Covariance and Correlation Flashcards

Flashcards about Covariance and Correlation

Covariance

A measure of how two variables change together.

Covariance Measurement

Compares data points to a defined point (x, y) to measure rise and fall.

yi – y

Distance from y

xi - x

Distance from x:

(xi – x)(yi – y)

Individual distance from xy:

∑ (xi – x)(yi – y)

Total distance from xy:

∑ (xi – x)(yi – y) df

Covariance (x,y)

∑ (yi – y)(yi – y) df

Variance of y

Big math difference

Covariance can be negative

Z transformation to Scale Covariance Zxi = xi - x sx

Centers these data Zx = 0

Zxi is unitless

Scales these data Szx = 0

Correlation

The preferred measure of the rise and fall of (x, y) because it gets around the unit issue -1 ≤ ρ ≤ 1

ρ

Correlation is standardized Covariation

Correlation Question

Asks the question: “Is there a true correlation between x and y?”

H0

ρx,y = 0

HA

ρx,y ≠ 0

𝑥

parameter μ

r

parameter ρ

Pearson correlation coefficient

r is known as the Pearson correlation coefficient

Hypothesis testing for correlation

How can we determine the probability that our sample correlation (r) is drawn from the true null correlation (ρ= 0)?

t score

t score = r − ρ 𝑆𝑒𝑟