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 example shows that when a=2, b=2, and X=100, both models predict Y will equal 1,000,000. Additional examples are given to further illustrate how to calculate predictions using logarithmic and exponential nonlinear regression models.

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