tugas multivariat - evan susandi

Tugas – Mata Kuliah Analisis Multivariat – Evan Susandi

Nama : Evan Susandi

NPM : 140720130003

1. Sebuah percobaan untuk membandingkan dua metode mengajar fisika yang berbeda yang

dilakukan pada “Morning” (pagi), “Afternoon” (siang), dan “Evening” (malam) menggunakan

pendekatan kuliah “Traditional” dan “Discovery”. Tabel berikut menyajikan nilai skor yang

diperoleh dari bidang “mechanical” (M), “heat” (H), “the sound” (S) untuk 24 siswa dalam

penelitian ini.

a. Menganalisis data, pengujian untuk (1) efek dari faktor, (2) pengaruh waktu, dan (3) efek

interaksi. Sertakan dalam analisis Anda tes kesetaraan matriks varians-kovarians dan

normalitas.

Analisis MANOVA dengan menggunakan R software:

#INPUT DATA VARIABEL DEPENDEN

M<-c(30,26,32,31,41,44,40,42,30,32,29,28,51,44,52,50,57,68,58,62,52,50,

50,53)

H<-c(131,126,134,137,104,105,102,102,74,71,69,67,140,145,141,142,120,

130,125,150,91,89,90,95)

S<-c(34,28,33,31,36,31,33,27,35,30,27,29,36,37,30,33,31,35,34,39,33,28,

28,41)

#INPUT DATA VARIABEL FAKTOR

METHOD<-factor(gl(2,12), labels=c("Traditional", "Discovery"))

TIME<-factor(gl(3, 4, len=24), labels=c("Morning", "Afternoon","Evening"))

D<-data.frame(M,H,S,METHOD,TIME)

Tugas – Analisis Multivariat

1. MANOVA 2. MULTIVARIAT REGRESSION


D

M H S METHOD TIME

1 30 131 34 Traditional Morning




5 41 104 36 Traditional Afternoon




9 30 74 35 Traditional Evening




13 51 140 36 Discovery Morning




17 57 120 31 Discovery Afternoon




21 52 91 33 Discovery Evening




#MEMBUAT MATRIKS VARIABEL DEPENDEN

Y<-cbind(M,H,S)

Y

M H S

[1,] 30 131 34

[2,] 26 126 28

[3,] 32 134 33

[4,] 31 137 31

[5,] 41 104 36

[6,] 44 105 31

[7,] 40 102 33

[8,] 42 102 27

[9,] 30 74 35

[10,] 32 71 30

[11,] 29 69 27

[12,] 28 67 29

[13,] 51 140 36

[14,] 44 145 37

[15,] 52 141 30

[16,] 50 142 33

[17,] 57 120 31

[18,] 68 130 35

[19,] 58 125 34

[20,] 62 150 39

[21,] 52 91 33

[22,] 50 89 28

[23,] 50 90 28

[24,] 53 95 41

#TABEL MANOVA

manova(Y~METHOD*TIME)

Call:

manova(Y ~ METHOD * TIME)


Terms:

METHOD TIME METHOD:TIME Residuals

resp 1 2440.167 709.333 5.333 158.500

resp 2 2320.667 13030.333 329.333 653.000

resp 3 40.042 15.083 0.583 274.250

Deg. of Freedom 1 2 2 18

Residual standard error: 2.9674166.0231043.903346

Estimated effects may be unbalanced

#UJI MANOVA

summary(manova(Y~METHOD*TIME))

Df Pillai approx F num Df den Df Pr(>F)

METHOD 1 0.94237 87.206 3 16 3.958e-10 ***

TIME 2 1.78667 47.459 6 34 4.141e-15 ***

METHOD:TIME 2 0.46699 1.726 6 34 0.1449

Residuals 18

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

summary(manova(Y~METHOD*TIME),test="W")

Df Wilks approx F num Df den Df Pr(>F)

METHOD 1 0.05763 87.206 3 16 3.958e-10 ***

TIME 2 0.00585 64.385 6 32 < 2.2e-16 ***

METHOD:TIME 2 0.54903 1.864 6 32 0.1178

Residuals 18

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

summary(manova(Y~METHOD*TIME),test="H")

Df Hotelling-Lawley approx F num Df den Df Pr(>F)

METHOD 1 16.351 87.206 3 16 3.958e-10 ***

TIME 2 34.455 86.136 6 30 < 2.2e-16 ***

METHOD:TIME 2 0.792 1.981 6 30 0.09997 .

Residuals 18

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

summary(manova(Y~METHOD*TIME),test="R")

Df Roy approx F num Df den Df Pr(>F)

METHOD 1 16.3510 87.206 3 16 3.958e-10 ***

TIME 2 29.9296 169.601 3 17 7.262e-13 ***

METHOD:TIME 2 0.7535 4.270 3 17 0.02027 *

Residuals 18

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

#Profile Plots

interaction.plot(TIME,METHOD,M)

interaction.plot(TIME,METHOD,H)

interaction.plot(TIME,METHOD,S)


#UJI NORMAL MULTIVARIAT

library(mvnormtest)

C <- t(D[1:3])

mshapiro.test(C)

Shapiro-Wilk normality test

data: Z

W = 0.956, p-value = 0.3642

#GRAFIK NORMAL MULTIVARIAT

center <- colMeans(Y) # centroid

n <- nrow(Y); p <- ncol(Y); cov <- cov(Y);

d <- mahalanobis(Y,center,cov) # distances

qqplot(qchisq(ppoints(n),df=p),d,

+ main="QQ Plot Assessing Multivariate Normality",

+ ylab="Mahalanobis D2")

abline(a=0,b=1)

30

35

40

45

50

55

60

TIME

me

an

of M

Morning Afternoon Evening

METHOD

Discovery

Traditional

70

80

90

10

01

10

12

01

30

14

0

TIME

me

an

of H


METHOD

Discovery

Traditional

31

32

33

34

TIME

me

an

of S


METHOD

Discovery

Traditional


b. Tidak mungkin dilakukan trend analysis, karena tidak terdapat autocorrelation antar waktu.

c. Multivariat Analisis Varians dilakukan untuk membandingkan dua metode mengajar fisika

yang berbeda yang dilakukan pada “Morning” (pagi), “Afternoon” (siang), dan “Evening”

(malam) menggunakan pendekatan kuliah “Traditional” dan “Discovery”. Dengan melakukan

uji asumsi yaitu uji normalitas multivariate dan homogeneity of variances dan covariance.

Terdapat perbedaan yang signifikan dua metode mengajar fisika menggunakan pendekatan

kuliah “Traditional” dan “Discovery” terhadap nilai skor yang diperoleh dari bidang

“mechanical” (M), “heat” (H), “the sound” (S) untuk 24 siswa dalam penelitian ini,

F(3,16)=87.206, p<0.001. Dan juga terdapat perbedaan yang signifikan mengajar yang

dilakukan pada “Morning” (pagi), “Afternoon” (siang), dan “Evening” (malam);

F(6,32)=47.459, p<0.001. Tetapi interaksi antara kedua faktor tidak mempengaruhi variabel

dependennya.

2. Multivariat Regresi

PPVT<-c(68,82,82,91,82,100,100,96,63,91,87,105,87,76,66,74,68,98,63,94,82,

89,80,64,102,71,102,96,55,96,74,78)

RPMT<-c(15,11,13,18,13,15,13,12,10,18,10,21,14,16,14,15,13,16,15,16,18,

15,19,11,20,12,16,13,16,18,15,19)

SAT<-c(24,8,88,82,90,77,58,14,1,98,8,88,4,14,38,4,64,88,14,99,50,36,88,14,

24,24,24,50,8,98,98,50)

0 2 4 6 8 10

02

46

8

QQ Plot Assessing Multivariate Normality

qchisq(ppoints(n), df = p)

Ma

ha

lan

ob

is D

2


Gr<-c(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)

N<-c(0,7,7,6,20,4,6,5,3,16,5,2,1,11,0,5,1,1,0,4,4,1,5,4,5,9,4,5,4,4,2,5)

S<-c(10,3,9,11,7,11,7,2,5,12,3,11,4,5,0,8,6,9,13,6,5,6,8,5,7,4,17,8,7,

7,6,10)

NS<-c(8,21,17,16,21,18,17,11,14,16,17,10,14,18,3,11,19,12,13,14,16,15,14,

11,17,8,21,20,19,10,14,18)

NT<-c(21,28,31,27,28,32,26,22,24,27,25,26,25,27,16,12,28,30,19,27,21,23,

25,16,26,16,27,28,20,23,25,27)

SS<-c(22,21,30,25,16,29,23,23,20,30,24,22,19,22,11,15,23,18,16,19,24,28,

24,22,15,14,31,26,13,19,17,26)

D<-data.frame(PPVT,RPMT,SAT,Gr,N,S,NS,NT,SS)

D

PPVT RPMT SAT Gr N S NS NT SS

1 68 15 24 1 0 10 8 21 22

2 82 11 8 1 7 3 21 28 21

3 82 13 88 1 7 9 17 31 30

4 91 18 82 1 6 11 16 27 25

5 82 13 90 1 20 7 21 28 16

6 100 15 77 1 4 11 18 32 29

7 100 13 58 1 6 7 17 26 23

8 96 12 14 1 5 2 11 22 23

9 63 10 1 1 3 5 14 24 20

10 91 18 98 1 16 12 16 27 30

11 87 10 8 1 5 3 17 25 24

12 105 21 88 1 2 11 10 26 22

13 87 14 4 1 1 4 14 25 19

14 76 16 14 1 11 5 18 27 22

15 66 14 38 1 0 0 3 16 11

16 74 15 4 1 5 8 11 12 15

17 68 13 64 1 1 6 19 28 23

18 98 16 88 1 1 9 12 30 18

19 63 15 14 1 0 13 13 19 16

20 94 16 99 1 4 6 14 27 19

21 82 18 50 1 4 5 16 21 24

22 89 15 36 1 1 6 15 23 28

23 80 19 88 1 5 8 14 25 24

24 64 11 14 1 4 5 11 16 22

25 102 20 24 1 5 7 17 26 15

26 71 12 24 1 9 4 8 16 14

27 102 16 24 1 4 17 21 27 31

28 96 13 50 1 5 8 20 28 26

29 55 16 8 1 4 7 19 20 13

30 96 18 98 1 4 7 10 23 19

31 74 15 98 1 2 6 14 25 17

32 78 19 50 1 5 10 18 27 26

a. R2y1,y3 ~ x1+x2+x3

# Multivariat Linear Regression

fit_a <- lm(cbind(PPVT,SAT)~Gr+N+S, data=D)

summary(fit_a) # show results

Response PPVT :

Call:

lm(formula = PPVT ~ Gr + N + S, data = D)


Residuals:

Min 1Q Median 3Q Max

-27.6164 -8.7124 0.2078 12.0739 19.0511

Coefficients: (1 not defined because of singularities)

Estimate Std. Error t value Pr(>|t|)

(Intercept) 73.4419 6.1473 11.947 1.01e-12 ***

Gr NA NA NA NA

N 0.3325 0.5669 0.587 0.562

S 1.1207 0.6976 1.606 0.119

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 13.59 on 29 degrees of freedom

Multiple R-squared: 0.09405, Adjusted R-squared: 0.03157

F-statistic: 1.505 on 2 and 29 DF, p-value: 0.2388

Response SAT :

Call:

lm(formula = SAT ~ Gr + N + S, data = D)

Residuals:


-51.997 -26.904 -0.661 22.414 59.123



(Intercept) 17.064 15.309 1.115 0.2742

Gr NA NA NA NA

N 1.723 1.412 1.220 0.2322

S 3.061 1.737 1.762 0.0886 .

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1




b. R2y1,y2 ~ x1+x3+x4

fit_b <- lm(cbind(PPVT,RPMT)~Gr+S+NS, data=D)


Response PPVT :

Call:


Residuals:


-27.6164 -8.7124 0.2078 12.0739 19.0511



(Intercept) 73.4419 6.1473 11.947 1.01e-12 ***

Gr NA NA NA NA

N 0.3325 0.5669 0.587 0.562

S 1.1207 0.6976 1.606 0.119

---


Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1




Response SAT :

Call:


Residuals:


-51.997 -26.904 -0.661 22.414 59.123



(Intercept) 17.064 15.309 1.115 0.2742

Gr NA NA NA NA

N 1.723 1.412 1.220 0.2322

S 3.061 1.737 1.762 0.0886 .

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1




c. R2y1,y3 ~ x1+x2+x3+x4+x5+x6

fit_c <- lm(cbind(PPVT,SAT)~Gr+N+S+NS+NT+SS, data=D)


Response PPVT :

Call:


Residuals:


-27.6164 -8.7124 0.2078 12.0739 19.0511



(Intercept) 73.4419 6.1473 11.947 1.01e-12 ***

Gr NA NA NA NA

N 0.3325 0.5669 0.587 0.562

S 1.1207 0.6976 1.606 0.119

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1




Response SAT :

Call:


Residuals:



-51.997 -26.904 -0.661 22.414 59.123



(Intercept) 17.064 15.309 1.115 0.2742

Gr NA NA NA NA

N 1.723 1.412 1.220 0.2322

S 3.061 1.737 1.762 0.0886 .

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1




tugas multivariat - evan susandi

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