Question

A measure of the relationship between two random variables and to what extent they change together is

• A. Co-variance
• B. Correlation
• C. Regression
• D. Coefficient of determination

Hint:

Remember:
- Covariance measures the direction of a relationship between two variables (unscaled).
- Correlation measures both the direction and strength of the relationship (scaled between \(-1\) and \(+1\)).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In statistics, researchers often want to measure how two random variables behave relative to one another to determine if they change together.

Step 2: Detailed Explanation:
Let us evaluate the statistical terms listed in the options:
- Covariance:
Covariance is a metric that measures the joint variability of two random variables.
If both variables tend to increase or decrease together, the covariance is positive.
If one variable increases while the other decreases, the covariance is negative.
It measures the direction of the linear relationship and shows to what extent the variables change together.
This matches the definition in the question.
- Correlation:
Correlation is a normalized version of covariance that measures both the strength and direction of the linear relationship on a scale from \(-1\) to \(+1\).
Because it is normalized, it does not depend on the scale of measurement.
- Regression:
A statistical method used to model and analyze the relationship between a dependent variable and one or more independent variables, allowing for prediction.
- Coefficient of determination (\( R^2 \)):
A metric that represents the proportion of the variance in the dependent variable that is predictable from the independent variable.
Therefore, covariance is the fundamental measure of how two variables change together.

Step 3: Final Answer:
Covariance is the statistical metric used to measure how two random variables change together.
Thus, the correct choice is (A).