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A free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not a parameter of this or any container expression. The idea is related to a placeholder (a symbol that will later be replaced by some value), or a wildcard character that stands for an unspecified symbol. In computer ...
A free parameter is a variable in a mathematical model which cannot be predicted precisely or constrained by the model [1] and must be estimated [2] experimentally or theoretically. A mathematical model, theory, or conjecture is more likely to be right and less likely to be the product of wishful thinking if it relies on few free parameters and ...
The formal parameter variable is said to bind the variable name wherever it occurs free in the body. Variable (names) that have already been matched to formal parameter variable are said to be bound. All other variables in the expression are called free. For example, in the following expression y is a bound variable and x is free: . . Also note ...
(with free variables x, y, and bound variable z) defining the notion of "aunt" in terms of "parent" and "sister". Another, more formal example, which defines the property of being a prime number, is "P(x) if ∀m,n∈: m>1 ∧ n>1 → x≠ m⋅n", (with free variable x and bound variables m,n). An example of a closed formula with truth value ...
The set of free variables of is the union of the set of free variables of and the set of free variables of . For example, the lambda term representing the identity λ x . x {\displaystyle \lambda x.x} has no free variables, but the function λ x . y {\displaystyle \lambda x.y} x {\displaystyle x} has a single free variable, y {\displaystyle y} .
A variable is considered dependent if it depends on an independent variable. Dependent variables are studied under the supposition or demand that they depend, by some law or rule (e.g., by a mathematical function), on the values of other variables. Independent variables, in turn, are not seen as depending on any other variable in the scope of ...
Again, each endogenous variable depends on potentially each exogenous variable. Without restrictions on the A and B, the coefficients of A and B cannot be identified from data on y and z: each row of the structural model is just a linear relation between y and z with unknown coefficients. (This is again the parameter identification problem.)
For example, with seven variables and four lags, each matrix of coefficients for a given lag length is 7 by 7, and the vector of constants has 7 elements, so a total of 49×4 + 7 = 203 parameters are estimated, substantially lowering the degrees of freedom of the regression (the number of data points minus the number of parameters to be ...