Interpreting Q-Q plot patterns for non-normal residuals with examples

📚 Quick Study Guide

• 📊 Q-Q Plot Basics: A Q-Q plot (quantile-quantile plot) compares the quantiles of two probability distributions. In the context of regression, it's used to assess whether the residuals are normally distributed.
• 📏 Ideal Scenario: If the residuals are perfectly normally distributed, the points on the Q-Q plot will fall exactly along the straight diagonal line.
• отклонение Deviations from Normality: Deviations from the straight line indicate non-normality. Different patterns suggest different types of non-normality.
• tail Heavy Tails: If the ends of the Q-Q plot curve away from the straight line, it suggests that the data has heavier tails than a normal distribution.
• hafif tail Light Tails: If the ends curve towards the straight line, the data has lighter tails than a normal distribution.
• Skewness Skewness: An S-shaped pattern indicates skewness. If the bottom end of the plot deviates to the right of the line and the top end deviates to the left, it suggests right skewness (positive skew). The reverse indicates left skewness (negative skew).
• Discreteness Discreteness: If the data is discrete, the Q-Q plot will show a step-like pattern.
• Transformations Transformations: If the residuals are not normally distributed, consider transformations of the dependent variable (e.g., logarithmic, square root, or Box-Cox transformations).

🧪 Practice Quiz

1. Which of the following indicates normally distributed residuals in a Q-Q plot?

   1. A) Points scattered randomly across the plot.
   2. B) Points forming a clear curve.
   3. C) Points falling along a straight diagonal line.
   4. D) Points clustered at the bottom left corner.

2. What does a Q-Q plot with ends curving away from the straight line suggest?

   1. A) Light tails
   2. B) Heavy tails
   3. C) Perfect normality
   4. D) Skewness

3. An S-shaped pattern in a Q-Q plot typically indicates:

   1. A) Heavy tails
   2. B) Light tails
   3. C) Skewness
   4. D) Perfect normality

4. If the bottom end of a Q-Q plot deviates to the right of the line, and the top end deviates to the left, this indicates:

   1. A) Left skewness
   2. B) Right skewness
   3. C) Light tails
   4. D) Heavy tails

5. A step-like pattern in a Q-Q plot suggests:

   1. A) Continuous data
   2. B) Discrete data
   3. C) Normally distributed data
   4. D) Skewed data

6. What should you consider if the Q-Q plot reveals non-normal residuals?

   1. A) Ignoring the non-normality
   2. B) Removing outliers
   3. C) Transformations of the dependent variable
   4. D) Increasing the sample size

7. Which transformation is commonly used to address right skewness in residuals?

   1. A) Squaring the data
   2. B) Taking the square root of the data
   3. C) Multiplying by a constant
   4. D) Subtracting a constant