Given that the bulk of family chores fell to women, and that they were five times more likely than men to head a single-parent family, the shortcomings of Finland's child day-care system affected women more than it did men.

Given the shortcomings of the beneficial acclimation hypothesis, researchers are continuing to search for a theory that will be supported by empirical data.

Given these shortcomings, those modern weapons that were available were allocated to the British Army, and the Home Guard was forced to supplement the meagre amount of outdated weapons and ammunition they had with ad hoc weapons.

* Given any Banach space X, the continuous linear operators A: X → X form a unitary associative algebra ( using composition of operators as multiplication ); this is a Banach algebra.

Given any expression involving complex numbers, bras, kets, inner products, outer products, and / or linear operators ( but not addition ), written in bra-ket notation, the parenthetical groupings do not matter ( i. e., the associative property holds ).

* Given any combination of complex numbers, bras, kets, inner products, outer products, and / or linear operators, written in bra-ket notation, its Hermitian conjugate can be computed by reversing the order of the components, and taking the Hermitian conjugate of each.

Given points P < sub > 0 </ sub > and P < sub > 1 </ sub >, a linear Bézier curve is simply a straight line between those two points.

Given a function f ∈ I < sub > x </ sub > ( a smooth function vanishing at x ) we can form the linear functional df < sub > x </ sub > as above.

Given any vector space V over a field F, the dual space V * is defined as the set of all linear maps ( linear functionals ).

Given a field K, the corresponding general linear groupoid GL < sub >*</ sub >( K ) consists of all invertible matrices whose entries range over K. Matrix multiplication interprets composition.

Given a basis of a vector space, every element of the vector space can be expressed uniquely as a finite linear combination of basis vectors.

A Clifford algebra Cℓ ( V, Q ) is a unital associative algebra over K together with a linear map satisfying for all defined by the following universal property: Given any associative algebra A over K and any linear map such that

Given the particular differential operators involved, this is a linear partial differential equation.

Given this inherent distortion, it is not unusual for a television or video projector to truthfully claim a linear contrast ratio ( difference between darkest and brightest output levels ) of 1000: 1 or greater, equivalent to 10 bits of audio precision even though it may only accept signals with 8-bit precision and use an LCD panel that only represents 6 or 7 bits per channel.

Given a linear homogeneous recurrence relation with constant coefficients of order d, let p ( t ) be the characteristic polynomial ( also " auxiliary polynomial ")

Given the two red points, the blue line is the linear interpolant between the points, and the value y at x may be found by linear interpolation.

Given a densely defined linear operator A on H, its adjoint A * is defined as follows:

Given a pre-Hilbert space H, an orthonormal basis for H is an orthonormal set of vectors with the property that every vector in H can be written as an infinite linear combination of the vectors in the basis.

Given that a dichotomous criterion violates these assumptions of linear regression, conducting linear regression with a dichotomous criterion may lead to errors in inference and at the very least, interpretation of the outcome will not be straightforward.

Given that the logit varies from it provides an adequate criterion upon which to conduct linear regression and the logit is easily converted back into the odds.

Given two normed vector spaces V and W ( over the same base field, either the real numbers R or the complex numbers C ), a linear map A: V → W is continuous if and only if there exists a real number c such that

Given two normed vector spaces V and W, a linear isometry is a linear map f: V → W that preserves the norms:

Given this difference, it is necessary that logistic regression take the natural logarithm of the odds ( referred to as the logit or log-odds ) to create a continuous criterion.

Given that both analyses are guided by the same goal, why is it that logistic regression is needed for analyses with a dichotomous criterion?

Given that the logit is not intuitive, researchers are likely to focus on a predictor's effect on the exponential function of the regression coefficient-the odds ratio ( see definition ).

Given that some common statistical packages ( e. g., SAS, SPSS ) do not provide likelihood ratio test statistics, it can be more difficult to assess the contribution of individual predictors in the multiple logistic regression case.

Fallacious evaluation: " Given that the counterattacks against Germany occurred only after they had conquered the greatest amount of territory under their control, regression to the mean can explain the retreat of German forces from occupied territories as a purely random fluctuation that would have happened without any intervention on the part of the USSR or the Western Allies.

Given a random sample from the population, we estimate the population parameters and obtain the sample linear regression model:

Given the form of the regression equation, we can interpret the coefficients as elasticities.

Given a model of some atomic positions, these positions and their respective Debye-Waller factors ( or B-factors, accounting for the thermal motion of the atom ) can be refined to fit the observed diffraction data, ideally yielding a better set of phases.

Given a set of training examples, each marked as belonging to one of two categories, an SVM training algorithm builds a model that assigns new examples into one category or the other.

Given the go-ahead, Marston developed Wonder Woman, basing her character on both Elizabeth and Olive Byrne, to be the model of an conventional, liberated, powerful modern woman.

Given local and transient influences on surface height, the values defined below are based on a " general purpose " model, refined as globally precisely as possible within 5 m of reference ellipsoid height, and to within 100 m of mean sea level ( neglecting geoid height ).

Given the ACE model, researchers can determine what proportion of variance in a trait is heritable, versus the proportions which are due to shared environment or unshared environment.

Given the limited spectrum a wholesale model as noted by the EU Commission reference 2 in such situation is chosen.

Given that deviance is a measure of the difference between a given model and the saturated model, smaller values indicate better fit.

Given a set of training examples, each marked as belonging to one of two categories, an SVM training algorithm builds a model that predicts whether a new example falls into one category or the other.

Given a model of a system, exhaustively and automatically check whether this model meets a given specification.

Given a model M of a Skolem theory T, the smallest substructure containing a certain set A is called the Skolem hull of A.

Given a probability space, consider a single-period binomial model.

Given a set of data and the desire to produce some kind of “ model ” of those data ( model, in this case, meaning a function fitted through the data ), there are a variety of functions that can be chosen for the fit.

Given such a model, the sentence

However, the modelling study also states that " Given the complex, three-dimensional nature of the real Pine Island glacier ... it should be clear that the [...] model is a very crude representation of reality.

:" Given that the structure of an econometric model consists of optimal decision rules of economic agents, and that optimal decision rules vary systematically with changes in the structure of series relevant to the decision maker, it follows that any change in policy will systematically alter the structure of econometric models.

Given the assumptions of the model ( for example, that the profits are reinvested and that capital accumulation does not substitute for skilled labor in production ), the process becomes self-sustaining and leads to modernization and economic development.

Given the model and realizations ( samples ) of the random vector, the task is to estimate both the mixing matrix and the sources.

Given a set of candidate models for the data, the preferred model is the one with the minimum AIC value.

Given a time series of data X < sub > t </ sub >, the ARMA model is a tool for understanding and, perhaps, predicting future values in this series.

Given a good model, it is best to make as many observations as practicable, depending of the expected reliability of prior knowledge, cost of observations, time and resources available, and accuracy required.

Given a model selection problem in which we have to choose between two models, on the basis of observed data D, the plausibility of the two different models M < sub > 1 </ sub > and M < sub > 2 </ sub >, parametrised by model parameter vectors and is assessed by the Bayes factor K given by