Lecture 2_Correlation

Question 1

What two pieces of info does the Pearson’s correlation coefficient describe?

Answer 1

the degree and nature of the linear relation between two variables.

Question 2

Degree of the linear relationship between the two variables =

Answer 2

magnitude (abs value) of r

Question 3

Nature of the linear relationship between the two variables =

Answer 3

sign of r
(+) → Direct
(-) → Inverse

Question 4

Correlation coefficients

Answer 4

describe the degree to which 2 variables are related

• standardized covariance r = CoVxy/ ( (SDx)(SDy) )

Question 5

What does it mean to say that Pearson’s correlation coefficient (r) is a standardized index?

Answer 5

it converts the values of each variable to Z scores so each axis has the same scale

Question 6

Centered data

Answer 6

process of subtracting the mean from every value in a set
• mean of centered set = 0
• measures of variability (V or SD) don’t change

Question 7

What are 3 measures of covariability?

Answer 7

• sum of cross-products
• Covariance
• Correlation coefficient (r)

Question 8

Coefficient of Determination

Answer 8

r^2
• the proportion of variance that X and Y have in common (visualize as overlapping areas in a Ballantine diagram)
• tells us the proportion of variance in Y that is attributable to X (limited to the linear relation between the two variables).
• index of the strength of the relation between the IV and the DV expressed as a proportion of variance

Question 9

Coefficient of Non-Determination

Answer 9

(1 - r^2) tells us the proportion of variance in Y that is not linearly related to X.
• In linear regression, used to express the proportion of variance in Y that is not predictable from X (quantifies errors in our predictions).