16.3.1. Definition

Try these first

1. 1.

   What does a positive covariance indicate?

   Hint

   Think about the behavior of the variables.

2. 2.

   What is the range of the correlation coefficient?

   Hint

   Consider the extremes in terms of relationships.

3. 3.

   What does a covariance of 0 indicate?

   • Positive relationship
   • Negative relationship
   • No linear relationship

   Hint

   Consider what zero implies about direction.

4. 4.

   True or False: A correlation of -1 indicates a perfect positive correlation.

   • True
   • False

   Hint

   Recall how the scale of correlation works.

5. 5.

   Given two random variables, X = {5, 10, 15} and Y = {1, 2, 3}, compute both the covariance and correlation and assess the strength of their relationship.

   Hint

   Use standard deviation and means in your calculations.

6. 6.

   In a real-world scenario, how would you interpret a high positive correlation between temperature and ice cream sales?

   Hint

   Consider the practical implications of seasonal businesses.