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Prediction
Published in Julian J. Faraway, Linear Models with Python, 2021
Extrapolation occurs when we try to predict the response for values of the predictor which lie outside the range of the original data. There are two different types of extrapolation — quantitative and qualitative. Quantitative extrapolation concerns x0 that are far from the original data. Prediction intervals become wider as we move further from the original data. For multivariate x0, the concept of distance from the original data is harder to define. In higher dimensions, most predictions will be substantial extrapolations. Let’s see what happens with a prediction for values at the 95th percentile of the data:
Statistics
Published in Dušan Teodorović, Miloš Nikolić, Quantitative Methods in Transportation, 2020
Dušan Teodorović, Miloš Nikolić
There are two major groups of quantitative forecasting techniques: (a) the extrapolation method (time series models); and (b) the explanatory method (regression models). Explanatory models (regression models) are very suitable approaches that allow us to look at various “what-if” scenarios. As we already explained in previous sections, when using the explanatory model, the value of a dependent variable (potential transportation demand, for example) is forecasted on the basis of known and quantifiable factors that induce the transportation demand (socio-economic characteristics and characteristics of the transportation system). By the extrapolation method, future transportation demand is forecasted on the basis of earlier characteristics of the demand over a period of time. The extrapolation method can be, above all, used to forecast the future values of a dependent variable under unchanged conditions.
Project Systems Scheduling
Published in Adedeji B. Badiru, Project Management, 2019
The use of time standards, on the other hand, may not reflect the changes occurring in the current operating environment due to new technology, work simplification, new personnel, and so on. The use of historical data and forecasting is very popular because estimates can be verified and validated by actual records. In the case of regression and forecasting, there is the danger of extrapolation beyond the data range used for fitting the regression and forecasting models. If the sample size in a historical data set is sufficient and the data can be assumed to reasonably represent prevailing operating conditions, the three PERT estimates can be computed as follows: a^=t¯−kRm^=t¯b^=t¯+kR
An Unbiased Estimation of Empirical Lognormal Fragility Functions with Uncertainties on the Ground Motion Intensity Measure
Published in Journal of Earthquake Engineering, 2020
Thomas Ader, Damian N. Grant, Matthew Free, Manuela Villani, Jorge Lopez, Robin Spence
The relationship between PGA and probability of damage, the fragility function, is often represented with a cumulative lognormal relationship. Although numerous alternative functional forms of fragility relationships have been proposed in the past [Rossetto, 2004; Lagomarsino and Giovinazzi, 2006; Cousins, 2014], the lognormal relationship is nowadays very widely adopted [Kircher et al., 1997; Kappos et al., 2006; Polidoro and Spence, 2015]. Its general S-shape reasonably fits the known development of damage probability as ground motion increases, and the ability to define the curve with no more than two parameters makes for a comparatively simple regression process. Given the wide uncertainty in the precise values of damage probability at any ground motion, no certainty in the form of the curve can be expected. It is worthwhile to note that, as with all forms of curve, extrapolation beyond the range of available data points is unwise.
An experimental study: laminar flame speed sensitivity from spherical flames in stoichiometric CH4–air mixtures
Published in Combustion Science and Technology, 2018
Travis Sikes, M. Sam Mannan, Eric L. Petersen
The raw-flame speed data, measured from the Z-type schlieren system, are in a stretched, burned state and must be processed to extrapolate it to an unstretched, burned state. In the literature, the linear extrapolation method (LM) has been used frequently. However, while LM can be accurate when the Lewis number is close to unity, nonlinear methods are much more capable of providing accurate flame speed measurements when the Lewis number deviates from unity (Chen, 2011; Clavin, 1985). One such nonlinear method, Eq. 1, first suggested by Markstein (1951) and later by Frankel and Sivashinsky (1983), attempts to account for nonlinear effects in the extrapolation. Equation 2, referred to herein as NM II, was first proposed by Kelley et al. (2009) and is based on the works of Ronney and Sivashinsky (1989) and Bechtold et al. (2005). A numerical study performed by Chen (2011) found that NM I is accurate when Le > 1, NM II is accurate when Le < 1, and both are sufficient near unity. Once is determined, it is multiplied by the burned-to-unburned density ratio, calculated using an equilibrium solver such as Chemkin or COSILAB, for the final unburned, unstretched flame speed,.
Resistance training intervention performed with different muscle action durations influences the maximal dynamic strength without promoting joint-angle specific strength gains
Published in Journal of Sports Sciences, 2021
Rodrigo César Ribeiro Diniz, Frank Douglas Tourino, Lucas Túlio de Lacerda, Hugo Cesar Martins Costa, Marcel Bahia Lanza, Gustavo Ferreira Pedrosa, Fernando Vitor Lima, Mauro Heleno Chagas
Despite the methodological precautions adopted, some limitations of the present study should be highlighted. Care should be taken in extrapolating the data due to the characteristics of the sample used. In particular, it is recommended that future studies investigate matched isoinertial dynamic resistance training protocols that promote greater differences in the torque–angle relationship to clarify its effect on angle-specificity measured through isometric tests. Finally, it should be noted that the present study uses a single monoarticular exercise, and its information must be interpreted with caution in other training configurations and exercises.