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Contoh Penerapan ANALISIS REGRESI BERGANDA

Contoh Penerapan ANALISIS REGRESI BERGANDA. Model Y = bo + b1 X1 + b2 X2 Y= b0 + b1 X1 + b2X2 + b12X1X2 +b11 X1 2 + b22 X2 2 Y = variabel tak bebas X1 dan X2 = variabel bebas. Model Y= bo + b1 X1 + b2 X2. Matrik rancangan X. Matrik rancangan.

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Contoh Penerapan ANALISIS REGRESI BERGANDA

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  1. Contoh PenerapanANALISIS REGRESI BERGANDA • Model Y = bo + b1 X1 + b2 X2 • Y= b0 + b1 X1 + b2X2 + b12X1X2 +b11 X12 + b22 X22 Y = variabel tak bebas X1 dan X2 = variabel bebas

  2. Model Y= bo + b1 X1 + b2 X2 • Matrik rancangan X

  3. Matrik rancangan

  4. Penduga parameter regresi • b = (X’X)-1 X’Y • (X’X)-1 = invers matrik X’X

  5. Anova Regresi

  6. Jumlah kuadrat • FK = ( 1’ Y)2/n = ( yi)2/n • JK Regresi (JKR)= b’ X’Y • JK Total (JKT) = Y’Y – FK • JKS = JKT – JKR • Koefisien determinasi R2= JKR/JKT

  7. Dugalah persamaan regresi Y = b0+b1N+ b2P+b12NP+b11N2+b22P2 bagi data respon hasil terhadap pemupukan Nitrogen dan Fosfor berikut :

  8. Uji kehomogenan regresi linier • Pendugaan regresi linier y = a + b x , dapat diperoleh dengan metode kuadrat terkecil. n  x iyi - ( x i)(  yi) Penduga b = ------------------------------  x i2 - ( x i)2 a = y – b x , y = rata-rata y ; x = rata-rata x

  9. Uji kehomogenan/keidentikan • Statistik uji [Sxy – SxSy/N]2 { Syy –sy2/N] - --------------------- - s2 } Sxx – Sx2/N w = -------------------------------------------------- {(N-2H)/(2(H-1)} , S2 N=total seluruh pengamatan, H=banyaknya regresi yang diuji, S2 = jumlah kuadrat sisaan seluruh regresi yang diuji, dan Sx= ( xhj), Sxx = ( xhj2), Sy= ( yhj), Syy = ( yhj2), Sxy= ( xhj yhj)

  10. Uji kesejajaran

  11. Uji kesamaan intersep

  12. Uji kehomogen, kesejajaran dan kesamaan intersep regresi linier bagi data berikut:

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