Nonlinear regression comes under the statistics part in the mathematics. It is form of regression that means the data which we observed are converted into a model by functions. The parameter used for modeling also are non linear. The parameters depend upon one or more variables and variables are independent. The data are substitute in the model by using a method known as successive approximation.
Now we do nonlinear regression analysis mathematically. The data used for modeling are error free. Suppose we have independent variable denoted as (x) and dependent variable(y) and all dependent variables are random variable then it is expressed as non linear function ƒ(x, ß). Some systematic error may be present but it reduces before the modeling. If independent variables are with error then it is known as error in variable model.
For modeling of non linear regression we can use a formula [v=Vm(s)/Km+(s)], this formula is given by Michaelis-Menten. This is also expressed as ƒ(x, ß)=ß1x/ß2+x, where ß1 is the parameter of (Vm), ß2 is the parameter of (Km) and (s) is independent variable of x. this function is said to be non linear because it can not be in the form of linear combination of ßs. The functions in non linear regression analysis may be exponential, logarithmic, Gaussian, trigonometric, power and Lorenz functions.
Nonlinear regression may be non parametric regression, semi parametric regression and non linear least square regression. Here we discuss about least square regression for non linear function. It is extended form of linear least square regression. We extend because using for larger and general form of functions. Concept wise very much similarity in both forms. Any function that is in closed form can be non linear regression model but there are several limitations in linear regression. Some advantages of least square forms, first availability of wide range of functions that can be modeled. Second efficient use of data. Third is it shares good combination with linear least square form. Fourth is answers are accurately and scientific. Some disadvantage also such as iterative procedure is very complicated. The presence of other data can affect the total result.
Looking out for more help on statistics watch out for my upcoming posts.
The process of fitting Non Linear Regression R is similar to that of fitting linear models expect that there is no formula for estimation, so we have to use iterative procedure that may also require supply initial estimates of parameter. You should know the biological interpretation of the parameter to provide intelligent initial value.
Now we do nonlinear regression analysis mathematically. The data used for modeling are error free. Suppose we have independent variable denoted as (x) and dependent variable(y) and all dependent variables are random variable then it is expressed as non linear function ƒ(x, ß). Some systematic error may be present but it reduces before the modeling. If independent variables are with error then it is known as error in variable model.
For modeling of non linear regression we can use a formula [v=Vm(s)/Km+(s)], this formula is given by Michaelis-Menten. This is also expressed as ƒ(x, ß)=ß1x/ß2+x, where ß1 is the parameter of (Vm), ß2 is the parameter of (Km) and (s) is independent variable of x. this function is said to be non linear because it can not be in the form of linear combination of ßs. The functions in non linear regression analysis may be exponential, logarithmic, Gaussian, trigonometric, power and Lorenz functions.
Nonlinear regression may be non parametric regression, semi parametric regression and non linear least square regression. Here we discuss about least square regression for non linear function. It is extended form of linear least square regression. We extend because using for larger and general form of functions. Concept wise very much similarity in both forms. Any function that is in closed form can be non linear regression model but there are several limitations in linear regression. Some advantages of least square forms, first availability of wide range of functions that can be modeled. Second efficient use of data. Third is it shares good combination with linear least square form. Fourth is answers are accurately and scientific. Some disadvantage also such as iterative procedure is very complicated. The presence of other data can affect the total result.
Looking out for more help on statistics watch out for my upcoming posts.
The process of fitting Non Linear Regression R is similar to that of fitting linear models expect that there is no formula for estimation, so we have to use iterative procedure that may also require supply initial estimates of parameter. You should know the biological interpretation of the parameter to provide intelligent initial value.
