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1. 簡單迴歸分析

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1. 簡單迴歸分析. 迴歸分析與相關分析的意義. 變數間的線性關係. 變數間的非線性關係. 正向線性關係. 負向線性關係. 無關係. 範例:廣告支出與銷售額的資料 單位:萬元. 廣告支出與銷售額的散佈圖. 廣告支出與銷售額的關係. 三個廣告支出與銷售額的直線關係. 建立迴歸模型. 簡單迴歸模型的假設條件. 簡單迴歸模型. 樣本觀察值散佈圖. 估計迴歸模型. 估計迴歸模型. 估計迴歸模型. 估計的迴歸方程式. 最小平方法的計算. 廣告支出與營業收入的迴歸結果. 汽車銷售額的迴歸估計式. 估計迴歸模型. Gauss-Markov 定理. - PowerPoint PPT Presentation

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Sheet1

k
j
i
r
j
i
X
X
L
1
E(Yi)

Sheet1
0
0
0
1
1
1

*
8.86
B
9.22
C
11.32
*
1772.bin
1773.bin
(autocorrelation) (homoscedasticity)
*
corr(i, j)0
0
y (fitted value)

o1… k (Partial Regression Coefficient)b0b1…bk
x,(Multicollinearity)
,N>K+2
ANOVAF
H1bi ≠0xyx(multicollinearity)xVIF(variance inflation factor)VIF≥10


*
FANOVAsig=0.0000.05
*

*
1.Analyze/regression/linear/MethodStepwise
(y) = 55.058+1.728(x1) + 0.931(x2)−68.270(x3)
$1000$17281$931(x3=1)(x3=0) $68270
*
*
*
8.1
Analyze/Regression/Linear/Dependent; Independent(s)female*female
(8.5)
(8.6)
*
OLS (8.7)(fitted value)( )( )(8.8)(Y1)OLS(8.8)
2SLSOLS(8.7)((8.7)(fitted value)( )(8.8)(Y1)OLS(8.8)

(8.9)
(8.10)

OLSE )
µ{«×¤j¤pªº²Î­p¤èªk
¡C
X
Y
Z
Y
i
ε
i
=Y
i
- E(Y
i
7,840,000
1,190,000
4,000,000
650,000
1,690,000
292,500
90,000
67,500
10,000
7,500
1,210,000
302,500
4,840,000
605,000
9,000,000
1,725,000


28,680,000
4,840,000

3,585,000
605,000
m

å
å
å
å
å
å
å
xz xy zy
6 7 38 -6.2 -1 -9.2 38.44 1 84.64 6.2 57.04 9.2
9 5 40 -3.2 -3 -7.2 10.24 9 51.84 9.6 23.04 21.6
12 14 53 -0.2 6 5.8 0.04 36 33.64 -1.2 -1.16 34.8
16 8 50 3.8 0 2.8 14.44 0 7.84 0 10.64 0
18 6 55 5.8 -2 7.8 33.64 4 60.84 -11.6 45.24 -15.6

61 40 236 0 0 0 96.80 50 238.80 3 134.80 50.0
b
ˆ
g
ˆ
X

Y

Z


(
å
å
å
¡C
-
F



XY
r
Y
X
Y 157 125 283 395 358 393 273 297 649 658 800 892
D
1
0 0 0 0 0 0 1 1 1 1 1 1
D
2
0 0 0 0 0 0 0 0 0 0 0 0
D
3
0 0 0 0 0 0 0 0 0 0 0 0
Y 386 494 1124 928 1198 1441 502 731 1662 1259 1610 2019
D
1
0 0 0 0 0 0 0 0 0 0 0 0
D
2
1 1 1 1 1 1 0 0 0 0 0 0
D
3
0 0 0 0 0 0 1 1 1 1 1 1
1

)(YE
A

825 660 1200 500 1050 480 1810 1350 980 630 1050

22.6 14.26 46.11 20.22 33.39 15.6 53.56 45.22 26.51 21.73 47.28

2 1 2 1 1.5 1 1 2 1 2 2

4 4 5 4 4 1 1 4 4 3 3
D
1 1 1 0 1 0 1 0 1 0 0

1680 500 730 1180 480 2200 1280 687 620 1380 920

56.66 20.22 21.76 30.85 15.6 36.58 30.46 28.59 21.5 34.5 31.68

2 1 1 2 1 2 2 2 1 2 2

1 4 3 4 1 1 1 3 4 3 4
D
0 0 1 1 0 0 0 0 0 1 0




D
D=1
Dependent Variable:
Observed Cum Prob