Stochastic Relationships and Scatter Diagrams Scatter Plotx y

Stochastic Relationships and Scatter Diagrams觀 念 • Scatter Plot可以顯示兩連續變數x, y之間的關 聯 形式與 依 強度： 變 項y 自變項x ©Ming-chi Chen 社會統計 3

Covariance, 共變量 ©Ming-chi Chen 社會統計 觀 念 12

Covariance, 共變量 ©Ming-chi Chen 社會統計 觀 念 13

例題 求x與y的covariance? ©Ming-chi Chen 社會統計 14

⊕ II I (14 -10)(85) =(4)(3) (6 -10)(3 -5)=(-4)(-2) ⊕ III ©Ming-chi Chen IV 社會統計 15

⊕ II I (13 -10)(85) =(-3)(3) (5 -10)(8 -5)=(-5)(3) III ©Ming-chi Chen ⊕ 社會統計 IV 16

Covariance, 共變量 觀 念 • 證明：if X, Y are independent, ©Ming-chi Chen 社會統計 18

The Population Correlation Coefficient, ρ 母體相關係數 ©Ming-chi Chen 社會統計 20

Sample Correlation Coefficient, r 樣本相關係數 • 樣本相關係數: ©Ming-chi Chen 社會統計 22

r = 0. 8 Y X (a) ©Ming-chi Chen 社會統計 25

Y r =. 95 X (b) ©Ming-chi Chen 社會統計 26

Y r=0 X (c) ©Ming-chi Chen 社會統計 27

Y r=0 X (a) ©Ming-chi Chen 社會統計 28

Y r = -. 90 X (d) ©Ming-chi Chen 社會統計 29

Y r = -0. 5 X (c) ©Ming-chi Chen 社會統計 30

例題 求x與y的correlation? ©Ming-chi Chen 社會統計 32

例題 求x與y的correlation? ©Ming-chi Chen 社會統計 33

相關係數與因果關係 • 相關僅代表兩變數間有線性關係，不必然 隱含因果關係，下列情況皆有可能 z ©Ming-chi Chen Two variables are said to be spuriously correlated when their correlations is nonzero and there is no reason to believe that the variables are related to one another. 社會統計 37

例題 ©Ming-chi Chen 社會統計 41