Dependent variable, defined

Measure of reaction time Half-life of a reaction The 100(1 — a/2)% point of the t distribution with v degrees of freedom Transformed dependent variable defined by Eq. (125) Variance of the parameter estimate b,... 

Turbulence is a 3D phenomenon, thus it is expected that turbulence in one dimension might be accompanied by similar effects in the other two directions. In addition, as mentioned above, the turbulent motions frequently cause variations in the other quantities too. Hence, all the dependent variables defining the system can be partitioned into mean and turbulent parts. 

Performance parameters reflect the outcome of a given step and indicate that the process gave the desired result [14] or quality attribute. They are uncontrolled performance variables [15] without a control action [35]. Their natural variation is defined by operating history specifically, their variability is characterized from known historical data or estimated based on similar process performance [35]. Similarly, output variables reflect the step outcome and indicate performance was acceptable in terms of performance attributes for the step (e.g., titer and yield) or properties of the product stream (e.g., product homogeneity, purity, contaminant levels, and chromatography peak shape) [3,14]. Still another term used is critical Ys (analogous to dependent variables), defined as product and process output variables that relate to critical quality attributes (CQAs), which are measurable outputs of each process step that are used to provide evidence that the step performed correctly [37]. 

We are now ready to perform an order-of-magnitude analysis on the fluid phase energy equation of (6.14.8). We introduce order-of-one independent and dependent variables defined below ... 

Kovacs (2), however, chose to rearrange equation (4) considering x(6) to be a dependent variable defined as T eff the effective retardation time, which could be measured by analyzing simple approach response (response to a single T jump starting with the system in equilibrium). Thus... 

If two variables are dependent, the value chosen in the simulation for the dependent variable can be linked to the randomly selected value of the first variable using the defined correlation. 

The usual practice in these appHcations is to concentrate on model development and computation rather than on statistical aspects. In general, nonlinear regression should be appHed only to problems in which there is a weU-defined, clear association between the independent and dependent variables. The generalization of statistics to the associated confidence intervals for nonlinear coefficients is not well developed. 

A function is a set of ordered elements such that no two ordered pairs have the same first element, denoted as (x,y) where x is the independent variable and y is the dependent variable. A function is established when a condition exists that determines y for each x, the condition usually being defined by an equation such as y = f(x) [2]. 

Conventional CA are defined by assigning to each of the N linearly connected sites, a time-dependent variable Oi t) (i=0,l,.,, N), belonging to a finite commutative ring TZk (usually represented by the integers modulo A , Zk). These site values, or colors, evolve iteratively according to a range-r mapping (j> ... 

Whenever one property is measured as a function of another, the question arises of which model should be chosen to relate the two. By far the most common model function is the linear one that is, the dependent variable y is defined as a linear combination containing two adjustable coefficients and X, the independent variable, namely. 

Model formulation. After the objective of modelling has been defined, a preliminary model is derived. At first, independent variables influencing the process performance (temperature, pressure, catalyst physical properties and activity, concentrations, impurities, type of solvent, etc.) must be identified based on the chemists knowledge about reactions involved and theories concerning organic and physical chemistry, mainly kinetics. Dependent variables (yields, selectivities, product properties) are defined. Although statistical models might be better from a physical point of view, in practice, deterministic models describe the vast majority of chemical processes sufficiently well. In principle model equations are derived based on the conservation law ... 

The Laplace transform of a time-dependent variable X(t) is denoted by Lap X t) or x(5) and is defined by means of the definite integral over the positive time domain ... 

The energy equation is solved in the form of a transport equation for static temperature. The temperature equation is obtained from the enthalpy equation, by taking the temperature as a dependent variable. The enthalpy equation is defined as,... 

However, if you extend this notion to an extreme and make 100,000 production runs of one unit each (actually one unit every 315 seconds), the decision obviously is impractical, since the cost of producing 100,000 units, one unit at a time, will be exorbitant. It therefore appears that the desired operating procedure lies somewhere in between the two extremes. To arrive at some quantitative answer to this problem, first define the three operating variables that appear to be important number of units of each run (D), the number of runs per year (n), and the total number of units produced per year (Q). Then you must obtain details about the costs of operations. In so doing, a cost (objective) function and a mathematical model will be developed, as discussed later on. After obtaining a cost model, any constraints on the variables are identified, which allows selection of independent and dependent variables. 

Define the objective function, the independent and the dependent variables, and the constraints first. Then set this problem up, and list all of the steps to solve it. You... 

The derivative of the function f(x) with respect to the dependent variable x is the scalar number defined as... 

One can assume that the dependent variables Y are defined relative to the variables X by at least n independent equations. Upon pre-multiplication by B 1 and post-multiplication by the (Z T)- this equation becomes... 

Independent variables P-value Power Also known as predictors or explanatory variables Another name for significance level usually 0.005 The effect of the experimental conditions on the dependent variable relative to sampling fluctuation. When the effect is maximized, the experiment is more powerful. Power can also he defined as the probability that there will not be a Type II error (1-/1). Conventionally, power should be at least 0.07... 

A nonintrinsic parameter is one that is introduced into a model for the purpose of allowing the specification of a preferred model from a larger group of rival models. To be useful, such a parameter must simplify the analysis procedures, allow a broadening of the data base of the analysis, or both. One type of nonintrinsic parameter useful in this regard enters as a multiplier of each of a series of predicted responses (C3, C4). For two models, such a method reduces (W4, W5) to defining a dependent variable... 

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