靼nc regr:_一一_
j
Q2. Explain the similar and dissimilar properties of pairs of multivariate methods below: (15 points)
l (l) Multivariate linear regression vs. Simultaneous equations
(2) Discrimination analysis vs. one-way MANOVA
(3) Discrimination analysis vs. Logistic regression
L,J 疝
j
I:,, 改勺
乂 遜
』L
Q3 . Table I shows the numbers of passengers choosing public or private transportation modes
- the effects of gender, weat}i'er and age on mode
across gender, weather and age. How
to test
choice? (20 points)
霹」#:=) K- 伊
.;;j 囧心 ck。 ia 之 駟
糾叭
严＼玉
巧
Sunny
Rainy
Age .S 20
Age> 20
严玉］
歸 丑］
fr \ !..J
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丶 I i I
.
(/ 1'
T-Tr.,M tr, invP<::tia 研 t证 fr,llr,~na hvnnthP.<::P.<:: h 囧rl r.n thP. rl 而 aivP.n in T~hlP. ?·(?" nnint<:: 丶
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(2) Public transportation {PT) supply has a unifo岡磾ct on PT ridership a~ross Taiwan -(Le., 白二
,· , ,
4 國¢
`.
J)
i
f passengers in choosmg public and private mod
Male
Female
Public
Private
Private
Public
5
15
20
10
12
18
12
8
22
10
8
10
4
16
15
15
\
笈L
Q4
Cr6}) - V的la t.讠vi._
Table 1 Numb
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t
c
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5
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Definition
Bus ridershi
Variables
I
;;
.\ -f. r;:.. '.'.
,, . ,'.、 ； . fl
. .
D: ---·- ..
- ·· 、 l)nit
;'.+,1
4、 w~\
辻＼
QS. Table 3 shows th9/estimation results of 竺!NOVA analysis of c,ustomer satisfaction (xi 9),
likelihood of future purchase (x2 l~~and curr nt purchase level (x22忻 across~1:_1s拉~~rt刃J_e (~I,
1: less than one year; 2: I to 5 years; 3: more than 5 years) and industry type (x2, 0: wholesaler;
- -1: retailer). Interpret the estimation results accordingly. (20 points)
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c
1/4
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翡i...Jr.~
砹叮，\
1,
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.-
.'.;
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、
~—~.:-;;:.;;
Source DF
Type I SS Mean Square F Value Pr> F
xi
2 30. 18262082
15.0913104 1
25.78 <.0001
x2
I
0.44146997
0.44146997
0.75 0.3874
xl*x2
2
0.33969426
0.16984713
0.29 0.7488
vK
V
Dependent Variable: x22
OF Sum of Squares Mean Square F Value Pr> F
Source
Model
5
5596.306975
1119.26 1395
Error
94
2176.693025
23.156309
Corrected Total
99
7773.000000
R-Square CoeffVar
RootMSE
x22 Mean
4.812100
58.40000
0.719961'-
8.239898
Source DF
Type I SS Mean Square F Value Pr> F
2664.922294
115.08 <.0001
238.711401
238.711401
10.31 0.0018
27.750985
13.875492
0.60 0.5513
xl
2 5329.844589
x2
I
xl*x2
2
Source DF
48.34 <.0001
vv/
Type II SS Mean Square F Value Pr>F
I 11.86 <.0001
238.711401
238.711401
10.31 0.0018
27.750985
13.875492
0.60 0.5513
x2
I
xl*x2
2
✓
2 5180.632913
VJ
2590.316457
xl
Source DF
Type III SS Mean Square F Value Pr> F
x1
2 5092. 78952 l
x2
I
xl*x2
2
2546.394761
109.97 <.0001
244.294518
244.294518
10.55 0.0016
27.750985
13.875492
0.60 0.5513
3/4
J
VV
V
..
MULTIVARIATE ANALYSIS (ITT5515)
岬） TERM EXAMINATION
Why蕡龘謚鷗崮』二肆囑f這諡謚己編af江龘齿靠霄＇氕严
｀甲釕囯山對[
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11V麩扣1國ivo.祁 一 11三严严 t1·n I;,, 回 (L .,
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If it is not hold, what problems will be for the methods of MANOVA, Multivariate regression,
Discrimination analysis, Logistic 7 ression, and Factor analysis, respyctively? (10 points)
選和漪 N-0, 丫园 F, I-(仞l)\Jlr 戶汔翊巴
庄
Q2. Explain the similar and dissiinilar properties of following pairs of multivariate methods:
伍 (1) Principal麟onents vs. Factor analysis 10 points) 叩打）銍攻姜 凪k飆
(2) Multivariate linear regression vs.
(10 points)
辶食~
(3) Discrimination analysis vs. Logi tic regression (10 points)
扭易
Simult諡涵 equations
丰＼虐
邛午
Q3. To identify the potential
factors- influencing p苧匣唧9血匣卫些呾age in Taipei City, a
dataset of ten-year monthly information (a total of 120 time senes observations) is collected,
which contains: y: public transportation patronage percentage(%), XI: number 『雪王 召戶
(in millions), X2: average income (in thousands), X3: bus production (in million us? X4:
number of registered cars and motorcycles (in thousands), XS: length of road (in thousand km).
The estimated regression model is shown in Table 1.
(1) Diagnose the estimated regression model and pro ose corresponding correction methods for
each of problems you identify. (10 points) PJ) 羞濁莖
(2) If you want to analyze the seasonal changes in the public transportation patronage, what will
you do? (off-peak seasons are Jw
癮山
Q4.
丶全
己
凸 ~~ 手 T丶 彧
邕古面 or~三辶 L
切 .
f
三钇、
·~
Q芝严莖陴皿呻sis, LQ罪瞬陴竺io~閂二~al 」子
componen~了dFac『『alys旦 (JO points) l 屯 傳 't)
I 曰 紅 尸
_owing_multivari~te methods are~
MANOVA, ~ultJ.vanate regression,
i \v___.
縻
靠
巧料
o:/.'.l( 邲5 必
（0 三蔻fr-
才f~
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r able I Estimated results of regression an~b7
The REG Procedure
Dependent Variable: y
Number of Observations Read
120
Number of Observations Used
120
Analysis of Variance
Sum of
Mean
Source
DF
Pr> F
FValue
Squares
Square
Model
<.0001
49.32
8953.56507
1790.71301
Error
19/
7044.43493
36.31152
Corrected Total
199
15998
RootMSE
R-Squarc / 0:5~97 fi:
6.02590
Dependent Mean
58.20000
( 0.5~?:f.
CocffVar
10.35379
Parameter Estimates
Parameter
Standard
Variance
D1IIIII
Variable
Estimate
Error
t Value
Pr> I~Inflation
Intercept
37.48072
3.12938
11.98
<.0001
0
XI
1.16527
0.64773
1.80
X2
-0.17502
0.26244
-0.67
X3
3.00494
0.41871
7.18
< 0001
L4066-3.... VrF:> I
X4
-3.94840
0.69607
-5.67
.
X5
0.72109
0.09476
7.61 #
<.0001~ 咋 \ 18 .98618/ 'i. /\
Durbin-Watson D 尹韶
1st Order Autocorrelatio
Heteroscedasticity Test
Equation
Statistic
DF
Pr
·· q
Variables
Test
y
White's Test
Pk
悔． 頃乒 怀
碼 R-Sq
勾 .07
14
rable 2 Results of ANOVAIMAONVA analyses
~I
/
Sum of
Mean Square
Squares
11274. 47222
2254.89444
24.34808
4723.52778
199
15998. 00000
Coeff Var
Root MSE
HC Mean
8.478312
4.934378
58.20000
DF
Type I SS
Mean Square
F Value
Pr> F
<.0001
之
2
10997. 53309
5498. 76654
225. 84
1
233. 57554
233. 57554
9. 59
0.0022 、/
o.4121
2
43.36359
21.68180
0 . 89
OF
Type III ss
Mean Square
F Value
Pr> F
2
11161 • 32808
5580. 66404
229 . 20
丶
1
228. 03846
228. 03846
9. 37
2
43.36359
21.68180
0.89
F墨］ ：二
DF
5
194
Tota 三
鬥
t>
Source
Model
Error
Corrected Total
A-Square
p . 286077,
Source
---ES
AGE
ES*AGE
Source
ES
AGE
ES*AGE
--
v 二
0.704743
Source
ES
AGE
ES*AGE
Source
ES
·
AGE
ES*AGE
Dependent Variable: CO
丨咒'!"三
圧严 · 科孑
- --
The GLM Procedure
Class Level Information
Class ·
Levels
Values
ES
3
1 2 3
AGE
2
0 1
Dependent Variable: HC
Source
Model
Error
Corrected
~
Sum of
DF
Squares
Mean Square
F Value __Er- >-f、 v
5
14.02347222
2.80469444
15.55/
<.0001 '
194
34. 99652778
0.18039447
199
49. 02000000
Coeff Var
Root MSE
co Mean
' . 98.77412 ·
0.424729
0.430000
DF
Type I SS
Mean Square
F Value
Pr > F
2
13.93544118
6.96772059
38.62
<.0001
1
0. 06243063
0. 06243063
0. 35
0. 5570 -;t.
2
0.02560041
0.01280021
0.07
0.9315 。 k
DF
Type III ss
Mean Square
F Value
P > F
2
13.82804214
6.91402107
1
0.06416934
0.06416934
0.36
0污
沃、
2
0.02560041
0,01280021
0.07
0,9315 V
丶
I/
38.33 汽pJ
f
2
.,....,
,'
Tukey's Studentized Range (HSD) Test for HC
Comparisons significant at the 0.05 level are indicated by *** .
Difference
ES
Between
Simultaneous 95%
Comparison
Means
Confidence Lim 拉 S
3 - 2
>)_:, I
8 . 3511
6.3214 10.3808 ***
3 - 1
17 . 9706
15.9719 19. 9693 ***
2 - 3
-8.3511
-6.3214 •••
-10.3808
2·1
9 . 6195
11. 6492 •••
7 . 5898
1 - 3
-17.9706
- 19.9693 -15.9719 ***
1 - 2
-9.6195
-11 .6492 ·7. 5898 *會＊
Tukey's Studentized Range (HSD) Test for CO
Difference
ES
Between
Simultaneous 95%
Comparison
Means
Confidence Limits
3 - 2
0 .15993
3 戸>->I
3·1
0 . 61765
0.. 44561
-0
01478 0.
0 .78968
33463
2 · 3
-0.15993
-0.33463 0.01478
2·1
0. 28302 0. 63243
0.45772
1 - 3
- 0.61765
-0.78968 -0.44561
-0.45772
-0.63243 -0.28302
1 - 2
5
．.：已
..刀
J ]
Multivariate Analysis of Variance
~國O勺已 o 砭L鍀
Character--:詛注-i-c-Roo-t-s-and-V.ecto r-s - of-:一 E一r-nvers·e• H, where
H = Type III SSCP Matrix for S
E = Error SSCP Matrix
Characteristic Vector V'EV=1
Characteristic
HC
CO
Root
Percent
0 . 03088269
2.43963509
99.17
0.01372317
0. 02032487
0 . 83
-0. 00587571
0 . 17065909
三ests for the Hypothesis of No Overall ES Effect
之
H = Type III SSCP Matrix for 邸＾，鬥 、 I ,
E -=Er繹 SSCP Matrix
S=2
M= -0.5
N=95 . 5
舄 3 寸 H C: 名 0~
Co
Statistic
Value
P-Value
Wilks'Lambda
O. 28493720
L籬
Pillai's Trace
0.72919148
<. 0001
Hotelling-Lawley Trace
2 . 45995996
<. 0001
Roy's Greatest Root
2. 43963509
<. 0001
Characteristic · Roots and Vectors of: E Inverse* H, where
H = Type III SSCP Matrix for GE
E = Error SSCP Matrix
Characteristic
Characteristic Vec~or
Root
Percent
HC
CO
0. 05717754
100. 00
0. 01468683
-0. 06842552
0. 00000000
0. 00
0. 00267328
0. 15936189
MANOVA Tests for the Hypothesis of No Overall AGE Effect
Ri 6 t 嶧玉 卟囧
H = Type III SSCP Matrix for@
/戸
E = Error SSCP Matrix
S=1
M=O
N=95 . 5
0
,-
.
J
<Q
I
;:;;;~t~:mbda
o. 94~~1~891
V'EV=1
)C:;:,__~」
寸）
P之繻o J
Pillai ' s Trace
O. 05408509
o. 0047
Hotelling - Lawley Trace
0 . 05717754
0.0047
Roy's Greatest Root
O. 05717754
O. 0047
MANOVA .Tesfs .for the Hypothesis of No Ov
l ' ES*AGE Effect
H = Type III SSCP Matrix for Esi"~G Z, ,, 主 逗
Stat1st1c
.~;';.'.':,。::" :::;~ C
Value~ , Va
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