16. Partial Differential Equations

Try these first

1. 1.

   What does a covariance of 0 indicate about the relationship between two variables?

   Hint

   Think about relationships in terms of direction.

2. 2.

   Define correlation in your own words.

   Hint

   Recall that it ranges from -1 to 1.

3. 3.

   What is the range of values for the correlation coefficient?

   • -1 to 1
   • 0 to 1
   • -∞ to ∞

   Hint

   Recall the properties of correlation.

4. 4.

   True or False: A covariance of 5 indicates a strong positive relationship between two variables.

   • True
   • False

   Hint

   Think about what covariance actually tells us.

5. 5.

   You have two datasets of daily temperatures and ice cream sales. The temperature dataset is X = {70, 75, 80, 85} and the sales dataset is Y = {200, 220, 240, 260}. Calculate the covariance and correlation. Discuss what this indicates about the relationship.

   Hint

   Follow the steps of calculating means and then apply covariance and correlation formulas.

6. 6.

   Create a scenario where two variables might show high covariance but low correlation. Explain the conditions.

   Hint

   Think about how outliers can affect linear relationships.