This document discusses nonlinear regression modeling and prediction. It provides an example of predicting Y given values of X using the equations Y = a + b logX and Y= aX^b. The constants a and b are determined from the regression coefficients. Predictions are made by plugging values of X into the equations. For instance, when a=2, b=2, and X=100, both equations predict a value of Y = 1,000,000.

1. Model Non Linear (Prediksi)
Jakarta, 30 Juli 2019
Prof. Dr. H. Aminullah Assagaf, SE., MS., MM., M.Ak
Email: assagaf29@yahoo.com
HP: +628113543409

2. STUDI KASUS HAL 342 (TABEL 8.6)
th n Y (AC) X (Q) Log Y Log X Catatan :
1 2 3 4 5=3x4 6=4x4 Ybar = Y/n = 0,8479
1 1 9,00 150 0,9542 2,1761 Xbar = X/n = 2,4646
2 1 7,20 275 0,8573 2,4393 xy = XY - (X) (Y) /n = (0,0526)
3 1 6,50 350 0,8129 2,5441 x^2 = X^2 - (X)^2 = 0,1451
4 1 5,85 500 0,7672 2,6990 b = xy /x^2 = (0,3626)
Sigma 4 28,55 1.275 3,3916 9,8585 a = Ybar - B( Xbar ) = 1,7416
log Y = log a + b logX
Mis : X = 1000 unit
th n Y (Q) X (VC) XY X^2 log Y = 1.7416 - 0.3626 (log 1000)
1 2 3 4 5=3x4 6=4x4 log Y = 1.7416 - 0.3626 (3) 0,6538 (1,0879)
1 1 0,9542 2,1761 2,0765 4,7354 log Y = 1.7416 - 1.0879
2 1 0,8573 2,4393 2,0913 5,9503 log Y = 0.6538
3 1 0,8129 2,5441 2,0681 6,4723 Y =10 ^ 0.6538 = 4.506
4 1 0,7672 2,6990 2,0705 7,2844
Sigma 4 3,3916 9,8585 8,3065 24,4424 ATAU
Y = a Q^b
Catatan : (mis : a = 2 dan b = 2) Mis : X atau Q = 1000 unit
Y = log a + b log X Y = aQ^b a = 1.7416 = 10 ^1.7416 = 55.1605 55,1605
mis : X = 100 mis : X atau Q = 100 Y = 55.1605 (1000 ^ - 0.3626) 0,0817
Y = 2 + 2 (log 100) a = 10^2 = 100 Y = 55.1605 (0.0817) = 4.506 4,506
Y = 2 + 2 (2) = 6 Y = 100(100^2)
Y = 10^6 = 1.000.000 Y = 100(10.000)
Y = 1.000.000 Y = 1.000.000

3. Coefficientsa
Model
Unstandardized Coefficients
Standardized
Coefficients
t Sig.B Std. Error Beta
1 (Constant) 17411.936 353.757 49.220 .000
LnX -.362 .014 -.998 -25.327 .002
a. Dependent Variable: lnY
Mis : X = 1000 unit
log Y = 1.7416 - 0.3626 (log 1000)
log Y = 1.7416 - 0.3626 (3) 0,6538 (1,0879)
log Y = 1.7416 - 1.0879
log Y = 0.6538
Y =10 ^ 0.6538 = 4.506
ATAU
Y = a Q^b
Mis : X atau Q = 1000 unit
a = 1.7416 = 10 ^1.7416 = 55.1605 55,1605
Y = 55.1605 (1000 ^ - 0.3626) 0,0817
Y = 55.1605 (0.0817) = 4.506 4,506

4. Contoh 2:
Contoh 1: a=2 dan b=2
mis: Y=a.X^b = 2.X^2 mis: Y=X1^a.X^b = X1^2.X2^^2
bila X=1000 bila X1=1000 dan X2=1000
maka: maka:
a=10^a=10^2 =100 a=X1^2=1000^2=1000.000
X^b=1000^2=1000.000 X^b=1000^2=1000.000
Y=a.X^b=100 x1000.000=100.000.000 Y=X1^a.X^b=1000^2 x 1000^2= 1000.000^2=1000.000.000.000=1 Triliun
ATAU ATAU
Y=a+ b log X Y=a+ b log X
a= 2 a= 2 (log 1000=3) = 6
b=2 (log 1000-3) =6 b=2 (log 1000-3) =6
Y=2 + 6 = 8 Y=6 + 6 = 12
Y=10^8=100.000.000 Y=10^12=1000.000.000.000 = 1 triliun

5. Contoh perhitungan model linear Log atau Ln
• Log(100)=2 100^(1/2)=10 (bilangan dasar 10)
• Ln(100)=4,6051702 100^(1/4,60517012)=2,7182818 (bilangan
dasar 2,718…)
• Model regresi nonlinear: hasil prediksi = 1 juta, untuk Y = a + b logx
atau Y= a. X^b, bila diketahui a=2 dan b=2
1) Y=a + b logX Y=2+ 2 logX  bila X=100, maka log(100)=2
Yest= 2 + 2(2) = 6 shingga Yest= 10^6=1.000.000
2) Y= a.X^b  Y=10^a . X^b  Y= 2 . X^2  bila X=100, maka
Y=10^2 . 100^2 = 100 . 10.000 = 1.000.000