Covariance and correlation are two of the most significantly used terms in the field of statistics and probability. Both are concepts that describe the relationship between two random variables to each other.
Covariance is a statistical technique used for determining the relationship between the movement of two random variables. In short, how much two random variables change together.
Positive covariance indicates that higher than average values of one variable tend to get paired with higher than the average values of the other variable.
Negative coigher than the average values of one variable tends to get paired with lower than variance results that haverage values of the other variable.
Correlation is also a statistical technique that determines how the change of one variable related to another variable affects the relationship. In short, it defines the degree of relation between two variables. There exist three types of correlations - positive and negative, and zero correlations.
A positive correlation is a relationship between the variables, where two variables move in the same direction. If one variable increases, the other also increases. If one variable decreases, the other also decreases.
In a negative correlation, when one variable value decreases, the other variable value increases and vice versa. In zero correlations, there exists no relationship between two variables.
Correlation and covariance are two popular statistical concepts solely used to measure the relationship between two random variables. Data scientists use these two concepts for comparing the samples from different populations. Covariance defines how two random variables vary together. And correlation states how the change of one variable affects the other.
The value of covariance gets affected due to the change in the scale of the variables. If one value gets multiplied with the constant, the other variable gets multiplied with a similar constant too. Therefore, the value of covariance changes. But, if you do the same with correlation, the value of the correlation doesn’t get influenced.
Another massive difference between these two is the range of values that they can assume. In correlation, coefficients lie in the range between [-1 and +1]. Incase of covariance, it can take any value between the range of [-∞ and +∞]. For more details, you can check out correlation versus covariance for your reference.
These two concepts have enormous applications in data science and data-driven industries. Thus, data scientists consider these two as vital tools for selection. And for multivariate analysis in data preprocessing and exploration.
Correlations help in investigating and establishing the relationship between variables and implemented before statistical modeling or data analysis. Principal Component Analysis (PCA) is one of the most significant applications of the same.
The prime purpose of using Principal Component Analysis or (PCA) is to reduce the dimensions of the large datasets. By transforming a large number of datasets into smaller ones that still contain the most information of large datasets.
While measuring two variables, correlations and covariance are the two best methods to find out the relationship between them. But, in the case of the multiple variables, the process can become complicated and time-consuming as well.
Thus, data scientists use PCA in Exploratory Data Analysis (EDA) and predictive analysis. Each uncorrelated derived variable (principal elements) is a linear combination of starting variables.