Statistik Koefisien Korelasi Moment Product Pearson Regresi
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Transcript of Statistik Koefisien Korelasi Moment Product Pearson Regresi
![Page 2: Statistik Koefisien Korelasi Moment Product Pearson Regresi](https://reader034.fdocument.pub/reader034/viewer/2022052206/5571fa1b49795991699149d0/html5/thumbnails/2.jpg)
Koefisien Korelasi Moment Product Pearson (r)
Dan Regresi
![Page 3: Statistik Koefisien Korelasi Moment Product Pearson Regresi](https://reader034.fdocument.pub/reader034/viewer/2022052206/5571fa1b49795991699149d0/html5/thumbnails/3.jpg)
Kegunaan
• Menguji signifikansi hubungan dua variabel
• Mengetahui kuat lemah hubungan
• Mengetahui besar kontribusi
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Ketentuan Aplikasi
– Data berskala interval atau rasio– Data berdistribusi normal– Signifikansi r, bandingkan dengan tabel r
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Rumus
• rxy=Koefisien Korelasi Moment Product Pearson• X=nilai variabel pertama (variabel bebas)• Y=nilai variabel ke dua (variabel terikat)• N=banyaknya sampel
2222 ..
...
YYNXXN
YXYXNrxy
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Contoh Aplikasi 1
• Suatu kajian IQ beberapa orang mahasiswa yang dikaitkan dengan berat badan pada saat dilahirkan, didapatkan data sebagai berikut:
•
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Selidiki dengan = 5%, apakah terdapat hubungan positif berat badan lahir dengan IQ saat ini?
NOMOR BBL IQ
1 3.20 124
2 2.50 118
3 2.80 120
4 3.00 120
5 2.50 114
6 3.50 120
7 2.00 110
8 2.75 122
9 1.90 100
10 2.35 118
11 2.65 118
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Penyelesaian
• Hipotesis– Ho : r = 0 , tidak ada hubungan bbl dengan iq– Ha : r > 0, ada hubungan + bbl dengan iq
• Nilai = 5%• Rumus
• Hitungan rumus statistik
2222 ..
...
YYNXXN
YXYXNrxy
![Page 9: Statistik Koefisien Korelasi Moment Product Pearson Regresi](https://reader034.fdocument.pub/reader034/viewer/2022052206/5571fa1b49795991699149d0/html5/thumbnails/9.jpg)
Hitungan rumus
NOMOR BBL (X) IQ (Y) X2 Y2 XY
1 3.20 124 10.24 15376 396.80
2 2.50 118 6.25 13924 295.00
3 2.80 120 7.84 14400 336.00
4 3.00 120 9.00 14400 360.00
5 2.50 114 6.25 12996 285.00
6 3.50 120 12.25 14400 420.00
7 2.00 110 4.00 12100 220.00
8 2.75 122 7.56 14884 335.50
9 1.90 100 3.61 10000 190.00
10 2.35 118 5.52 13924 277.30
11 2.65 118 7.02 13924 312.70
JUMLAH 29.15 1284 79.55 150328 3428.30
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Hitungan rumus
7986,0
1284150328.1115,2955,79.11
1284.15,293,3428.11
..
...
22
2222
xy
xy
xy
r
r
YYNXXN
YXYXNr
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• Nilai df– Df = n – 1 = 11 – 1 = 10
• Nilai r tabel ; – Nilai r tabel ; df = 10 ; = 5%, maka r = 0,497
• Daerah penolakan 0,7986 > 0,497 ; Ho ditolak,Ha diterima
• Kesimpulan – Ada hubungan + bbl dengan iq
![Page 12: Statistik Koefisien Korelasi Moment Product Pearson Regresi](https://reader034.fdocument.pub/reader034/viewer/2022052206/5571fa1b49795991699149d0/html5/thumbnails/12.jpg)
Tingkat Signifikansi untuk tes satu sisidf 0,050 0,025 0,010 0,005
Tingkat Signifikansi untuk tes dua sisi 0,100 0,050 0,020 0,0101 0,988 0,997 0,9995 0,99992 0,900 0,950 0,980 0,9903 0,805 0,878 0,934 0,9594 0,729 0,811 0,882 0,9175 0,669 0,754 0,833 0,8746 0,622 0,707 0,789 0,8347 0,582 0,666 0,750 0,7988 0,549 0,632 0,716 0,7659 0,521 0,602 0,685 0,735
10 0,497 0,576 0,658 0,70811 0,476 0,553 0,634 0,68412 0,458 0,532 0,612 0,66113 0,441 0,514 0,592 0,64114 0,426 0,497 0,574 0,62315 0,412 0,482 0,558 0,60616 0,400 0,468 0,542 0,59017 0,389 0,456 0,528 0,57518 0,378 0,444 0,516 0,56119 0,369 0,433 0,503 0,54920 0,360 0,423 0,492 0,53721 0,352 0,413 0,482 0,52622 0,344 0,404 0,472 0,51523 0,337 0,396 0,462 0,50524 0,330 0,388 0,453 0,49625 0,323 0,381 0,445 0,48726 0,317 0,374 0,437 0,47027 0,311 0,367 0,430 0,47128 0,306 0,361 0,423 0,46329 0,301 0,355 0,416 0,45630 0,296 0,349 0,409 0,44935 0,275 0,325 0,381 0,41840 0,257 0,304 0,358 0,39345 0,243 0,288 0,338 0,37250 0,231 0,273 0,322 0,35460 0,211 0,250 0,295 0,32570 0,195 0,232 0,274 0,30380 0,183 0,217 0,256 0,28390 0,173 0,205 0,242 0,267
100 0,164 0,195 0,230 0,254
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Regresi
• Garis prediksi
• Data skala interval dan ratio
• Distribusi normal
• Signifikansi ; Independensi, Linieritas, Keberartian
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Regresi
bXaY
22
2
X.X.N
Y.X.XY.XXbYa
22
2
2XX.N
Y.XY.X.N
N
XX
N
Y.XY.X
b
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1164,87a
15,2955,79.11
3,3428.15,291284.55,79a
XX.N
Y.X.XY.XXbYa
2
22
2
![Page 16: Statistik Koefisien Korelasi Moment Product Pearson Regresi](https://reader034.fdocument.pub/reader034/viewer/2022052206/5571fa1b49795991699149d0/html5/thumbnails/16.jpg)
1739,11b
15,2955,79.11
1284.15,293,3428.11b
XX.N
Y.XY.X.Nb
XX.N
Y.XY.X.N
N
XX
N
Y.XY.X
b
2
22
22
2
2
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XY
bXaY
.1739,111164,87
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Uji Independensi
• Penyelesaian
• Hipotesis– Ho : = 0 IQ tidak terikat (independent)
terhadap BBL – Ha : 0 IQ terikat (dependent) terhadap
BBL
• Level signifikansi = 1% = 0,01
• Rumus statistik penguji
![Page 19: Statistik Koefisien Korelasi Moment Product Pearson Regresi](https://reader034.fdocument.pub/reader034/viewer/2022052206/5571fa1b49795991699149d0/html5/thumbnails/19.jpg)
bSE
bt
0
N
XX
SSE YX
b 2
2
2
2
...22
N
YXbYaYSYX
Rumus statistik penguji
![Page 20: Statistik Koefisien Korelasi Moment Product Pearson Regresi](https://reader034.fdocument.pub/reader034/viewer/2022052206/5571fa1b49795991699149d0/html5/thumbnails/20.jpg)
806,21115,29
55,79
11247,182
2
2
2
b
b
YXb
SE
SE
N
XX
SSE
![Page 21: Statistik Koefisien Korelasi Moment Product Pearson Regresi](https://reader034.fdocument.pub/reader034/viewer/2022052206/5571fa1b49795991699149d0/html5/thumbnails/21.jpg)
11247,18
211
3,3428.1739,111284.1164,871503282
...
2
2
22
YX
YX
YX
S
S
N
YXbYaYS
![Page 22: Statistik Koefisien Korelasi Moment Product Pearson Regresi](https://reader034.fdocument.pub/reader034/viewer/2022052206/5571fa1b49795991699149d0/html5/thumbnails/22.jpg)
9818,3
806,2
01739,11
0
t
t
SE
bt
b
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• Df/dk/db– Df = N –2 = 11 – 2 = 9
• Nilai tabel – Nilai t tabel uji dua sisi, = 5%, df = 9, nilai t tabel = 2,262
• Daerah penolakan– Menggunakan gambar
– Menggunakan rumus 3,98 > 2,262 ; berarti Ho ditolak, Ha diterima
• Kesimpulan– Variabel Iq (dependent variable/Y) terikat terhadap variabel bbl
(independent variable/X), pada = 5%.
![Page 24: Statistik Koefisien Korelasi Moment Product Pearson Regresi](https://reader034.fdocument.pub/reader034/viewer/2022052206/5571fa1b49795991699149d0/html5/thumbnails/24.jpg)
Contoh Aplikasi 2
• Suatu studi di daerah pinggiran hutan yang dilakukan terhadap 30 sumber air bersih yang berdekatan dengan hutan hujan tropis tua. Dalam hutan diduga telah terjadi pelapukan zat organik tumbuhan, sehingga menyebabkan menjadi asam. Hasil pendataan sebagai berikut di bawah ini. Selidikilah dengan =5%, apakah semakin dekat dengan hutan kondisi air semakin asam?
![Page 25: Statistik Koefisien Korelasi Moment Product Pearson Regresi](https://reader034.fdocument.pub/reader034/viewer/2022052206/5571fa1b49795991699149d0/html5/thumbnails/25.jpg)
NO JARAK (X) PH (Y) 1 4 4 2 2 2 3 6 6 4 7 6 5 11 7 6 4 4 7 13 9 8 10 8 9 7 6
10 5 3 11 10 7 12 9 6 13 8 6 14 12 7 15 13 10 16 10 8 17 12 7 18 9 7 19 8 7 20 5 5 21 8 7 22 9 8 23 14 11 24 15 10 25 14 9 26 14 9 27 16 11 28 10 7 29 7 6 30 6 6
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Penyelesaian
• Hipotesis– Ho : r = 0 , tidak ada hubungan jarak dengan ph– Ha : r > 0, ada hubungan + jarak dengan ph
• Nilai = 5%• Rumus
• Hitungan rumus statistik
2222 ..
...
YYNXXN
YXYXNrxy
![Page 27: Statistik Koefisien Korelasi Moment Product Pearson Regresi](https://reader034.fdocument.pub/reader034/viewer/2022052206/5571fa1b49795991699149d0/html5/thumbnails/27.jpg)
NO JARAK (X) PH (Y) X2 Y2 XY 1 4 4 16 16 16 2 2 2 4 4 4 3 6 6 36 36 36 4 7 6 49 36 42 5 11 7 121 49 77 6 4 4 16 16 16 7 13 9 169 81 117 8 10 8 100 64 80 9 7 6 49 36 42
10 5 3 25 9 15 11 10 7 100 49 70 12 9 6 81 36 54 13 8 6 64 36 48 14 12 7 144 49 84 15 13 10 169 100 130 16 10 8 100 64 80 17 12 7 144 49 84 18 9 7 81 49 63 19 8 7 64 49 56 20 5 5 25 25 25 21 8 7 64 49 56 22 9 8 81 64 72 23 14 11 196 121 154 24 15 10 225 100 150 25 14 9 196 81 126 26 14 9 196 81 126 27 16 11 256 121 176 28 10 7 100 49 70 29 7 6 49 36 42 30 6 6 36 36 36
JUMLAH 278 209 2.956 1.591 2.147
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929,0
2091591.302782956.30
209.2782147.30
..
...
22
2222
xy
xy
xy
r
r
YYNXXN
YXYXNr
![Page 29: Statistik Koefisien Korelasi Moment Product Pearson Regresi](https://reader034.fdocument.pub/reader034/viewer/2022052206/5571fa1b49795991699149d0/html5/thumbnails/29.jpg)
• Nilai Df = n – 1 = 30 – 1 = 29
• Nilai r tabel ; df=29 ; = 0,05, maka r = 0,301
• Daerah penolakan 0,929 > 0,301 ; Ho ditolak,Ha diterima
• Kesimpulan
Ada hubungan positif jarak dengan ph, pada = 0,05
![Page 30: Statistik Koefisien Korelasi Moment Product Pearson Regresi](https://reader034.fdocument.pub/reader034/viewer/2022052206/5571fa1b49795991699149d0/html5/thumbnails/30.jpg)
Regresi Jarak dengan pH
bXaY
22
2
X.X.N
Y.X.XY.XXbYa
N
XX
N
YXYX
b 2
2
..
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8373,1
2782956.30
2147.278209.2956
..
...
2
22
2
XbYa
XbYa
XXN
YXXYXXbYa
![Page 32: Statistik Koefisien Korelasi Moment Product Pearson Regresi](https://reader034.fdocument.pub/reader034/viewer/2022052206/5571fa1b49795991699149d0/html5/thumbnails/32.jpg)
5535,030278
2956
30209.278
2147
..
2
2
2
b
b
N
XX
N
YXYX
b
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XY
bXaY
.55,084,1
![Page 34: Statistik Koefisien Korelasi Moment Product Pearson Regresi](https://reader034.fdocument.pub/reader034/viewer/2022052206/5571fa1b49795991699149d0/html5/thumbnails/34.jpg)
Uji Independensi
• Penyelesaian
• Hipotesis– Ho : = 0 pH tidak terikat (independent)
terhadap jarak – Ha : 0 pH terikat (dependent) terhadap
jarak
• Level signifikansi = 1% = 0,01
• Rumus statistik penguji
![Page 35: Statistik Koefisien Korelasi Moment Product Pearson Regresi](https://reader034.fdocument.pub/reader034/viewer/2022052206/5571fa1b49795991699149d0/html5/thumbnails/35.jpg)
Rumus statistik penguji
bSE
0bt
N
XX
SSE YX
b 2
2
2
2
...22
N
YXbYaYSYX
![Page 36: Statistik Koefisien Korelasi Moment Product Pearson Regresi](https://reader034.fdocument.pub/reader034/viewer/2022052206/5571fa1b49795991699149d0/html5/thumbnails/36.jpg)
6657,0
230
2147.5535,0209.8373,115912
...
2
2
22
YX
YX
YX
S
S
N
YXbYaYS
![Page 37: Statistik Koefisien Korelasi Moment Product Pearson Regresi](https://reader034.fdocument.pub/reader034/viewer/2022052206/5571fa1b49795991699149d0/html5/thumbnails/37.jpg)
0419,030278
2956
6657,02
2
2
2
b
b
YXb
SE
SE
N
XX
SSE
![Page 38: Statistik Koefisien Korelasi Moment Product Pearson Regresi](https://reader034.fdocument.pub/reader034/viewer/2022052206/5571fa1b49795991699149d0/html5/thumbnails/38.jpg)
21,13
0419,0
5535,0
0
t
t
SE
bt
b
![Page 39: Statistik Koefisien Korelasi Moment Product Pearson Regresi](https://reader034.fdocument.pub/reader034/viewer/2022052206/5571fa1b49795991699149d0/html5/thumbnails/39.jpg)
• Df/dk/db– Df = N –2 = 30 – 2 = 28
• Nilai tabel • Nilai tabel pada tabel t
– Uji dua sisi, = 1%, df = 28, nilai t tabel = 2,763
• Daerah penolakan– Menggunakan gambar
– Menggunakan rumus 13,2100 > 2,763 ; berarti Ho ditolak, Ha diterima
• Kesimpulan– Variabel kualitas air (pH) (dependent variable/Y) terikat terhadap
variabel jarak sumber air dengan sumber pencemar (independent variable/X), pada = 1%.
![Page 40: Statistik Koefisien Korelasi Moment Product Pearson Regresi](https://reader034.fdocument.pub/reader034/viewer/2022052206/5571fa1b49795991699149d0/html5/thumbnails/40.jpg)
Tingkat Signifikansi untuk tes satu sisi0,40 0,25 0,10 0,05 0,025 0,01 0,005 0,0025 0,001 0,0005
Tingkat Signifikansi untuk tes dua sisiDf 0,80 0,50 0,20 0,10 0,05 0,02 0,01 0,005 0,002 0,0011 0,325 1,000 3,078 6,314 12,706 31,821 63,657 127,32 318,31 636,622 0,289 0,816 1,886 2,920 4,303 6,965 9,925 14,089 22,327 31,5983 0,277 0,765 1,638 2,353 3,182 4,541 5,841 7,453 10,214 12,9244 0,271 0,741 1,533 2,132 2,776 3,747 4,604 5,598 7,173 8,6105 0,267 0,727 1,476 2,015 2,571 3,365 4,032 4,773 5,893 6,8696 0,265 0,718 1,440 1,943 2,447 3,143 3,707 4,317 5,208 5,9597 0,263 0,711 1,415 1,895 2,365 2,998 3,499 4,029 4,785 5,4088 0,262 0,706 1,397 1,860 2,306 2,896 3,355 3,833 4,501 5,0419 0,261 0,703 1,383 1,833 2,262 2,821 3,250 3,690 4,297 4,781
10 0,260 0,700 1,372 1,812 2,228 2,764 3,169 3,581 4,144 4,58711 0,260 0,697 1,363 1,796 2,201 2,718 3,106 3,497 4,025 4,43712 0,259 0,695 1,356 1,782 2,179 2,681 3,055 3,428 3,930 4,31813 0,259 0,694 1,350 1,771 2,160 2,650 3,012 3,372 3,852 4,22114 0,258 0,692 1,345 1,761 2,145 2,624 2,977 3,326 3,787 4,14015 0,258 0,691 1,341 1,753 2,131 2,602 2,947 3,286 3,733 4,07316 0,258 0,690 1,337 1,746 2,120 2,583 2,921 3,252 3,686 4,01517 0,257 0,689 1,333 1,740 2,110 2,567 2,898 3,222 3,646 3,96518 0,257 0,688 1,330 1,734 2,101 2,552 2,878 3,197 3,610 3,92219 0,257 0,688 1,328 1,729 2,093 2,539 2,861 3,174 3,579 3,88320 0,257 0,687 1,325 1,725 2,086 2,528 2,845 3,153 3,552 3,85021 0,257 0,686 1,323 1,721 2,080 2,518 2,831 3,135 3,527 3,81922 0,256 0,686 1,321 1,717 2,074 2,508 2,819 3,119 3,505 3,79223 0,256 0,685 1,319 1,714 2,069 2,500 2,807 3,104 3,485 3,76724 0,256 0,685 1,318 1,711 2,064 2,492 2,797 3,091 3,467 3,74525 0,256 0,684 1,316 1,708 2,060 2,485 2,787 3,078 3,450 3,72526 0,256 0,684 1,315 1,706 2,056 2,479 2,779 3,067 3,435 3,70727 0,256 0,684 1,314 1,703 2,052 2,473 2,771 3,057 3,421 3,69028 0,256 0,683 1,313 1,701 2,048 2,467 2,763 3,047 3,408 3,67429 0,256 0,683 1,311 1,699 2,045 2,462 2,756 3,038 3,396 3,65930 0,256 0,683 1,310 1,697 2,042 2,457 2,750 3,030 3,385 3,64640 0,255 0,681 1,303 1,684 2,021 2,423 2,704 2,971 3,307 3,55160 0,254 0,679 1,296 1,671 2,000 2,390 2,660 2,915 3,232 3,460
120 0,254 0,677 1,289 1,658 1,980 2,358 2,617 2,860 3,160 3,373 0,253 0,674 1,282 1,645 1,960 2,326 2,576 2,807 3,090 3,291