The document discusses nonlinear regression, highlighting its modeling of dependent variables as non-linear functions of parameters and independent variables. It reviews common models including power, exponential, and polynomial forms, and demonstrates how to estimate parameters using specific examples. Additionally, it provides instructions for performing regression and calculating correlation in Excel.

1. Nonlinear Regression
Dr. Yogesh A. Garde
Assistant Professor (Agril. Statistics)

2. Nonlinear regression
• Nonlinear regression is a regression in which the
dependent or criterion variables are modeled as a
non-linear function of model parameters and one
or more independent variables.
• There are several common models, which is given
by:
• X transformation,
• Quadratic or curvilinear eq.
• Power model
• Exponential model
y = aXb
ln y = ln a + b ln X
y = abx
Log y = ln a + logb X
Linear regression
y = a + bX +e
X2
, √X, 1/X
y = aebx
ln y = ln a + bx
Y=A + BX

3. The form of the nonlinear regression
•

4. Estimate the value of A and B by:
A -0.6326
B 1.9188
Example:
a = antilog A = antilog(-0.6326) = 0.23302
b = 1.9188
X = antilog V
B
𝐵=∑𝑈𝑉−¿¿¿ 𝐴=𝑈 −𝐵𝑉
Thus power curve of best fit is Y = 0.23302(X)1.9188

5. Example:
Let
Estimate the value of A and B by:
A 0.4604
B 0.2564
𝐵=∑𝑈𝑋−¿¿¿ 𝐴=𝑈 −𝐵 𝑋

6. • Correlation and regression on excel
Y X
4 11
6 12
8 13
9 14
10 15
15 16
17 17
16 18
11 19
14 20
11 12 13 14 15 16 17 18 19 20
0
2
4
6
8
10
12
14
16
18
f(x) = 1.17575757575758 x + 4.53333333333333
R² = 0.655451062347614
=CORREL(A2:A11,B2:B11)

9. Assignment
• Write steps to fitting of linear and nonlinear
regression line in excel
• Fit regression line using excel on any kind of data
• Calculate correlation coefficient on excel

10. Thank You