Korelasi Linier KUSWANTO-2013. Korelasi Keeratan hubungan antara 2 variabel yang saling bebas Walaupun dilambangkan dengan X dan Y namun keduanya diasumsikan.

Presentasi berjudul: "Korelasi Linier KUSWANTO-2013. Korelasi Keeratan hubungan antara 2 variabel yang saling bebas Walaupun dilambangkan dengan X dan Y namun keduanya diasumsikan."— Transcript presentasi:

1 Korelasi Linier KUSWANTO-2013

2 Korelasi Keeratan hubungan antara 2 variabel yang saling bebas Walaupun dilambangkan dengan X dan Y namun keduanya diasumsikan tidak saling tergantung Keeratan bisa positip, bisa negatip

3 Possitive Correlation Correlation is common in everyday sayings – –“the bigger they are the harder they fall” – –“the longer the lover” – –“he comes I am happy --he doest’n come I am sad Each implies two variable quantities, with the magnitude of one changing with the magnitude of the other Also, as one increases, so does the other – called direct or positive correlation. What about negative correlation?

4 NEGATIVE CORRELATION Negative correlation is common : “The more often he comes, I am not happy” “The bigger the mellon, the smaller the leaf’ The lazier she is, I love her Here as one increases, the other variable decreases – called inverse or negative correlation. Find out others more!!

5 Scattergrams (diagram pencar) Y X Y X Y X Y yY Positive correlationNegative correlationNo correlation

6 yield height Here we see that yield is positively related to height EXAMPLE Similar relationships may apply in agriculture: –How does height of plant relate to yield? –How does amount of pesticide affect plasma protein in pest?

7  x 2  y 2  xy r = Correlation Coefficient: Attention the regression formula  next A measurement of the closeness of the relationship between two variables is the coefficient of correlation (r). r can never be greater than 1 or less than -1. r has no units, so is not a measure of change of one variable with respect to the other, but is a measure of the intensity of the association [  X 2 –(  X) 2 /n]  XY –{(  X)(  Y)}/n = [  Y 2 –(  Y) 2 /n]

8 PAY ATTENTION! = ∑xy (huruf x dan y kecil) = ∑x (huruf x kecil) = ∑y (huruf y kecil)

9 S r = 1- r 2 n - 2 We may then use this SE to test if r = 0 (that is if there is no correlation) H O : r = 0 (no correlation) H A : r ≠ 0 (there is a correlation) t hit = r SrSr H o is rejected if t ≥ t  (2), Siapkan tabel t = 1- r 2 n - 2 r Uji Nyata Koefisien Korelasi = n - 2r 1- r 2

10 Exercise!! Do it now!! Hitunglah nilai korelasi antara tinggi tanaman dan diameter batang dari data tsb Ujilah tingkat nyata koefisien korelasinya NoX (height) Y (diameter) 1154 2175 3206 4258 5288 63010

11 Ingat rumus korelasi …! No X (height) Y (diameter) X2X2 Y2Y2 XY 1154 2175 3206 4258 5288 63010 Jumlah  x 2  y 2  xy r = = [  X 2 –(  X) 2 /n]  XY –{(  X)(  Y)}/n [  Y 2 –(  Y) 2 /n]

12 Exercise!! Do it now!! No X (height) Y (diameter) X2X2 Y2Y2 XY 1154225 2175289 3206400 4258625 5288784 63010900 Jumlah  x 2  y 2  xy r = = [  X 2 –(  X) 2 /n]  XY –{(  X)(  Y)}/n [  Y 2 –(  Y) 2 /n]

13 Exercise!! Do it now!! No X (height) Y (diameter) X2X2 Y2Y2 XY 115422516 217528925 320640036 425862564 528878464 63010900100 Jumlah  x 2  y 2  xy r = = [  X 2 –(  X) 2 /n]  XY –{(  X)(  Y)}/n [  Y 2 –(  Y) 2 /n]

14 Exercise!! Do it now!! No X (height) Y (diameter) X2X2 Y2Y2 XY 11542251660 21752892585 320640036120 425862564200 528878464224 63010900100300 Jumlah  x 2  y 2  xy r = = [  X 2 –(  X) 2 /n]  XY –{(  X)(  Y)}/n [  Y 2 –(  Y) 2 /n]

15 Exercise!! Do it now!! No X (height) Y (diameter) X2X2 Y2Y2 XY 11542251660 21752892585 320640036120 425862564200 528878464224 63010900100300 Jumlah135413223305989  x 2  y 2  xy r = = Test your coefficient! [  X 2 –(  X) 2 /n]  XY –{(  X)(  Y)}/n [  Y 2 –(  Y) 2 /n]

16 Perhitungan r = [  X 2 –(  X) 2 /n]  XY –{(  X)(  Y)}/n [  Y 2 –(  Y) 2 /n] [3223–(135) 2 /6] 989 –{(135)(41)}/6 [  305–(41) 2 /6] = 0,98 = = n - 2r 1- r 2 t hit 6 - 20,98 1- 0,98 2 = Bandingkan dengan t tabel 5% dan 1%. Apabila lebih besar dari t 5% : nyata (*), dan apabila lebih besar dari t 1% : sangat nyata (**) = 14,69

17 Kesimpulan dan interpretasi Terdapat korelasi sangat nyata (p=0,01) antara tinggi tanaman dan diameter batang Keeratan hubungan antara tinggi tanaman dan diameter batang sebesar 0,98. Peningkatan nilai tinggi tanaman akan diikuti oleh peningkatan diameter batang.

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19 Bahan Diskusi Cari satu pasang data, sesuai dengan latar belakang sdr. Lakukan analisis korelasi linier, ujilah nilai korelasi tersebut, kemudian berikan kesimpulan dan interpretasinya.

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