Covariance and Correlation Coefficient Quiz: University Level Questions

📚 Quick Study Guide

• ➕ Covariance: Measures the degree to which two variables change together. A positive value means they tend to increase or decrease together, while a negative value means one increases as the other decreases. The formula for sample covariance is: $cov(X,Y) = \frac{\sum_{i=1}^{n} (X_i - \bar{X})(Y_i - \bar{Y})}{n-1}$
• ➗ Correlation Coefficient: Standardizes covariance to a range between -1 and 1. It indicates both the strength and direction of a linear relationship. The formula for Pearson's correlation coefficient is: $r = \frac{cov(X,Y)}{s_X s_Y}$, where $s_X$ and $s_Y$ are the sample standard deviations of X and Y respectively.
• 📉 Interpretation of Correlation:
  • 1️⃣ +1: Perfect positive correlation (as one variable increases, the other increases proportionally).
  • 0️⃣ 0: No linear correlation.
  • -1️⃣ -1: Perfect negative correlation (as one variable increases, the other decreases proportionally).
• ⚠️ Important Note: Correlation does not imply causation! Just because two variables are correlated doesn't mean one causes the other.

Practice Quiz

1. What does a covariance of zero between two variables indicate?
   1. A. A perfect positive linear relationship
   2. B. A perfect negative linear relationship
   3. C. No linear relationship
   4. D. A non-linear relationship
2. The correlation coefficient ranges between:
   1. A. 0 and 1
   2. B. -1 and 0
   3. C. -∞ and +∞
   4. D. -1 and +1
3. If the covariance between X and Y is -50, and the standard deviations of X and Y are 5 and 10 respectively, what is the correlation coefficient?
   1. A. 0.5
   2. B. -0.5
   3. C. 1
   4. D. -1
4. Which of the following is true regarding the relationship between covariance and correlation?
   1. A. Covariance is always greater than correlation.
   2. B. Correlation is a standardized version of covariance.
   3. C. Covariance is always between -1 and 1.
   4. D. Correlation and covariance are the same thing.
5. What does a correlation coefficient of 0.9 indicate?
   1. A. A weak positive correlation
   2. B. A strong positive correlation
   3. C. A weak negative correlation
   4. D. A strong negative correlation
6. Which of the following is NOT a limitation of using correlation coefficient?
   1. A. It only measures linear relationships.
   2. B. It is sensitive to outliers.
   3. C. It implies causation.
   4. D. It can be misleading with non-linear relationships.
7. If two variables have a positive correlation, then:
   1. A. As one variable increases, the other tends to decrease.
   2. B. As one variable increases, the other tends to increase.
   3. C. The variables are unrelated.
   4. D. One variable causes the other to increase.