* If it is required to use a single number X as an estimate for the value of numbers, then the arithmetic mean does this best, in the sense of minimizing the sum of squares ( x < sub > i </ sub > − X )< sup > 2 </ sup > of the residuals.

If the pressure from particles within the magnetosphere is neglected, it is possible to estimate the distance to the part of the magnetosphere that faces the Sun.

If this link is proven causal, researchers estimate that NSAIDs would be responsible for up to 20 percent of hospital admissions for congestive heart failure.

If they both used the Attic stadion of about 185 meters, then the older estimate is 1 / 6 too large, and Ptolemy's value is 1 / 6 too small, a difference explained as due to ancient scientists ' use of simple methods of measuring the earth, which were corrupted either high or low by a factor of 5 / 6, due to air's bending of horizontal light rays by 1 / 6 of the Earth's curvature.

If it is assumed that the calculation occurs near room temperature (~ 300 K ) the Von Neumann-Landauer Limit can be applied to estimate the energy required as ~ 10 < sup > 18 </ sup > joules, which is equivalent to consuming 30 gigawatts of power for one year.

If analytical expressions are impossible to obtain either the partial derivatives must be calculated by numerical approximation or an estimate must be made of the Jacobian.

understood, it is not known precisely how long it will take white dwarfs to cool to blackness .< sup >, § IIIE, IVA .</ sup > Barrow and Tipler estimate that it would take 10 < sup > 15 </ sup > years for a white dwarf to cool to 5 K ; however, if weakly interacting massive particles exist, it is possible that interactions with these particles will keep some white dwarfs much warmer than this for approximately 10 < sup > 25 </ sup > years .< sup >, § IIIE .</ sup > If protons are not stable, white dwarfs will also be kept warm by energy released from proton decay.

If a given class and feature value never occur together in the training set then the frequency-based probability estimate will be zero.

If an accurate estimate of the field at some other place and time is needed, the measurements must be converted to a model and the model used to make predictions.

If General Greene's estimate of the total American loss was accurate, then they had between 1, 160 and 1, 260 killed, wounded or deserted during the battle.

If each command object has a < tt > getEstimatedDuration ()</ tt > method, the program can easily estimate the total duration.

If the signal being analyzed can be considered a stationary process, the STFT is a good smoothed estimate of its power spectral density.

If the quality of cars is not observable by the buyers, then it seems reasonable for them to estimate the quality of a car offered to market using the average quality of all cars.

If the risk estimate takes into account information on the number of individuals exposed, it is termed a " population risk " and is in units of expected increased cases per a time period.

If the risk estimate does not take into account the number of individuals exposed, it is termed an " individual risk " and is in units of incidence rate per a time period.

If one took a uniform prior, then the maximum likelihood estimate for the population probability is the observed probability, and one may compute a credible region around this or another estimate.

If the upper limit of the falls is accepted as described above, the expedition photographs may be used to estimate the height of the falls.

If we additionally assume that the image plane is perpendicular to the ground plane ( an imaginary plane Tangential to the surface of the Earth ), and that the waterfall flows on a plane that is parallel to the image plane, we can estimate the height by measuring the vertical separation of waterfall head and base in

If we assume that a noisy signal or image is noiseless when we try to make a statistical estimate of g, our estimate will be incorrect.

If there are n data points to estimate parameters of both models from, then one can calculate the F statistic ( coefficient of determination ), given by

If T is a statistic that is approximately normally distributed under the null hypothesis, the next step in performing a Z-test is to estimate the expected value θ of T under the null hypothesis, and then obtain an estimate s of the standard deviation of T. We then calculate the standard score Z = ( T − θ ) / s, from which one-tailed and two-tailed p-values can be calculated as Φ (−| Z |) and 2Φ (−| Z |), respectively, where Φ is the standard normal cumulative distribution function.

If you were a man '' --

If she, Pamela, were being held responsible for his crimes, then hers must be the final act of expiation.

If someone were to drop a match in here, this place would go up like a haystack ''.

If the other pilots were worried, they did not show it.

If it were the enemy, tactically his position was correct.

If it were not for an old professor who made me read the classics I would have been stymied on what to do, and now I understand why they are classics ; ;

If it were not that I knew who it was I could have mistaken it for my Aunt so well did her clothes fit him.

If an automobile were approaching him, he would know what was required of him, even though he might not be able to act quickly enough.

If there were only darkness, all would be clear.

If there were only the mess, all would be clear ; ;

If these people were denied a voice ( do they have a moral right to a voice??

If we were creating a wholly new society, we could insist that our social, political, economic and philosophic institutions foster rather than hamper man ; ;

If living Jews were unavailable for study, the Bible was at hand.

If his scholarship and formal musicianship were not all they might have been, Mercer demonstrated at an early age that he was gifted with a remarkable ear for rhythm and dialect.

If she were not at home, Mama would see to it that a fresh white rose was there.

If the Stearns were not there, grace would be omitted.

If anything, the conservative Democrats were more opposed to Hearst than the Republicans.

If the hardships of the winter at Valley Forge were trying for healthy men, they were, of course, much more so for those not in good health.

If his circumspection in regard to Philip's sensibilities went so far that he even refused to grant a dispensation for the marriage of Amadee's daughter, Agnes, to the son of the dauphin of Vienne -- a truly peacemaking move according to thirteenth-century ideas, for Savoy and Dauphine were as usual fighting on opposite sides -- for fear that he might seem to be favoring the anti-French coalition, he would certainly never take the far more drastic step of ordering the return of Gascony to Edward, even though, as he admitted to the English ambassadors, he had been advised that the original cession was invalid.

If there were no West Berlin problem, imperialist quarters would have invented an excuse for stepping up the armaments race to try to solve the internal and external problems besetting the United States and its NATO partners.

If the new Soviet series has followed the general pattern of previous Russian tests, the shots were roughly half fission and half fusion, meaning a fission yield of 30 to 40 megatons thus far.

If the Hessian troops sent here willy-nilly by the Hessian Government to fight for England in the 1770's were mercenaries, what shall we call the UN troops sent to the Congo willy-nilly by their governments to fight for the United Nations??

If the UN troops are not mercenaries then the Hessians were not mercenaries either.

If he were to go with White, he would be out there two days, not just listening in the dark at some point between here and Papa-san, but moving ever deeper into enemy land -- behind Papa-san -- itself.