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The covariance between two random variables is -551351. What can be said about their relationship?Group of answer choicesThe variables must be independent of one another.The two variables have a very weak negative relationship.The two variables have a very strong negative relationship.The line of best fit between the two variables would be downward sloping.

Question

The covariance between two random variables is -551351. What can be said about their relationship?Group of answer choicesThe variables must be independent of one another.The two variables have a very weak negative relationship.The two variables have a very strong negative relationship.The line of best fit between the two variables would be downward sloping.

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Solution

Covariance is a measure of how much two random variables vary together. It's similar to correlation, but while correlation measures the relative strength of the relationship between two variables, covariance measures the actual amount that the variables vary together.

In this case, the covariance between the two variables is -551351. This is a large negative number, which tells us a few things:

  1. The negative sign indicates that the variables have a negative relationship. This means that as one variable increases, the other variable tends to decrease, and vice versa.

  2. The large magnitude of the covariance (551351) suggests that this negative relationship is very strong. The variables don't just tend to move in opposite directions; they move in opposite directions a lot.

  3. Because of this strong negative relationship, the line of best fit between the two variables would be downward sloping. This line would show that as one variable increases, the other decreases.

So, the correct answer is: The two variables have a very strong negative relationship and the line of best fit between the two variables would be downward sloping.

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