1

UTS STATISTIK PROGRAM PASCA SARJANA PENGAJAR : TOTO WARSA, Ir., M.S. PENYUSUN: Nama : Ade Setiawan NPM : 150220060003 PERTANYAAN DAN JAWABAN

Pertanyaan: a. Hitung nilai β0 dan β1 untuk model regresi Y = β0 + β1X + ε dan tentukanlah persamaan

garis regresinya! b. Lakukan Uji statitik, Analisis Varians dan termasuk Simpangan Model dan Galat Murninya! c. Kerjakan point a dan b untuk data yang sudah di tranformasi logaritma

2

Jawab:

1. Analisis data sebelum ditransformasikan:

No X Y X2 Y2 XY Ulangan JKGM 1 20.0 90 400.00 8100 1800.0 2 20.0 105 400.00 11025 2100.0 2 112.50000 3 20.5 90 420.25 8100 1845.0 4 20.5 90 420.25 8100 1845.0 5 20.5 100 420.25 10000 2050.0 6 20.5 110 420.25 12100 2255.0 4 275.00000 7 21.0 100 441.00 10000 2100.0 8 21.0 105 441.00 11025 2205.0 2 12.50000 9 21.5 100 462.25 10000 2150.0 10 21.5 105 462.25 11025 2257.5 11 21.5 110 462.25 12100 2365.0 12 21.5 110 462.25 12100 2365.0 13 21.5 110 462.25 12100 2365.0 14 21.5 110 462.25 12100 2365.0 15 21.5 110 462.25 12100 2365.0 16 21.5 110 462.25 12100 2365.0 17 21.5 115 462.25 13225 2472.5 18 21.5 115 462.25 13225 2472.5 19 21.5 115 462.25 13225 2472.5 20 21.5 115 462.25 13225 2472.5 21 21.5 120 462.25 14400 2580.0 13 307.69231 22 22.0 110 484.00 12100 2420.0 23 22.0 110 484.00 12100 2420.0 24 22.0 115 484.00 13225 2530.0 25 22.0 115 484.00 13225 2530.0 26 22.0 115 484.00 13225 2530.0 27 22.0 115 484.00 13225 2530.0 28 22.0 120 484.00 14400 2640.0 29 22.0 120 484.00 14400 2640.0 30 22.0 120 484.00 14400 2640.0 31 22.0 120 484.00 14400 2640.0 32 22.0 120 484.00 14400 2640.0 33 22.0 120 484.00 14400 2640.0 34 22.0 120 484.00 14400 2640.0 35 22.0 120 484.00 14400 2640.0 36 22.0 120 484.00 14400 2640.0 37 22.0 125 484.00 15625 2750.0 38 22.0 125 484.00 15625 2750.0 39 22.0 125 484.00 15625 2750.0 40 22.0 130 484.00 16900 2860.0 41 22.0 130 484.00 16900 2860.0 20 573.75000 42 22.5 115 506.25 13225 2587.5 43 22.5 115 506.25 13225 2587.5 44 22.5 115 506.25 13225 2587.5 45 22.5 120 506.25 14400 2700.0 46 22.5 120 506.25 14400 2700.0 47 22.5 120 506.25 14400 2700.0

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No X Y X2 Y2 XY Ulangan JKGM 48 22.5 120 506.25 14400 2700.0 49 22.5 120 506.25 14400 2700.0 50 22.5 120 506.25 14400 2700.0 51 22.5 125 506.25 15625 2812.5 52 22.5 125 506.25 15625 2812.5 53 22.5 125 506.25 15625 2812.5 54 22.5 125 506.25 15625 2812.5 55 22.5 125 506.25 15625 2812.5 56 22.5 130 506.25 16900 2925.0 57 22.5 130 506.25 16900 2925.0 58 22.5 130 506.25 16900 2925.0 59 22.5 130 506.25 16900 2925.0 60 22.5 135 506.25 18225 3037.5 61 22.5 135 506.25 18225 3037.5 62 22.5 135 506.25 18225 3037.5 63 22.5 140 506.25 19600 3150.0 64 22.5 150 506.25 22500 3375.0 23 1660.86957 65 23.0 125 529.00 15625 2875.0 66 23.0 130 529.00 16900 2990.0 67 23.0 140 529.00 19600 3220.0 68 23.0 140 529.00 19600 3220.0 69 23.0 140 529.00 19600 3220.0 70 23.0 140 529.00 19600 3220.0 71 23.0 145 529.00 21025 3335.0 72 23.0 145 529.00 21025 3335.0 73 23.0 145 529.00 21025 3335.0 9 388.88889 74 23.5 145 552.25 21025 3407.5 75 23.5 150 552.25 22500 3525.0 76 23.5 155 552.25 24025 3642.5 77 23.5 170 552.25 28900 3995.0 4 350.0000078 24.0 165 576.00 27225 3960.0 79 24.0 170 576.00 28900 4080.0 2 12.50000 80 25.0 170 625.00 28900 4250.0 Jumlah 1775 9910 39443 1250800 220930 3693.7008 Rataan 22.1875 123.875

99101775123.875022.1875

=Σ=Σ==

i

iYXYX

3693.7008220930125080039443

2

2

==Σ=Σ=Σ

JKGMYX

YX

i

i

i

4

a. Jika model regresinya Y = β0 + β1X + ε, tentukanlah persamaan garis regresinya!

17.4766480

)1775(39443

80)9910)(1775(220930

)(

2

22

1

=

−

−=

Σ−Σ

ΣΣ−Σ

=

nX

X

nYX

YX

ii

iiii

β

-263.88792.1875)17.47664(2123.8750

10

=−=

−= XY ββ

Sehingga persamaan regresinya: Y = -263.88785 + 17.47664 X

Koefisien Korelasi:

0.89018280

)9910(125080080

)1775(39443

80)9910)(1775(220930

)()(

22

22

22

=

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛−

−=

⎟⎟⎠

⎞⎜⎜⎝

⎛ Σ−Σ⎟⎟

⎠

⎞⎜⎜⎝

⎛ Σ−Σ

ΣΣ−Σ

=

nY

YnX

X

nYX

YXr

ii

ii

iiii

yx

Koefisien Determinasi:

0.7924240.890182)( 2

22

=== yxrR

5

b. Uji Statistik (Analisis Varians termasuk Simpangan Model dan Galat Murni)

71121.8132523693.70076-4815.51

Re

23693.70076

4815.5124183837523198

ReRe

2359811838380

991017752209304766417

Re

75231982512276011250800

25122760180

9910

1

2

22

===

=

=−=

=

=⎥⎦⎤

⎢⎣⎡=

⎥⎦⎤

⎢⎣⎡ −=

==

−=

=

==

sidu-JKGMJKJKSM

JKGM

..gJKT-JKsiduJK

.

))((-.

nΣYΣX

YΣXβgresiJK

..-

FKΣYJKT

.

)(n

)(ΣΣFK

iiii

i

i

Tabel Analisis Varians Regresi: Sumber Ragam DB JK RJK F-hit F.05 F.01Regresi 1 18383.235981 18383.24 297.77 3.96 6.97Residu 78 4815.514019 61.73736 SM 8 1121.813257 140.2267 2.66* 2.07 2.78 GM 70 3693.700762 52.76715 Total 79 23198.750000

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2. Analisis data setelah ditransformasikan:

No X Y X2 Y2 XY Ulangan JKGM 1 1.30 1.95 1.69 3.8025 2.5350 2 1.30 2.02 1.69 4.0804 2.6260 2 0.00245 3 1.31 1.95 1.72 3.8025 2.5545 4 1.31 1.95 1.72 3.8025 2.5545 5 1.31 2.00 1.72 4.0000 2.6200 6 1.31 2.04 1.72 4.1616 2.6724 4 0.00570 7 1.32 2.00 1.74 4.0000 2.6400 8 1.32 2.02 1.74 4.0804 2.6664 2 0.00020 9 1.33 2.00 1.77 4.0000 2.6600 10 1.33 2.02 1.77 4.0804 2.6866 11 1.33 2.04 1.77 4.1616 2.7132 12 1.33 2.04 1.77 4.1616 2.7132 13 1.33 2.04 1.77 4.1616 2.7132 14 1.33 2.04 1.77 4.1616 2.7132 15 1.33 2.04 1.77 4.1616 2.7132 16 1.33 2.04 1.77 4.1616 2.7132 17 1.33 2.06 1.77 4.2436 2.7398 18 1.33 2.06 1.77 4.2436 2.7398 19 1.33 2.06 1.77 4.2436 2.7398 20 1.33 2.06 1.77 4.2436 2.7398 21 1.33 2.08 1.77 4.3264 2.7664 13 0.00492 22 1.34 2.04 1.80 4.1616 2.7336 23 1.34 2.04 1.80 4.1616 2.7336 24 1.34 2.06 1.80 4.2436 2.7604 25 1.34 2.06 1.80 4.2436 2.7604 26 1.34 2.06 1.80 4.2436 2.7604 27 1.34 2.06 1.80 4.2436 2.7604 28 1.34 2.08 1.80 4.3264 2.7872 29 1.34 2.08 1.80 4.3264 2.7872 30 1.34 2.08 1.80 4.3264 2.7872 31 1.34 2.08 1.80 4.3264 2.7872 32 1.34 2.08 1.80 4.3264 2.7872 33 1.34 2.08 1.80 4.3264 2.7872 34 1.34 2.08 1.80 4.3264 2.7872 35 1.34 2.08 1.80 4.3264 2.7872 36 1.34 2.08 1.80 4.3264 2.7872 37 1.34 2.10 1.80 4.4100 2.8140 38 1.34 2.10 1.80 4.4100 2.8140 39 1.34 2.10 1.80 4.4100 2.8140 40 1.34 2.11 1.80 4.4521 2.8274 41 1.34 2.11 1.80 4.4521 2.8274 20 0.00772 42 1.35 2.06 1.82 4.2436 2.7810 43 1.35 2.06 1.82 4.2436 2.7810 44 1.35 2.06 1.82 4.2436 2.7810 45 1.35 2.08 1.82 4.3264 2.8080 46 1.35 2.08 1.82 4.3264 2.8080 47 1.35 2.08 1.82 4.3264 2.8080 48 1.35 2.08 1.82 4.3264 2.8080 49 1.35 2.08 1.82 4.3264 2.8080

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No X Y X2 Y2 XY Ulangan JKGM 50 1.35 2.08 1.82 4.3264 2.8080 51 1.35 2.10 1.82 4.4100 2.8350 52 1.35 2.10 1.82 4.4100 2.8350 53 1.35 2.10 1.82 4.4100 2.8350 54 1.35 2.10 1.82 4.4100 2.8350 55 1.35 2.10 1.82 4.4100 2.8350 56 1.35 2.11 1.82 4.4521 2.8485 57 1.35 2.11 1.82 4.4521 2.8485 58 1.35 2.11 1.82 4.4521 2.8485 59 1.35 2.11 1.82 4.4521 2.8485 60 1.35 2.13 1.82 4.5369 2.8755 61 1.35 2.13 1.82 4.5369 2.8755 62 1.35 2.13 1.82 4.5369 2.8755 63 1.35 2.15 1.82 4.6225 2.9025 64 1.35 2.18 1.82 4.7524 2.9430 23 0.01918 65 1.36 2.10 1.85 4.4100 2.8560 66 1.36 2.11 1.85 4.4521 2.8696 67 1.36 2.15 1.85 4.6225 2.9240 68 1.36 2.15 1.85 4.6225 2.9240 69 1.36 2.15 1.85 4.6225 2.9240 70 1.36 2.15 1.85 4.6225 2.9240 71 1.36 2.16 1.85 4.6656 2.9376 72 1.36 2.16 1.85 4.6656 2.9376 73 1.36 2.16 1.85 4.6656 2.9376 9 0.00400 74 1.37 2.16 1.88 4.6656 2.9592 75 1.37 2.18 1.88 4.7524 2.9866 76 1.37 2.19 1.88 4.7961 3.0003 77 1.37 2.23 1.88 4.9729 3.0551 4 0.00260 78 1.38 2.22 1.90 4.9284 3.0636 79 1.38 2.23 1.90 4.9729 3.0774 2 0.00005 80 1.40 2.23 1.96 4.9729 3.1220 107.5 167.12 144.4772 349.3934 224.6412 0.046825686

1.3438 2.0890 1.805965 4.3674175 2.808015

167.12107.52.08901.3438

=Σ=Σ==

i

iYXYX

0.04682569224.6412349.3934144.4772

2

2

==Σ=Σ=Σ

JKGMYX

YX

i

i

i

8

a. Jika model regresinya Y = β0Xβ1ε, tentukanlah β0 dan β1 serta persamaan garis regresinya! Jika persamaan Y = β0Xβ1ε, di rubah jadi bentuk logaritma: Log Y = Log β0 + β1 Log X + Log ε atau Y* = β0

* + β1X* + ε*

3.06126780

)107.5(144.4772

80)167.12)(107.5(224.6412

)(

2

22

1

=

−

−=

Σ−Σ

ΣΣ−Σ

=

nX

X

nYX

YX

ii

iiii

β

-2.024577.3438)3.061267(12.0890

1*

0

=−=

−= XY ββ

Persamaan regresinya: Y* = -2.0246 + 3.0613 X Dari persamaan tersebut bisa didapatkan nilai β0 dan β1:

β0 = 10β0 = 10(-2.024577362) = 0.0094498 ; dan β1 = 3.06127 Sehingga persamaan regresinya: Y = 0.00945 X 3.06127

Koefisien Korelasi:

0.89809680

)167.12(349.393480

)107.5(144.4772

80)167.12)(107.5(224.6412

)()(

22

22

22

=

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛−

−=

⎟⎟⎠

⎞⎜⎜⎝

⎛ Σ−Σ⎟⎟

⎠

⎞⎜⎜⎝

⎛ Σ−Σ

ΣΣ−Σ

=

nY

YnX

X

nYX

YXr

ii

ii

iiii

yx

Koefisien Determinasi:

0.7924240.890182)( 2

22

=== yxrR

9

b. Uji Statistik (Analisis Varians termasuk Simpangan Model dan Galat Murni)

0.0072790468260-0.054105

Re

0468260

0.0541050.2256150.279720

ReRe

0.22561580

167.12107.5224.64123.061267

Re

0.279720349.113680 349.393400

349.11368080

167.12

1

2

22

===

=

=−=

=

=⎥⎦⎤

⎢⎣⎡=

⎥⎦⎤

⎢⎣⎡ −=

==

−=

=

=Σ

=

.sidu-JKGMJKJKSM

.JKGM

gJKT-JKsiduJK

))((-

nΣYΣX

YΣXβgresiJK

-FKΣYJKT

)(n

)Y(FK

iiii

i

i

Tabel Analisis Varians Regresi: Sumber Ragam DB JK RJK F-hit F.05 F.01Regresi 1 0.225615 0.225615 325.26 3.96 6.97 Residu 78 0.054105 0.000694 SM 8 0.007279 0.000910 1.36tn 2.07 2.78 GM 70 0.046826 0.000669 Total 79 0.279720