Hello !

A mathematical model is a function that establishes a relationship between a dependent variable Y and one or more independent variables X [Y = f (X1, X2, ..., Xn)]. Most of the models (in their integrated form) used in Forest Biometrics derived from first-order Differential Equations (differential form of the model) that express the primary relationship between the variables. An equation is the result of fitting a mathematical model with a database. In other words, an equation is a model with its estimated parameters. From a regression model (example: Schumacher) we can obtain several equations resulting from its adjustment to different databases.

Regards!

model and equation mean the same and can be use to replace another while simply mean the elements that make up a model or set.

An equation is a mathematical expression that can be transformed into an equality to zero and that involves one or several variables so that, depending on the values they take, the equality can be true or false.

A function is a way of relating the elements of a set (say A) with those of another set (say B) that fulfills the condition of assigning to each element of A only one of B.

A model is an expression that allows predicting the values that one (or several) dependent variables should take corresponding to the values of one or more variables, called independent. The terms dependent and independent may change, according to the discipline that uses the models. There are two main kinds of models: deterministics and non deterministic, which involve an error term.

Broadly speaking:

Function: You throw things into a function, F, scaling them to make numbers and get a number out, say N. For example, if thing 1 is a pound you divide by say a fixed 1 pound to produce a number. If thing 2 is a volt you divide by say a fixed 23 volts to produce a number. So:

F (thing1/scale1, thing2/scale2, . . ., thingn/scalen) = N.

Where each of the scaling factors, scale i, is fixed. Here, starting with things, we generate a function which is a relationship in this case between sets of numbers.

An equation just means two things are equal. For a number "q," If F=q, we can try to find the values of the things, if any, that make the function equal to q. This is called solving the equation.

A model is used to generate a relationship between things and so used to produce a function.

Hello !

A mathematical model is a function that establishes a relationship between a dependent variable Y and one or more independent variables X [Y = f (X1, X2, ..., Xn)]. Most of the models (in their integrated form) used in Forest Biometrics derived from first-order Differential Equations (differential form of the model) that express the primary relationship between the variables. An equation is the result of fitting a mathematical model with a database. In other words, an equation is a model with its estimated parameters. From a regression model (example: Schumacher) we can obtain several equations resulting from its adjustment to different databases.

Regards!