Chapter 5 Introduction to Correlation

Chapter 5 Correlation and Regression

Introduction to Correlation

Correlation Between Variables r = .00

Y

X

Pearson Product Moment Correlation Coefficient 𝒓=

𝑵

𝑵

𝑿𝒀 −

𝑿𝟐 −

𝑿

𝟐

𝑿 𝑵

𝒀 𝒀𝟐 −

𝒀

𝟐

-1.00 < r < 1.00 Interpret absolute value of r LINEAR relationship Coefficient of Determination (r2) Will ALWAYS be some error (SEE) if r not perfect

Coefficient of Determination (r2) Percent of shared variation Ability to predict Y from X Error

r = .9 r2 = .81

Coefficient of Determination (r2) Percent of shared variation Ability to predict Y from X Error

r = .707 r2 = .50

Coefficient of Determination (r2) Percent of shared variation Ability to predict Y from X Error

r = .50 r2 = .25

Coefficient of Determination (r2) Percent of shared variation Ability to predict Y from X Error

Error Error