Lecture 8: Correlation & Covariance

These flashcards cover the key concepts related to correlation and covariance as discussed in the lecture.

Descriptive Statistics

Statistics that summarize data from a sample or population, including measures of central tendency, variances, and relationships.

Correlation Coefficient

A statistical measure that describes the extent to which two variables are related, indicating both magnitude and direction.

Pearson Correlation Coefficient (r)

A specific correlation coefficient that quantifies the linear relationship between two variables, ranging from -1.00 to +1.00.

Covariance

A measure that indicates the direction of the linear relationship between two variables; it can be positive, negative, or zero.

Positive Covariance

Indicates that as one variable increases, the other variable also tends to increase.

Negative Covariance

Indicates that as one variable increases, the other variable tends to decrease.

Zero Covariance

Indicates that there is no systematic linear relationship between two variables.

Formula for Covariance

Cov(x,y) = $\frac{σ(x−\bar{x})(y−\bar{y})}{n−1}$ where σ is the standard deviation.

Correlation vs Covariance

Correlation is standardized covariance that quantifies both magnitude and direction of the relationship, independent of units.

Magnitude of Covariance

Depends on the units of measurement of the two variables, hence not standardized.

Standardization of Covariance

The process of dividing covariance by the standard deviations of the two variables to calculate the correlation coefficient.