to get the correlation in this series of articles! Let's calculate the correlation now:
As this value needs the covariance of the two variables, our function pretty much works out that value once again. Once the covariance is computed, we then calculate the standard deviation for each variable. From there, the correlation is simply dividing the covariance with the multiplication of the squares of the standard deviation. Running this code we get the following output, confirming that these properties have a positive (sign of the value, either +, -, or none if 0) and strong (the value is close to 1) relationship:
ConclusionIn this article, we learned two statistical instruments: covariance and correlation in detail. We've learned what their values mean for our data, how they are represented in Mathematics and how to implement them in Python. Both of these measures can be very helpful in determining relationships between two variables. How do you find covariance and correlation in Python?cov() function. Covariance provides the a measure of strength of correlation between two variable or more set of variables. The covariance matrix element Cij is the covariance of xi and xj. How do you calculate covariance in Python?The covariance may be computed using the Numpy function np. cov() . For example, we have two sets of data x and y , np. cov(x, y) returns a 2D array where entries [0,1] and [1,0] are the covariances. How does Python calculate correlation?To calculate the correlation between two variables in Python, we can use the Numpy corrcoef() function. How do you calculate covariance and correlation?Correlation looks at the strength of the relationship between two variables. To calculate the correlation between two variable, the covariance value is divided by the standard deviation of both variables. |