Sample covariance matrix
Okay, let's imagine that we have a basket of fruits. We have different types of fruits like apples, bananas, oranges, and pears. Now, we want to know if there is a relationship between the different types of fruits in our basket. For instance, if we have more apples, do we also have more bananas?
A sample covariance matrix is like a table that helps us check if there is any connection between different types of fruits in our basket. But instead of fruits, we have numbers. Let's say we have different sets of numbers like 1, 3, 6, and 8.
To create a covariance matrix, we first need to calculate the average (mean) of each set of numbers. We can do this by adding up all the numbers in each set and then dividing by how many numbers are in that set. For example, if we have the set of numbers 1, 2, 3, and 4, we add them up (1+2+3+4=10) and divide by 4 (since there are 4 numbers) to get an average of 2.5.
Once we have the averages for each set of numbers, we need to calculate how much each number in the set differs from its average. We call this the "deviation." For example, if we have a set of numbers like 1, 3, 4, and 5, and the average is 3.25, then the deviation for the number 1 would be (-2.25), the deviation for the number 3 would be (-0.25), the deviation for the number 4 would be (0.75), and the deviation for the number 5 would be (1.75).
We then multiply the deviations of each pair of numbers from different sets together, and add those products up. Finally, we divide that sum by how many numbers we have to get the covariance.
The sample covariance matrix is simply a table where each entry in the table represents the covariance between two sets of numbers. By looking at the covariance matrix, we can see whether there is a positive or negative relationship between the different sets of numbers. If the number is positive, then the two sets of numbers tend to increase or decrease together. If the number is negative, then as one set of numbers increases, the other tends to decrease.
In summary, a sample covariance matrix helps us understand if there is a relationship between different sets of numbers, and in what direction that relationship goes.
A sample covariance matrix is like a table that helps us check if there is any connection between different types of fruits in our basket. But instead of fruits, we have numbers. Let's say we have different sets of numbers like 1, 3, 6, and 8.
To create a covariance matrix, we first need to calculate the average (mean) of each set of numbers. We can do this by adding up all the numbers in each set and then dividing by how many numbers are in that set. For example, if we have the set of numbers 1, 2, 3, and 4, we add them up (1+2+3+4=10) and divide by 4 (since there are 4 numbers) to get an average of 2.5.
Once we have the averages for each set of numbers, we need to calculate how much each number in the set differs from its average. We call this the "deviation." For example, if we have a set of numbers like 1, 3, 4, and 5, and the average is 3.25, then the deviation for the number 1 would be (-2.25), the deviation for the number 3 would be (-0.25), the deviation for the number 4 would be (0.75), and the deviation for the number 5 would be (1.75).
We then multiply the deviations of each pair of numbers from different sets together, and add those products up. Finally, we divide that sum by how many numbers we have to get the covariance.
The sample covariance matrix is simply a table where each entry in the table represents the covariance between two sets of numbers. By looking at the covariance matrix, we can see whether there is a positive or negative relationship between the different sets of numbers. If the number is positive, then the two sets of numbers tend to increase or decrease together. If the number is negative, then as one set of numbers increases, the other tends to decrease.
In summary, a sample covariance matrix helps us understand if there is a relationship between different sets of numbers, and in what direction that relationship goes.
Related topics others have asked about: