By observing the fitting of different variable curves related to the process, it can
be deduced if such variable plays, or not, a crucial role in the regulation of the
studied process.
2.3.2.2 Multiple Linear Regression
In many cases, y will depend on several independent variables such as
x 1 ; x 2 ; x 3 ; . . .; x n . This case can be treated by the multiple linear regression (MLR)
method.
For example, Sousa et al. (2010) used MLR to model the pollen and fungal
spores, considering nonbiological pollutant concentrations, the daily mean of
ozone (O 3 ) and PM 10 concentrations and meteorological parameters temperature
(T), relative humidity (RH), precipitation (PP), and wind velocity (WV) as
predictors. As results the models for each pollen and fungal spore were different
depending on the analyzed period, which means that the correlations identified as
statistically significant cannot be, even so, consistent enough.
2.3.2.3 Nonlinear Regression
In many applications, the regression functions will depend in a nonlinear way on
the regression coefficients.
Nonlinear regression models are important tools as many crop and soil processes are better represented by nonlinear than by linear models, depending on the
objective and the application domain, different priorities are set when fitting
nonlinear models and these include obtaining acceptable parameter estimates, and
a good model fit while meeting standard assumptions of statistical models.
A nonlinear regression model was used for Aufhammeret et al. (2006), in order to
model the role of brown clouds using a panel of yields and weather outcomes in India.
2.3.2.4 Logistic Type
There are indeed many phenomena in nature exhibiting a fast (virtually exponential) initial growth that then slow down after a certain point (where the curve
reaches an inflection point) until a point of equilibrium or saturation of the system
(carrying capacity). The logistic curve was introduced by Verhulst in the nineteenth century. The objective of Verhulst was to study population growth. In the
1920s, the interest in such method revived because of its excellence for modeling
the development and evolution of many other growth phenomena (Román-Román
and Torres Ruiz 2012). This type of models has been used in Ecology, Demography, and in Biology and Medicine, for the analysis of the growth of bacteria,
tumors, and several species of animals and plants.
2 Mathematical Modeling of Biosystems
59
be deduced if such variable plays, or not, a crucial role in the regulation of the
studied process.
2.3.2.2 Multiple Linear Regression
In many cases, y will depend on several independent variables such as
x 1 ; x 2 ; x 3 ; . . .; x n . This case can be treated by the multiple linear regression (MLR)
method.
For example, Sousa et al. (2010) used MLR to model the pollen and fungal
spores, considering nonbiological pollutant concentrations, the daily mean of
ozone (O 3 ) and PM 10 concentrations and meteorological parameters temperature
(T), relative humidity (RH), precipitation (PP), and wind velocity (WV) as
predictors. As results the models for each pollen and fungal spore were different
depending on the analyzed period, which means that the correlations identified as
statistically significant cannot be, even so, consistent enough.
2.3.2.3 Nonlinear Regression
In many applications, the regression functions will depend in a nonlinear way on
the regression coefficients.
Nonlinear regression models are important tools as many crop and soil processes are better represented by nonlinear than by linear models, depending on the
objective and the application domain, different priorities are set when fitting
nonlinear models and these include obtaining acceptable parameter estimates, and
a good model fit while meeting standard assumptions of statistical models.
A nonlinear regression model was used for Aufhammeret et al. (2006), in order to
model the role of brown clouds using a panel of yields and weather outcomes in India.
2.3.2.4 Logistic Type
There are indeed many phenomena in nature exhibiting a fast (virtually exponential) initial growth that then slow down after a certain point (where the curve
reaches an inflection point) until a point of equilibrium or saturation of the system
(carrying capacity). The logistic curve was introduced by Verhulst in the nineteenth century. The objective of Verhulst was to study population growth. In the
1920s, the interest in such method revived because of its excellence for modeling
the development and evolution of many other growth phenomena (Román-Román
and Torres Ruiz 2012). This type of models has been used in Ecology, Demography, and in Biology and Medicine, for the analysis of the growth of bacteria,
tumors, and several species of animals and plants.
2 Mathematical Modeling of Biosystems
59