Independent variables

Variable, independent An experimental factor that can be controlled (temperature, pressure, order of test, etc.) or independently measured (hours of sunshine, specimen thickness, etc.). Independent variables may be qualitative (such as a qualitative difference in operating technique) or quantitative (such as temperature, pressure, or duration). Thus, if variable A is a function of variable B, than B is the independent variable. 

Such a string may be useful when two types of variables independently affect the quality of a solution. Suppose that an analytical laboratory monitors the air quality at a downtown site, measuring the level of fifteen different pollutants. A theoretical model is established that links the amount of these pollutants measured at the monitoring point with the amounts of each pollutant released at twenty different sites around the city. Because there are fifteen pollutants and twenty pollution sources, a 15 x 20 matrix is required to model the problem and GA strings can be constructed in this form. 

Prove that the following are undecidable for 2-variable independent variable schemes P- and P2 ... 

Dependent (basic) variables Independent (nonbasic) variables Constants... 

In optimization using a process simulator to represent the model of the process, the degrees of freedom are the number of decision variables (independent variables) whose values are to be determined by the optimization, hence the results of an optimization yield a fully determined set of variables, both independent and dependent. Chapter 2 discussed the concept of the degrees of freedom. Example 15.1 demonstrates the identification of the degrees of freedom in a small process. 

Notably, in logistic regression-like other multivariate analyses-the effects of causal variables can be shown to influence probabilities of outcomes in response variables independently of one another. The likelihood of using a lawn care company is significantly higher for women than men, for example, no matter the income or education of individuals. 

To make data more readily understandable, the use of transform ations is sometimes advisable. Transformation involves changing the scale of the variables (independent, dependent, or both), to accomplish one or more of the following purposes ... 

Since the chemical potential is an intensive variable, independent of the absolute number of ions present, it can be determined at one point in a system and will be valid for all phases present. This is very useful for geologists in that one need not determine the size of the system for a measurement. However, it is essential to know over what area or distance the chemical potential of an element is constant. The scale of the system must be known in order to use this measurement in an estimate of phase equilibrium. 

Reactor design is often discussed in terms of independent and dependent variables. Independent variables are choices such as reactor type and internals, catalyst type, inlet temperature, pressure, and fresH feed composition. Dependent variables result from independent variable selection. They may be constrained or unconstrained. Con-... 

In the present work we will deal with all the above problems and provide a unified framework to deal with the error correction for static or dynamic systems using multicomponent mass and energy balances. The topological character of the complex process is exploited for an easy classification of the measured and unmeasured variable independently of the linearity or nonlinearity of the balance equations. 

We then calculate the Sums of Squares of y explained by the two independent variables independently of each other. These are... 

Data set variables can be distinguished by their role in the models as independent and dependent variables. Independent variables (or explanatory variables, predictor variables) are those variables assumed to be capable of taking part in a function suitable to model the response variable. Dependent variables (or response variables) are variables (often obtained from experimental measurements) for which the interest is to find a statistical dependence on one or more independent variables. Independent variables constitute the data matrix X, while dependent variables are collected into a matrix Y with n rows and r columns (r = 1 when only one response variable is defined) (Figure D-2). 

PPP eigenvalues eigenvalue-based descriptors PPP pairs - substructure descriptors PPP triangles substructure descriptors predictor variables independent variables -> data set prime ID number ID numbers... 

The first step is to draw a schematic diagram of the battery with a clear definition of the desired predicted variables (dependent variables) and the provided variables (independent variables). As mentioned before, a battery is a combination of several electrochemical cells connected in series or in parallel depending on the desired voltage and capacity, which increases the complexity of the model. 

The above derivation can be generalized to a system of N particles, noting that the variation must be effected for each variable independently. Hence, in terms of L the equations of motion are ... 

We suppose the random force to be Gaussian, and a linear operator does not change this property. Thus the velocity v t) is Gaussian as well if the initial condition t)(0) is a random Gaussian variable independent of the random force. The mean value of the velocity reads... 

Independent variables Dependent variables Independent variables... 

Because there are two equations and six variables, it is possible to specify four external variables independently. For example, these might be product rate and product, feed, and tails compositions. In such a case the other two variables would be given by... 

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