Stochastic Relationships and Scatter Diagrams 0 2 2007

Stochastic Relationships and Scatter Diagrams 截距 0 2 ©蘇國賢 2007

Deterministic Relationship and Stochastic Relationships 在Y=f(X)的函數關係中，若每一個x值僅對應於單 一的y值，則X, Y之間的關係為完全決定的函數關 係，稱為確定模型(deterministic) Deterministic Relationships 電腦每台$960元，X為電腦台數，Y為總收益 4 ©蘇國賢 2007

Deterministic Relationship and Stochastic Relationships 華氏與攝氏的關係為確定模型(deterministic) 所有的資料點都 剛好落在線上 5 ©蘇國賢 2007

Deterministic Relationship and Stochastic Relationships ei的來源： (1)行為的隨機性(human indeterminacy) (2)測量的誤差(measurement error) (3)其他無法觀察到影響Y的因素(omission of the influence of innumerable chance events) 8 ©蘇國賢 2007

F(Y|X) Y E(y 1) E(y 2) x 1 E(y 3) x 2 x 3 12 ©蘇國賢 2007

Method of Least Squares 尋求迴歸係數的估計式有許多種方法，最常用 的為 普通最小平方法(ordinary least squares method)及最大概似法(Maximum likelihood method) 21 ©蘇國賢 2007

Method of Least Squares 24 ©蘇國賢 2007

Residual Sum of Squares 當b 0=? b 1 =? 時SSE會是最小值？ 26 ©蘇國賢 2007

Stochastic Relationships and Scatter Diagrams 直線上任兩 點P 1 P 2，從P 1 移至P 2，x軸 座標移動 △x = x 2 - x 1 觀 念 依 變 項y y軸座標移動 △y = y 2 - y 1 自變項x 27 ©蘇國賢 2007

Stochastic Relationships and Scatter Diagrams 直線上任兩 點P 1 P 2，此線 的斜率定義 為： 觀 念 依 變 項y 自變項x 28 ©蘇國賢 2007

微分(derivative)簡介 Secant line 割線 34 ©蘇國賢 2007

微分(derivative)簡介 Secant line 割線 35 ©蘇國賢 2007

微分(derivative)簡介 Secant line 割線 36 ©蘇國賢 2007

微分(derivative)簡介 Tangent line 切線 37 ©蘇國賢 2007

Slope of the Tangent Line Tangent lin 切線 38 ©蘇國賢 2007

Slope of the Tangent Line Tangent lin 切線 39 ©蘇國賢 2007

Slope of the Tangent Line 40 ©蘇國賢 2007

Slope of the Tangent Line Tangent lin 切線 41 ©蘇國賢 2007

Slope of the Tangent Line Tangent lin 切線 m = -4 m=2 42 ©蘇國賢 2007

Derivative • The derivative of function f with respect to x is the function f ' defined by 43 ©蘇國賢 2007

Notation for the derivative • f ' (x) 讀做�"f prime of x" • y ' 讀做 "y prime" • "the derivative of y with respect to x" "dee y dee x" • "the derivative of f(x) with respect to x" "dee f(x) dee x" 44 ©蘇國賢 2007

Let f(x) = x 3, Find the derivative 45 ©蘇國賢 2007

Let f(x) = x 2 -5 x+1, Find the derivative 46 ©蘇國賢 2007

Basic Rules for Differentiation • Rule 1: the derivative of a constant is zero 47 ©蘇國賢 2007

Basic Rules for Differentiation • Rule 2: the derivative of a linear function 48 ©蘇國賢 2007

Basic Rules for Differentiation • Rule 3: the derivative of a power function 49 ©蘇國賢 2007

Residual Sum of Squares 當b 0=? b 1 =? 時SSE會是最小值？ 51 ©蘇國賢 2007

Residual Sum of Squares SSE會有最小值 52 ©蘇國賢 2007

Residual Sum of Squares 53 ©蘇國賢 2007

Residual Sum of Squares Normal Equation 將(1)式兩邊除以n 54 ©蘇國賢 2007

Residual Sum of Squares 將(1)式乘以Σxi 將(2)式乘以n 55 ©蘇國賢 2007

Residual Sum of Squares 將(5)-(4) 56 ©蘇國賢 2007

Residual Sum of Squares 上下同除n 57 ©蘇國賢 2007

Residual Sum of Squares 58 ©蘇國賢 2007

Residual Sum of Squares 59 ©蘇國賢 2007

Sample Correlation Coefficient, r 樣本相關係數 • 樣本相關係數: 60 ©蘇國賢 2007

STATA 64 ©蘇國賢 2007

例題 求x與y的correlation? 65 ©蘇國賢 2007

變異數的分解 總變異量 Sum of Square Total 解釋變異量 Regression Sum of Square 未解釋變異量 Sum of Square Error 75 ©蘇國賢 2007

r=0. 994 r 2=0. 989 83 ©蘇國賢 2007

r=0. 921 r 2=0. 849 84 ©蘇國賢 2007

Page 136 85 ©蘇國賢 2007

r 2 Variance of value y = 5. 30091 Variance of predicted y= 5. 24135 86 ©蘇國賢 2007