Question

What does a negative covariance mean?

Answer 1

Hint: Covariance is an important concept in statistics. Covariance is used to determine the relationship between any two specific random variables in a problem. We explain the term covariance and what a negative covariance is. We also provide an example for better understanding of the concept.

Complete step-by-step solution:
We explain the term covariance first. Covariance gives us the degree to which one random variable is related to the other random variable. This specifies the rate at which one variable would change for a specific amount of change in the other variable. This concept is similar to variance by in case of variance, it is applied for a single variable, whereas covariance is applied to two variables taken at a time.
There are 2 types of covariance:
Positive covariance
Negative covariance
Positive covariance occurs when one variable increases with the increase in the other variable, this means that the change in the two variables occur in the same direction.
In the case of negative covariance, value of one variable decreases with the increase in the other variable, this means that the change in the two variables occur in the opposite directions. This can be explained using an example. Let us take the example of a car travelling on the road. Let us consider two variables: the distance covered and the fuel left in the tank. As the amount of distance covered increases, the amount of fuel left in the tank reduces. This shows that a reduction in one variable causes an increase in the other, showing that the two variables have negative covariance.

Note: Covariance is an important concept required to solve important problems in our daily life. Stock markets use the basic principle of covariance. Knowing this concept helps us overcome many of our day-to-day problems and its key to know about covariance and its properties.