RAPIER - A FORTRAN 4 program for multiple linear regression analysis providing internally evaluated remodeling
FORTRAN 4 program for multiple linear regression analysis
Henry, B.↗
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A multiple linear regression analysis of hot corrosion attack on a series of nickel base turbine alloys
Multiple linear regression analysis was used to determine an equation for estimating hot corrosion attack for a series of Ni base cast turbine alloys. The U transform (i.e., 1/sin (% A/100) to the 1/2) was shown to give the best estimate of the dependent variable, y. A complete second degree equation is described for the centered" weight chemistries for the elements Cr, Al, Ti, Mo, W, Cb, Ta, and Co. In addition linear terms for the minor elements C, B, and Zr were added for a basic 47 term equation. The best reduced equation was determined by the stepwise selection method with essentially 13 terms. The Cr term was found to be the most important accounting for 60 percent of the explained variability hot corrosion attack.
Barrett, C. A.↗
Performance of an Axisymmetric Rocket Based Combined Cycle Engine During Rocket Only Operation Using Linear Regression Analysis
The all rocket mode of operation is shown to be a critical factor in the overall performance of a rocket based combined cycle (RBCC) vehicle. An axisymmetric RBCC engine was used to determine specific impulse efficiency values based upon both full flow and gas generator configurations. Design of experiments methodology was used to construct a test matrix and multiple linear regression analysis was used to build parametric models. The main parameters investigated in this study were: rocket chamber pressure, rocket exit area ratio, injected secondary flow, mixer-ejector inlet area, mixer-ejector area ratio, and mixer-ejector length-to-inlet diameter ratio. A perfect gas computational fluid dynamics analysis, using both the Spalart-Allmaras and k-omega turbulence models, was performed with the NPARC code to obtain values of vacuum specific impulse. Results from the multiple linear regression analysis showed that for both the full flow and gas generator configurations increasing mixer-ejector area ratio and rocket area ratio increase performance, while increasing mixer-ejector inlet area ratio and mixer-ejector length-to-diameter ratio decrease performance. Increasing injected secondary flow increased performance for the gas generator analysis, but was not statistically significant for the full flow analysis. Chamber pressure was found to be not statistically significant.
Smith, Timothy D.↗
Application of non-linear regression analysis and of analysis of variance to the determina- tion of periods of events defined by irregularly spaced observations
Accurate periods of periodic events observed at irregular intervals of time
TIME FACTOR↗
Non-linear regression analysis and analysis of variance of periods defined by irregular observations
Nonlinear regression and variance analyses of periods defined by irregular observations
VARIANCE↗
Multiple linear regression analysis
Program rapidly selects best-suited set of coefficients. User supplies only vectors of independent and dependent data and specifies confidence level required. Program uses stepwise statistical procedure for relating minimal set of variables to set of observations; final regression contains only most statistically significant coefficients. Program is written in FORTRAN IV for batch execution and has been implemented on NOVA 1200.
Edwards, T. R.↗
Effect of removing the common mode errors on linear regression analysis of noise amplitudes in position time series of a regional GPS network & a case study of GPS stations in Southern California
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Weiping Jiang↗
Literature review of some selected types of results and statistical analyses of total-ozone data
The depletion of ozone in the stratosphere is examined, and causes for the depletion are cited. Ground station and satellite measurements of ozone, which are taken on a worldwide basis, are discussed. Instruments used in ozone measurement are discussed, such as the Dobson spectrophotometer, which is credited with providing the longest and most extensive series of observations for ground based observation of stratospheric ozone. Other ground based instruments used to measure ozone are also discussed. The statistical differences of ground based measurements of ozone from these different instruments are compared to each other, and to satellite measurements. Mathematical methods (i.e., trend analysis or linear regression analysis) of analyzing the variability of ozone concentration with respect to time and lattitude are described. Various time series models which can be employed in accounting for ozone concentration variability are examined.
Myers, R. H.↗
Regression Bias in using Solar Wind Measurements
Simultaneous solar wind measurements from the solar wind monitors, WIND and ACE, differ due to the spatial and temporal structure of the solar wind. Correlation studies that use these measurements as input may infer an incorrect correlation due to uncertainties arising from this spatial and temporal structure, especially at extreme and rare solar wind values. In particular, regression analysis will lead to a regression function whose slope is biased towards the mean value of the measurement parameter. This article demonstrates this regression bias by comparing simultaneous ACE and WIND solar wind measurements. A non-linear regression analysis between them leads to a perception of underestimation of extreme values of one measurement on average over the other. Using numerical experiments, we show that popular regression analysis techniques such as linear least-squares, orthogonal least-squares, and non-linear regression are not immune to this bias. Hence while using solar wind parameters as an independent variable in a correlation or regression analysis, random uncertainty in the independent variable can create unintended biases in the response of the dependent variable. More generally, the regression to the mean effect can impact both event-based, statistical studies of magnetospheric response to solar wind forcing.
magnetosphere↗
Can Functional Cardiac Age be Predicted from ECG in a Normal Healthy Population
In a normal healthy population, we desired to determine the most age-dependent conventional and advanced ECG parameters. We hypothesized that changes in several ECG parameters might correlate with age and together reliably characterize the functional age of the heart. Methods: An initial study population of 313 apparently healthy subjects was ultimately reduced to 148 subjects (74 men, 84 women, in the range from 10 to 75 years of age) after exclusion criteria. In all subjects, ECG recordings (resting 5-minute 12-lead high frequency ECG) were evaluated via custom software programs to calculate up to 85 different conventional and advanced ECG parameters including beat-to-beat QT and RR variability, waveform complexity, and signal-averaged, high-frequency and spatial/spatiotemporal ECG parameters. The prediction of functional age was evaluated by multiple linear regression analysis using the best 5 univariate predictors. Results: Ignoring what were ultimately small differences between males and females, the functional age was found to be predicted (R2= 0.69, P < 0.001) from a linear combination of 5 independent variables: QRS elevation in the frontal plane (p<0.001), a new repolarization parameter QTcorr (p<0.001), mean high frequency QRS amplitude (p=0.009), the variability parameter % VLF of RRV (p=0.021) and the P-wave width (p=0.10). Here, QTcorr represents the correlation between the calculated QT and the measured QT signal. Conclusions: In apparently healthy subjects with normal conventional ECGs, functional cardiac age can be estimated by multiple linear regression analysis of mostly advanced ECG results. Because some parameters in the regression formula, such as QTcorr, high frequency QRS amplitude and P-wave width also change with disease in the same direction as with increased age, increased functional age of the heart may reflect subtle age-related pathologies in cardiac electrical function that are usually hidden on conventional ECG.
Schlegel, Todd↗
Molecular Static Third-Order Polarizabilities of Carbon-Cage Fullerene and Their Correlation with Three Geometric Properties: Symmetry, Aromaticity, and Size
The static third-order polarizabilities (gamma) of C60, C70, five isomers of C78 and two isomers of C84 were analyzed in terms of three properties, from a geometric point of view: symmetry, aromaticity and size. The polarizability values were based on the finite field approximation using a semiempirical Hamiltonian (AM1) and applied to molecular structures obtained from density functional theory calculations. Symmetry was characterized by the molecular group order. The selection of 6-member rings as aromatic was determined from an analysis of bond lengths. Maximum interatomic distance and surface area were the parameters considered with respect to size. Based on triple linear regression analysis, it was found that the static linear polarizability (alpha) and gamma in these molecules respond differently to geometrical properties: alpha depends almost exclusively on surface area while gamma is affected by a combination of number of aromatic rings, length and group order, in decreasing importance. In the case of alpha, valence electron contributions provide the same information as all-electron estimates. For gamma, the best correlation coefficients are obtained when all-electron estimates are used and when the dependent parameter is ln(gamma) instead of gamma.
Moore, C. E.↗
An improved multiple linear regression and data analysis computer program package
NEWRAP, an improved version of a previous multiple linear regression program called RAPIER, CREDUC, and CRSPLT, allows for a complete regression analysis including cross plots of the independent and dependent variables, correlation coefficients, regression coefficients, analysis of variance tables, t-statistics and their probability levels, rejection of independent variables, plots of residuals against the independent and dependent variables, and a canonical reduction of quadratic response functions useful in optimum seeking experimentation. A major improvement over RAPIER is that all regression calculations are done in double precision arithmetic.
Sidik, S. M.↗
Assessing the Transferability of Statistical Predictive Models for Leaf Area Index Between Two Airborne Discrete Return LiDAR Sensor Designs Within Multiple Intensely Managed Loblolly Pine Forest Locations in the South-Eastern USA
Leaf area is an important forest structural variable which serves as the primary means of mass and energy exchange within vegetated ecosystems. The objective of the current study was to determine if leaf area index (LAI) could be estimated accurately and consistently in five intensively managed pine plantation forests using two multiple-return airborne LiDAR datasets. Field measurements of LAI were made using the LiCOR LAI2000 and LAI2200 instruments within 116 plots were established of varying size and within a variety of stand conditions (i.e. stand age, nutrient regime and stem density) in North Carolina and Virginia in 2008 and 2013. A number of common LiDAR return height and intensity distribution metrics were calculated (e.g. average return height), in addition to ten indices, with two additional variants, utilized in the surrounding literature which have been used to estimate LAI and fractional cover, were calculated from return heights and intensity, for each plot extent. Each of the indices was assessed for correlation with each other, and was used as independent variables in linear regression analysis with field LAI as the dependent variable. All LiDAR derived metrics were also entered into a forward stepwise linear regression. The results from each of the indices varied from an R2 of 0.33 (S.E. 0.87) to 0.89 (S.E. 0.36). Those indices calculated using ratios of all returns produced the strongest correlations, such as the Above and Below Ratio Index (ABRI) and Laser Penetration Index 1 (LPI1). The regression model produced from a combination of three metrics did not improve correlations greatly (R2 0.90; S.E. 0.35). The results indicate that LAI can be predicted over a range of intensively managed pine plantation forest environments accurately when using different LiDAR sensor designs. Those indices which incorporated counts of specific return numbers (e.g. first returns) or return intensity correlated poorly with field measurements. There were disparities between the number of different types of returns and intensity values when comparing the results from two LiDAR sensors, indicating that predictive models developed using such metrics are not transferable between datasets with different acquisition parameters. Each of the indices were significantly correlated with one another, with one exception (LAI proxy), in particular those indices calculated from all returns, which indicates similarities in information content for those indices. It can then be argued that LiDAR indices have reached a similar stage in development to those calculated from optical-spectral sensors, but which offer a number of advantages, such as the reduction or removal of saturation issues in areas of high biomass.
Sumnall, Matthew↗
Smooth Pursuit Saccade Amplitude Modulation During Exposure to Microgravity
Russian investigators have reported changes in pursuit tracking of a vertically moving point stimulus during space flight. Early in microgravity, changes were manifested by decreased eye movement amplitude (undershooting) and the appearance of correction saccades. As the flight progressed, pursuit of the moving point stimulus deteriorated while associated saccadic movements were unchanged. Immediately postflight there was an improved execution of active head movements indicating that the deficiencies in pursuit function noted in microgravity may be of central origin. In contrast, tests of two cosmonauts showed that horizontal and vertical smooth pursuit were unchanged inflight. However, results of corresponding saccadic tasks showed a tendency toward the overshooting of a horizontal target early inflight with high accuracy developing later inflight, accompanied by an increased saccade velocity and a trend toward decreased saccade latency. Based on these equivocal results, we have further investigated the effects of space flight on the smooth pursuit mechanism during and after short duration flight, and postflight on returning MIR crewmembers. Sinusoidal target movement was presented horizontally at frequencies of 0.33 and 1.0 Hz. Subjects were asked to perform two trials for each stimulus combination: (1) moving eyes-only (EO) and (2) moving eyes and head (EH) with the target motion. Peak amplitude was 30 deg for 0.33 Hz trials and 15 deg for the 1.0 Hz trials. The relationship between saccade amplitude and peak velocity were plotted as a main sequence for each phase of flight, and linear regression analysis allowed us to determine the slope of each main sequence plot. The linear slopes were then combined for each flight phase for each individual subject. The main sequence for both EO and EH trials at both the 0.33 and 1.0 Hz frequencies during flight for the short duration flyers showed a reduction in saccade velocity and amplitude when compared to the preflight main sequence . This difference in the regression slopes between flight phase, head/eye condition (EO or EH), and pursuit target frequency was observed across all subjects (statistically significant at the p<0.02, df= 2). It is interesting to note that postflight for the short duration flyers there was an immediate recovery to the preflight main sequence across all trials. There were no significant differences observed between the preflight slopes for either head movement condition (EO vs. EH). When the immediate postflight (R+O) regression slopes were compared with the preflight slopes, there was a tendency (not significant) for both saccade amplitude and peak velocity to increase during the postflight testing. This tendency had vanished by R+ 1. Of particular interest was the redistribution of saccades during the latter stages of the flight and immediately postflight in the EO condition. At the 1.0 Hz frequency the saccades tended to be clustered near the lowest target velocity. It was also interesting to note that gaze performance (eye in skull + head in space) was consistently better during the EH condition; a finding also observed by our Russian colleagues. As the results of the long duration flight become available we expect that they will not only show that postflight effects will be similar to those observed during the short duration flights, but will also last for a greater period of time following flight. It is not clear what mechanism is responsible for the decreased peak saccadic velocity during flight unless the change is related to the control of retinal slip. For example, it is possible that saccades will tend to initially undershoot their targets by a small percentage and these saccades are then followed, if vision is available, by a small augmenting corrective saccade. It has been postulated that the functional significance of this undershooting tendency is to maintain the spatial representation of the target on the same side of the fovea (as opposedo racing across the fovea) and hence in the same cerebral hemisphere that initiated the primary saccade thus minimizing delays caused by an intra-hemispheric transfer of information . One could also speculate that with saccade velocities greater than normal, additional corrective saccades would be required to bring the target back on the fovea. A less plausible explanation of our findings could be fatigue. Yet it seems unlikely that our subjects would show lower velocities on all inflight test days while showing increased saccade velocities immediately following space flight where fatigue is usually the greatest. Finally, the redistribution effect noted late inflight is likely caused by adaptive changes. Overall, corrective saccades appeared to be used in maintaining gaze on target; reducing retinal slip and assisting space travelers in maintaining clear vision throughout the different phases of the space flight.
Reschke, M. F.↗
A rotor optimization using regression analysis
The design and development of helicopter rotors is subject to the many design variables and their interactions that effect rotor operation. Until recently, selection of rotor design variables to achieve specified rotor operational qualities has been a costly, time consuming, repetitive task. For the past several years, Kaman Aerospace Corporation has successfully applied multiple linear regression analysis, coupled with optimization and sensitivity procedures, in the analytical design of rotor systems. It is concluded that approximating equations can be developed rapidly for a multiplicity of objective and constraint functions and optimizations can be performed in a rapid and cost effective manner; the number and/or range of design variables can be increased by expanding the data base and developing approximating functions to reflect the expanded design space; the order of the approximating equations can be expanded easily to improve correlation between analyzer results and the approximating equations; gradients of the approximating equations can be calculated easily and these gradients are smooth functions reducing the risk of numerical problems in the optimization; the use of approximating functions allows the problem to be started easily and rapidly from various initial designs to enhance the probability of finding a global optimum; and the approximating equations are independent of the analysis or optimization codes used.
Giansante, N.↗
Effects of 40Ar and 56Fe ions on retinal photoreceptor cells of the rabbit: implications for manned missions to Mars
Losses of photoreceptor cells (rods) from the retinas of New Zealand white (NZW) rabbits were detectable within 2 years after localized acute irradiation of optic and proximal tissues with > or = 7 Gy of 530 MeV u-1 40Ar ions or > or = 2 Gy of 465 MeV u-1 56Fe ions in the Bragg plateau region of energy deposition. Those limits were determined only from an analysis of variance of dose groups because the shapes of the dose response curves at early post-irradiation times are not known, a concern being addressed by experiments in progress. Losses of photoreceptor cells for the period 0.5-2.5 years post-irradiation, determined by provisional linear regression analysis, were approximately 1.7% Gy-1 and 2.5% Gy-1 for 40Ar and 56Fe ions, respectively.
NASA Discipline Radiation Health↗
Measurements of CCl3F, CCl2F2, CCl4, N2O and SF6 in the Northern Hemisphere stratosphere
An overview of the Department of Energy's High Altitude Sampling Program and some recent trace gas measurement results are presented. Analysis of whole air samples, collected in pressurized bottles, provides information on stratospheric inventories and distributions for CCl3F, CCl2F2, CCl4, N2O and SF6 in the Northern Hemisphere. Based on a linear regression analysis of the data the estimated mean Northern Hemisphere stratospheric concentration of each gas increased as follows: CCl3F changed from 54 to 142 p1/1 (4/74-11/83); CCl2F2 changed from 133 to 268 p1/1 (4/76-11/83); SF6 changed from 160 to 480 f1/1 (4/74-11/83); CC1, changed from 58 to 91 p1/1 (4/75-11/83); N2O changed from 246 to 261 n1/1 (4/76-11/83). The calculated mean Northern Hemisphere stratospheric concentrations of N2O, CCl3F, CCl2F2, and CCl4 after 1980 show larger than expected fluctuations with time. Recent volcanic activity may be a partial cause for these fluctuations through induced changes in stratospheric dynamical processes.
Leifer, R.↗
Analysis of relativistic nucleus-nucleus interactions in emulsion chambers
The development of a computer-assisted method is reported for the determination of the angular distribution data for secondary particles produced in relativistic nucleus-nucleus collisions in emulsions. The method is applied to emulsion detectors that were placed in a constant, uniform magnetic field and exposed to beams of 60 and 200 GeV/nucleon O-16 ions at the Super Proton Synchrotron (SPS) of the European Center for Nuclear Research (CERN). Linear regression analysis is used to determine the azimuthal and polar emission angles from measured track coordinate data. The software, written in BASIC, is designed to be machine independent, and adaptable to an automated system for acquiring the track coordinates. The fitting algorithm is deterministic, and takes into account the experimental uncertainty in the measured points. Further, a procedure for using the track data to estimate the linear momenta of the charged particles observed in the detectors is included.
Mcguire, Stephen C.↗