16.1.2. Mathematical Formula

Try these first

1. 1.

   What does covariance measure?

   Hint

   Think about whether they increase or decrease together.

2. 2.

   What is the correlation coefficient range?

   Hint

   Consider the extreme values it can take.

3. 3.

   What does a positive covariance indicate?

   • Variables increase together
   • Variables decrease together
   • No relationship

   Hint

   Think about how both variables interact.

4. 4.

   The correlation coefficient can only be found between which two values?

   • -1 and 0
   • 0 and 1
   • -1 and 1

   Hint

   Recall the extremes of correlation.

5. 5.

   Consider two datasets: A = {10, 20, 30, 40, 50} and B = {5, 15, 25, 35, 40}. Calculate the covariance and correlation. Discuss their implications.

   Hint

   Don't forget to calculate means first and standard deviations while solving.

6. 6.

   You are analyzing the height and weight of a sample of plants. The covariance between height and weight is found to be positive. What does this suggest about their relationship, and how might environmental factors play a role?

   Hint

   Consider the biological growth environments that affect both height and weight.