Overview
The lecture introduces the concept of covariance, explaining how it measures the relationship between two traits by considering the deviations of data points from their respective means.
Covariance Explanation
- Covariance quantifies the relationship between two traits (variables) by analyzing how they vary together.
- To compute covariance, first find the mean of each trait (X and Y).
- For each data point, calculate its deviation from the mean for both X and Y.
- Multiply these deviations for each data point (e.g., deviation in X times deviation in Y).
- Sum all these products across all data points; this sum forms the numerator for covariance calculation.
- If both deviations are negative or both positive, the product is positive, increasing the sum.
- If one deviation is positive and the other negative, the product is negative, decreasing the sum.
- A positive covariance indicates traits increase together; a negative covariance indicates one increases as the other decreases.
Key Terms & Definitions
- Covariance — A statistical measure indicating the direction of the linear relationship between two variables.
- Deviation — The difference between a data point and the mean of the dataset.
- Mean — The average value of a set of numbers.
Action Items / Next Steps
- Practice calculating covariance with different data sets.
- Review the formula for covariance and understand each component.