Korelasi Linier KUSWANTO-2013

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

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?

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!!

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

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?

 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]

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

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

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)

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

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

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

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

Exercise!! Do it now!! No X (height) Y (diameter) X2X2 Y2Y2 XY Jumlah  x 2  y 2  xy r = = Test your coefficient! [  X 2 –(  X) 2 /n]  XY –{(  X)(  Y)}/n [  Y 2 –(  Y) 2 /n]

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 , ,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

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.

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