The linear regression line is the expected value of the criterion given the predictor ( s ) and is equal to the intercept ( the value of the criterion when the predictor ( s ) are equal to zero ) plus the product of the regression coefficient and some given value of the predictor plus some error term-this implies that it is possible for the expected value of the criterion given the value of the predictor to take on any value as the predictor ( s ) ranges from ; however, this is not the case with a dichotomous criterion.

The homogeneity of slopes assumption implies that we perform this regression analysis subject to the constraint that all regression equations ( slopes ) across the cells of the design are the same.

A constant growth factor implies exponential growth in the above variables, so differentiating gives a linear relationship between the growth factors which can be deduced in a simple regression.

This result implies that all these secondary regressions are unnecessary: using projection matrices to make the variables orthogonal to each other will lead to the same results as running the regression with all non-orthogonal included.

A low coefficient implies that changes in price have little influence on demand.

Since p is prime, for all n = 1, ..., p − 1 the binomial coefficient is divisible by p, which implies that

Least cost location then implies marketing the product at the least cost to the consumer, much like retailers attempt to obtain large market shares today.

Faulkner's is not the mind of the apologist which Mr. O'Donnell implies that it is.

Such, he implies, is the case with his friend, who is not really a new convert himself but merely a favorer of new converts.

This, no doubt, is part of what Gilbert Seldes implies when he says of the arts, `` They give form and meaning to life which might otherwise seem shapeless and without sense ''.

A randomization of `` ups '' and `` downs '' is more likely than ordered `` ups '' and `` downs '' in position ( 3 ) since the hydrogen atoms are well separated and so the position of one could hardly affect the position of another, and also since ordered `` up '' and `` down '' implies a larger unit cell, for which no evidence exists.

Since C is rational, this correspondence has K coincidences, each of which implies a line of the pencil which meets its image.

In I knew you when you were a child, and you were pretty then dominant stress on then implies that the young woman spoken to is still pretty.

The very idea of there being `` count rules '' implies that there is some sort of proportion to be expected between the amount of congestive activity and the extent of the breakaway ( run up or run down ) movement.

In contrast to this Stoic-patristic view, Utopia implies that the nature of man is such that to rely on individual conscience to supply the deficiencies of municipal law is to embark on the bottomless sea of human sinfulness in a sieve.

The respectability which money confers implies a different etiquette, and, upon taking up the life of a London gentleman, Pip must learn from Herbert Pocket that `` the spoon is not generally used over-hand, but under ''.

The general tone of articles appearing in such important newspapers as the Manchester Guardian and the Sunday Observer implies a kindly recognition that the Catholic Church is now at least of equal stature in England with the Protestant churches.

For a randomized experiment, the assumption of unit-treatment additivity implies that the variance is constant for all treatments.

The statement of the axiom of choice does not specify whether the collection of nonempty sets is finite or infinite, and thus implies that every finite collection of nonempty sets has a choice function.

For example, while the axiom of choice implies that there is a well-ordering of the real numbers, there are models of set theory with the axiom of choice in which no well-ordering of the reals is definable.

Another argument against the axiom of choice is that it implies the existence of counterintuitive objects.

The much stronger axiom of determinacy, or AD, implies that every set of reals is Lebesgue measurable, has the property of Baire, and has the perfect set property ( all three of these results are refuted by AC itself ).

This is to avoid the notion that a writing system that represents sounds must be either a syllabary or an alphabet, which implies that a system like Aramaic must be either a syllabary ( as argued by Gelb ) or an incomplete or deficient alphabet ( as most other writers have said ); rather, it is a different type.

" Christie strongly implies that this " quiet retreat in the Ardennes " near Spa is the Poirot family home.

it was noted by Bohr that the existence of any sort of wave packet implies uncertainty in the wave frequency and wavelength, since a spread of frequencies is needed to create the packet itself.

In states where a quantum mechanical particle is bound, it must be localized as a wave packet, and the existence of the packet and its minimum size implies a spread and minimal value in particle wavelength, and thus also momentum and energy.

Although the Greek word " techně " is often mistranslated as " art ," it actually implies mastery of any sort of craft.

This implies that, as a general rule, the " operator " of a truly pluralistic framework, i. e. the state in a pluralistic society, must not be biased: it may not take sides with any one group, give undue privileges to one group and discriminate against another one.

This implies that the MESFET gate should, in transistor mode, be biased such that one does not have a forward conducting metal semiconductor diode instead of a reversed biased depletion zone controlling the underlying channel.

Ceratosaurus fossils are noticeably less common than those of Allosaurus, but whether this implies Ceratosaurus being rarer is uncertain ( animals with certain lifestyles are more biased toward fossilization than others ).

In constructive set theory, however, Diaconescu's theorem shows that the axiom of choice implies the law of the excluded middle ( unlike in Martin-Löf type theory, where it does not ).

Atchison was sworn in for his new term as President pro tempore minutes before both Fillmore and Taylor, which might theoretically make him Acting President for at least that length of time ; however, this also implies that many times when the Vice President is sworn in before the President, the Vice President is the de facto Acting President.

But the report expressed concerns that the Roman Catholic dogmatic definitions of these concepts implies them to be " revealed by God ", stating: " The question arises for Anglicans, however, as to whether these doctrines concerning Mary are revealed by God in a way which must be held by believers as a matter of faith.

There are exceptions within subjectivism however, such as ideal observer theory, which implies that moral facts may be known through a rational process, and individualist ethical subjectivism, which holds that moral facts are merely personal opinions and so may be known only through introspection.

It is true, however, that condition 1 implies condition 2 in the context of all spaces.

This, however, implies the acceptation of a concept of media as power, which is widely but not generally shared.

For example, Joyce's phrase " they were yung and easily freudened " clearly implies the more conventional " they were young and easily frightened ", however the former also makes an apt pun on the names of two famous psychoanalysts, Jung and Freud.

Entropy, however, implies heat and therefore temperature.

Its genus, Trichocephalus, was recorded as a more accurate name, however the generic name trichuris, which means “ hair tail ” ( which implies that the posterior end of the worm is the attenuated section ), remains the dominant name form used today.

Antigone, however, implies that Eteocles and Polynices had been given shared rule following Oedipus ' excommunication, that Eteocles had taken control, and that only afterwards did Creon rule.

As of the 2010 census, the population was 920, 581 ; however, Atlanta mayor Kasim Reed suspects significant undercounting in the City of Atlanta, which implies similar concerns for Fulton County as a whole – the 2009 estimate of the county's population was 1, 020, 014, 10. 8 % higher than the 2010 census results.

In the earlier work of Marx, however, the idea of creative destruction or annihilation ( German: Vernichtung ) implies not only that capitalism destroys and reconfigures previous economic orders, but also that it must ceaselessly devalue existing wealth ( whether through war, dereliction, or regular and periodic economic crises ) in order to clear the ground for the creation of new wealth.

" It is unclear, however, whether this implies a re-establishment of the literal forms of hunter-gatherer societies or a broader kind of learning from their ways of life in order to construct non-alienated relations.

The French term bourgeois ' origins are that of ' middle class ' however Marxist usage implies bankers or merchants.

This is sometimes known as reconstruction archaeology or reconstructional archaeology ; however, reconstruction implies an exact replica of the past, when it is in fact just a construction of one person's idea of the past ; the more archaeologically correct term is a working construction of the past.

If that player intends to become declarer, however, he has to make a call of at least “ 18 ” ( picking up the Skat in that situation implies the call ).

The manufacture of pottery typically implies some form of sedentary life due to the fact that pottery is highly breakable and thus generally useless to hunter-gatherers who are constantly on the move ; however this does not seem to have been the case with the first Jōmon people, who perhaps numbered some 20, 000 over the whole archipelago.

Islamic scholarship has not however gone through the same process for a variety of reasons: The doctrine of Tawhid implies that the cosmos is a unified harmonious whole, centered around the omnipotent and omnipresent God.

In the entry in the parish register he is described as a " stranger ," which, however, implies nothing more than that he belonged to another parish.

It is not known whether the Generalized Suslin Hypothesis is consistent with the Generalized Continuum Hypothesis ; however, since the combination implies the negation of the square principle at a singular strong limit cardinal — in fact, at all singular cardinals and all regular successor cardinals — it implies that the axiom of determinacy holds in L ( R ) and is believed to imply the existence of an inner model with a superstrong cardinal.

These intrigues did not however lead to a helot uprising ; Thucydides indeed implies that Pausanias was turned in by the helots ( I, 132, 5-... the evidence even of the helots themselves.

The term ‘ cross-cap ’, however, often implies that the surface has been deformed so that its boundary is an ordinary circle.

An odd permutation of the corners implies an odd permutation of the centres and vice versa ; however, even and odd permutations of the centres are indistinguishable due to the identical appearance of the pieces.