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7. Covariance and Correlation

k. calculate and interpret covariance and correlation;

What is covariance and correlation a measure of? These are a measure of the degree to which two random variables are related to each other.

What is the formula for the covariance between two variables R_i and R_j? - \(Cov(R_i, R_j) = E[(R_i - E(R_i)) \times (R_j - E(R_j))]\)

What does it mean when a covariance is a negative number? It means that, on average, there is an inverse relationship between the two numbers. When one is high, the other is lower.

What does a covariance of zero mean? Covariance = zero means two variables are unrelated to each other

What does a covariance > 0 mean? Covariance > 0 means that the two variables are related to each other. When one goes up the other one goes up, and vice versa.

What is the covariance of a variable to itself? The same as it’s variance.

What is the formula for correlation between two variables R_i and R_j? - \(\rho(R_i, R_j) = \frac{Cov(R_i, R_j)}{\sigma(R_i) \times \sigma(R_j)}\) - Could also be corr(R_i, R_j) or \rho_i_j

What are the numerical boundaries of correlation? Correlation will always be between -1 and 1

What does a correlation of zero mean? Correlation equals zero means there is no linear (straight line) relationship between the variables

What does a correlation closer to one or closer to negative one mean? The closer correlation gets to one or negative one indicates a stronger positive or inverse correlation.