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At least 253 records · Page 14
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NASA NTRS2010

Regional Model Nesting Within GFS Daily Forecasts Over West Africa

The study uses the RM3, the regional climate model at the Center for Climate Systems Research of Columbia University and the NASA/Goddard Institute for Space Studies (CCSR/GISS). The paper evaluates 30 48-hour RM3 weather forecasts over West Africa during September 2006 made on a 0.5 grid nested within 1 Global Forecast System (GFS) global forecasts. September 2006 was the Special Observing Period #3 of the African Monsoon Multidisciplinary Analysis (AMMA). Archived GFS initial conditions and lateral boundary conditions for the simulations from the US National Weather Service, National Oceanographic and Atmospheric Administration were interpolated four times daily. Results for precipitation forecasts are validated against Tropical Rainfall Measurement Mission (TRMM) satellite estimates and data from the Famine Early Warning System (FEWS), which includes rain gauge measurements, and forecasts of circulation are compared to reanalysis 2. Performance statistics for the precipitation forecasts include bias, root-mean-square errors and spatial correlation coefficients. The nested regional model forecasts are compared to GFS forecasts to gauge whether nesting provides additional realistic information. They are also compared to RM3 simulations driven by reanalysis 2, representing high potential skill forecasts, to gauge the sensitivity of results to lateral boundary conditions. Nested RM3/GFS forecasts generate excessive moisture advection toward West Africa, which in turn causes prodigious amounts of model precipitation. This problem is corrected by empirical adjustments in the preparation of lateral boundary conditions and initial conditions. The resulting modified simulations improve on the GFS precipitation forecasts, achieving time-space correlations with TRMM of 0.77 on the first day and 0.63 on the second day. One realtime RM3/GFS precipitation forecast made at and posted by the African Centre of Meteorological Application for Development (ACMAD) in Niamey, Niger is shown.

Druyan, Leonard M.↗
NASA NTRS2022

Simultaneous Retrievals of Biomass Burning Aerosols and Trace Gases From the Ultraviolet to Near-Infrared Over Northern Thailand During the 2019 Pre-Monsoon Season

With the advent of spaceborne spectroradiometers in a geostationary constellation, measuring high spectral resolution ultraviolet–visible (UV-VIS) and selected near-/shortwave-infrared (NIR/SWIR) radiances can enable the probing of the life cycle of key atmospheric trace gases and aerosols at higher temporal resolutions over the globe. The UV-VIS measurements are important for retrieving several key trace gases (e.g., O 3 , SO 2 , NO 2 , and HCHO) and particularly for deriving aerosol characteristics (e.g., aerosol absorption and vertical profile). This study examines the merit of simultaneous retrievals of trace gases and aerosols using a ground-based spectroradiometer covering the UV-NIR to monitor their physicochemical processes and to obtain reliable aerosol information for various applications. During the 2019 pre-monsoon season over northern Thailand, we deployed a ground-based SMART–s (Spectral Measurements for Atmospheric Radiative Transfer–spectroradiometer) instrument, which is an extended-range Pandora with reliable radiometric calibration in the 330–820 nm range, to retrieve remotely sensed chemical and aerosol properties for the first time near biomass burning sources. The high spectral resolution (∼ 1.0 nm full width half maximum with ∼ 3.7 × oversampling) of sun and sky measurements from SMART–s provides several key trace gases (e.g., O 3 , NO 2 , and H 2 O) and aerosol properties covering the UV where significant light absorption occurs by the carbonaceous particles. During the measurement period, highly correlated total column amounts of NO 2 and aerosol optical thickness (т aer ) retrieved from SMART–s (correlation coefficient, R=0.74) indicated their common emissions from biomass burning events. The SMART–s retrievals of the spectral single scattering albedo (ω 0 ) of smoke aerosols showed an abrupt decrease in the UV, which is an important parameter dictating photochemical processes in the atmosphere. The values of ω 0 and column precipitable water vapor (H 2 O) gradually increase with the mixing of biomass burning smoke particles and higher water vapor concentrations when approaching the monsoon season. The retrieved ω 0 and weighted mean radius of fine-mode aerosols from SMART–s showed positive correlations with the H 2 O (R=0.81 for ω 0 at 330 nm and 0.56 for the volume-weighted mean radius), whereas the real part of the refractive index of fine-mode aerosol (n f ) showed negative correlations (R = -0.61 at 330 nm), which suggest that aerosol aging processes including hygroscopic growth (e.g., humidification and cloud processing) can be a major factor affecting the temporal trends of aerosol optical properties. Retrieved n f and ω 0 were closer to those of the water droplet (i.e., n f of about 1.33 and ω 0 of about 1.0) under lower amounts of NO 2 during the measurement period; considering that the NO 2 amounts in the smoke may indicate the aging of the plume after emission due to its short lifetime, the tendency is also consistent with active hygroscopic processes of the aerosols over this area. Retrieved UV aerosol properties from SMART–s generally support the assumed smoke aerosol models (i.e., the spectral shape of aerosol absorption) used in NASA's current satellite algorithms, and their spectral ω 0 retrievals from ground and satellites showed good agreements (R = 0.73–0.79). However, temporal and spectral variabilities in the aerosol absorption properties in the UV emphasize the importance of a realistic optical model of aerosols for further improvements in satellite retrievals.

biomass burning↗
NASA NTRS1976

Snow backscatter in the 1-8 GHz region

The 1-8 GHz microwave active spectrometer system was used to measure the backscatter response of snow covered ground. The scattering coefficient was measured for all linear polarization combinations at angles of incidence between nadir and 70 deg. Ground truth data consisted of soil moisture, soil temperature profile, snow depth, snow temperature profile, and snow water equivalent. The radar sensitivity to snow water equivalent increased in magnitude with increasing frequency and was almost angle independent for angles of incidence higher than 30 deg, particularly at the higher frequencies. In the 50 deg to 70 deg angular range and in the 6 to 8 GHz frequency range, the sensitivity was typically between -0.4 dB/.1 g/sq cm and -0.5 dB/,1 g/sq cm, and the associated linear correlation coefficient had a magnitude of about 0.8.

Ulaby, F. T.↗
NASA NTRS2013

On the Performance of Global Magnetohydrodynamic Models in the Earth's Magnetosphere

We study the performance of four magnetohydrodynamic models (BATS-R-US, GUMICS, LFM, Open GGCM) in the Earths magnetosphere. Using the Community Coordinated Modeling Centers Run-on-Request system, we compare model predictions with magnetic field measurements of the Cluster, Geotail and Wind spacecraft during a multiple substorm event. We also compare model cross polar cap potential results to those obtained from the Super Dual Auroral Radar Network(SuperDARN) and the model magnetopause standoff distances to an empirical magnetopause model. The correlation coefficient (CC) and prediction efficiency (PE) metrics are used to objectively evaluate model performance quantitatively. For all four models, the best performance outside geosynchronous orbit is found on the dayside. Generally, the performance of models decreases steadily down stream from the Earth. On the dayside most CCs are above 0.5 with CCs for Bx and Bz close to 0.9 for three out of four models. In the magnetotail at a distance of about -130 Earth radii from Earth, the prediction efficiency of all models is below that of using an average value for the prediction with the exception of Bz. Bx is most often best predicted and correlated both on the dayside and the nightside close to the Earth whereas in the far tail the CC and PE for Bz are substantially higher than other components in all models. We also find that increasing the resolution or coupling an additional physics module does notautomatically increase the model performance in the magnetosphere.

geomagnetic tail↗
NASA NTRS2006

Examination of the Armagh Observatory Annual Mean Temperature Record, 1844-2004

The long-term annual mean temperature record (1844-2004) of the Armagh Observatory (Armagh, Northern Ireland, United Kingdom) is examined for evidence of systematic variation, in particular, as related to solar/geomagnetic forcing and secular variation. Indeed, both are apparent in the temperature record. Moving averages for 10 years of temperature are found to highly correlate against both 10-year moving averages of the aa-geomagnetic index and sunspot number, having correlation coefficients of approx. 0.7, inferring that nearly half the variance in the 10-year moving average of temperature can be explained by solar/geomagnetic forcing. The residuals appear episodic in nature, with cooling seen in the 1880s and again near 1980. Seven of the last 10 years of the temperature record has exceeded 10 C, unprecedented in the overall record. Variation of sunspot cyclic averages and 2-cycle moving averages of temperature strongly associate with similar averages for the solar/geomagnetic cycle, with the residuals displaying an apparent 9-cycle variation and a steep rise in temperature associated with cycle 23. Hale cycle averages of temperature for even-odd pairs of sunspot cycles correlate against similar averages for the solar/geomagnetic cycle and, especially, against the length of the Hale cycle. Indications are that annual mean temperature will likely exceed 10 C over the next decade.

Wilson, Robert M.↗
NASA NTRS2017

Evaluating Soil Moisture Retrievals from ESA's SMOS and NASA's SMAP Brightness Temperature Datasets

Two satellites are currently monitoring surface soil moisture (SM) using L-band observations: SMOS (Soil Moisture and Ocean Salinity), a joint ESA (European Space Agency), CNES (Centre national d'tudes spatiales), and CDTI (the Spanish government agency with responsibility for space) satellite launched on November 2, 2009 and SMAP (Soil Moisture Active Passive), a National Aeronautics and Space Administration (NASA) satellite successfully launched in January 2015. In this study, we used a multilinear regression approach to retrieve SM from SMAP data to create a global dataset of SM, which is consistent with SM data retrieved from SMOS. This was achieved by calibrating coefficients of the regression model using the CATDS (Centre Aval de Traitement des Donnes) SMOS Level 3 SM and the horizontally and vertically polarized brightness temperatures (TB) at 40 deg incidence angle, over the 2013 - 2014 period. Next, this model was applied to SMAP L3 TB data from Apr 2015 to Jul 2016. The retrieved SM from SMAP (referred to here as SMAP_Reg) was compared to: (i) the operational SMAP L3 SM (SMAP_SCA), retrieved using the baseline Single Channel retrieval Algorithm (SCA); and (ii) the operational SMOSL3 SM, derived from the multiangular inversion of the L-MEB model (L-MEB algorithm) (SMOSL3). This inter-comparison was made against in situ soil moisture measurements from more than 400 sites spread over the globe, which are used here as a reference soil moisture dataset. The in situ observations were obtained from the International Soil Moisture Network (ISMN; https:ismn.geo.tuwien.ac.at) in North of America (PBO_H2O, SCAN, SNOTEL, iRON, and USCRN), in Australia (Oznet), Africa (DAHRA), and in Europe (REMEDHUS, SMOSMANIA, FMI, and RSMN). The agreement was analyzed in terms of four classical statistical criteria: Root Mean Squared Error (RMSE),Bias, Unbiased RMSE (UnbRMSE), and correlation coefficient (R). Results of the comparison of these various products with in situ observations show that the performance of both SMAP products i.e. SMAP_SCA and SMAP_Reg is 48 similar and marginally better to that of the SMOSL3 product particularly over the PBO_H2O, SCAN, and USCRN sites. However, SMOSL3 SM was closer to the in situ observations over the DAHRA and Oznet sites. We found that the correlation between all three datasets and in situ measurements is best (R 0.80) over the Oznet sites and worst (R 0.58) over the SNOTEL sites for SMAP_SCA and over the DAHRA and SMOSMANIA sites (R 0.51 and R 0.45 for SMAP_Reg and SMOSL3, respectively). The Bias values showed that all products are generally dry, except over RSMN, DAHRA, and Oznet (and FMI for SMAP_SCA). Finally, our analysis provided interesting insights that can be useful to improve the consistency between SMAP and SMOS datasets.

SMOS↗
NASA NTRS2011

Reliability of Upright and Supine Power Measurements Using an Inertial Load Cycle Ergometer

Practical, reliable, and time efficient methods of measuring muscular power are desirable for both research and applied testing situations. The inertial-load cycling method (ILC; Power/Cycle, Austin, TX) requires subjects to pedal as fast as possible against the inertial load of a flywheel for only 3-5 seconds, which could help reduce the time and effort required for maximal power testing. PURPOSE: 1) To test the intramachine reliability of ILC over 3 separate sessions, 2) to compare postural stance (upright vs. supine) during testing, and 3) to compare the maximal power (Pmax) output measured using ILC to that obtained from traditional isokinetic and leg press testing. METHODS: Subjects (n = 12) were tested on 4 non-consecutive days. The following tests were done on the first day of testing: isometric knee extension, isokinetic knee extension at several speeds, isokinetic power/endurance at 180/sec (Biodex System 4), leg press maximal isometric force, and leg press power/endurance. The other 3 days consisted exclusively of ILC testing. Subjects performed 6 ILC tests in an upright position and 6 ILC tests in a supine position on each day. The starting position was counterbalanced. Mixed-effects linear modeling was used to determine if any differences existed between testing days and between upright and supine for Pmax and revolutions per minute at Pmax (RPMpk). Mixed-modeling was also used to calculate intraclass correlation coefficients (ICC) to determine the reliability of the ILC on each testing day for Pmax and RPMpk (ICCs were calculated separately for upright and supine). gKendall fs Tau a h was used to determine the association between ILC Pmax and isokinetic and leg press data. RESULTS: For Pmax, significant differences were found between days 1 and 2 (upright: p = 0.018; supine: p = 0.014) and between days 1 and 3 (upright: p = 0.001; supine: p = 0.002), but not between days 2 and 3 (upright: p = 0.422; supine: p = 0.501). Pmax ICC values were greater than or equal to 0.97 for all days in both positions. Also, no significant differences between upright and supine postures were found for Pmax. No significant differences between days were found for RPMpk; however, there was a significant posture effect (upright greater than supine). Moderate correlations were observed between ILC Pmax and isokinetic and leg press tests (upright: 0.64-0.79, supine: 0.52-0.82). CONCLUSIONS: Overall, ILC is a very reliable test. Since a significant difference was found between day 1 and the other ILC testing days, it is suggested that day 1 of ILC testing should be used as a familiarization session to allow for subject learning. No significant difference in Pmax was seen from test 3 to test 6. However, an increase of 1.3% was observed from test 4 to test 6. Therefore, although 4 tests may be sufficient for most subjects to produce Pmax, in some cases 6 tests may be required. PRACTICAL APPLICATIONS: No differences were seen in Pmax between upright and supine positions despite differing RPMpk. This suggests that ILC testing can be used to provide reliable testing both in an upright position (appropriate for athletes) and in research (e.g., bed rest) or rehabilitation settings where supine testing is necessary. Future research should evaluate whether peak power measurements obtained with the ILC are sensitive to changes such as that observed with training and de-training.

Wickwire, P. J.↗
NASA NTRS2013

Parametric Thermal Soak Model for Earth Entry Vehicles

The analysis and design of an Earth Entry Vehicle (EEV) is multidisciplinary in nature, requiring the application many disciplines. An integrated tool called Multi Mission System Analysis for Planetary Entry Descent and Landing or M-SAPE is being developed as part of Entry Vehicle Technology project under In-Space Technology program. Integration of a multidisciplinary problem is a challenging task. Automation of the execution process and data transfer among disciplines can be accomplished to provide significant benefits. Thermal soak analysis and temperature predictions of various interior components of entry vehicle, including the impact foam and payload container are part of the solution that M-SAPE will offer to spacecraft designers. The present paper focuses on the thermal soak analysis of an entry vehicle design based on the Mars Sample Return entry vehicle geometry and discusses a technical approach to develop parametric models for thermal soak analysis that will be integrated into M-SAPE. One of the main objectives is to be able to identify the important parameters and to develop correlation coefficients so that, for a given trajectory, can estimate the peak payload temperature based on relevant trajectory parameters and vehicle geometry. The models are being developed for two primary thermal protection (TPS) materials: 1) carbon phenolic that was used for Galileo and Pioneer Venus probes and, 2) Phenolic Impregnated Carbon Ablator (PICA), TPS material for Mars Science Lab mission. Several representative trajectories were selected from a very large trade space to include in the thermal analysis in order to develop an effective parametric thermal soak model. The selected trajectories covered a wide range of heatload and heatflux combinations. Non-linear, fully transient, thermal finite element simulations were performed for the selected trajectories to generate the temperature histories at the interior of the vehicle. Figure 1 shows the finite element model that was used for the simulations. The results indicate that it takes several hours for the thermal energy to soak into the interior of the vehicle and achieve maximum payload temperatures. In addition, a strong correlation between the heatload and peak payload container temperature is observed that will help establishing the parametric thermal soak model.

Agrawal, Parul↗
NASA NTRS1984

Satellite passive microwave rain rate measurement over croplands during spring, summer and fall

Rain-rate algorithms for spring, summer and fall that have been developed from comparisons between the brightness temperatures measured by the Nimbus-7 Scanning Multichannel Microwave Radiometer (SMMR) and rain rates derived from operational WSR-57 radars over land are described. Data were utilized from a total of 25 SMMR passes and 234 radars, resulting in about 12,000 observations of about 1600 sq/km areas. Multiple correlation coefficients of 0.63, 0.80 and 0.75 are achieved for the spring, summer and fall algorithms, respectively. Most of this information is in the form of multifrequency contrast in brightness temperature, which is interpreted as a measurement of the degree to which the land-emitted radiation is attenuated by the rain systems. The SMMR 37-GHz channel has more information on rain rate than any other channel. By combining the lower frequency channels with the 37-GHz observations, variations in land and precipitation thermometric temperatures can be removed, leaving rain attenuation as the major effect on brightness temperature. Polarization screening at 37 GHz is found to be sufficient to screen out cases of wet ground, which is only important when the ground is relatively vegetation free. Heavy rain cases are found to be significant part of the algorithms' success, because of the strong microwve signatures (low-brightness temperatures) that result from the presence of precipitation-sized ice in the upper portions of heavily precipitating storms. If IR data are combined with the summer microwave data, an improved (0.85) correlation with radar rain rates is achieved.

Spencer, R. W.↗
NASA NTRS2018

Evaluation of Modeling NO2 Concentrations Driven by Satellite-Derived and Bottom-Up Emission Inventories Using In-Situ Measurements Over China

Chemical transport models together with emission inventories are widely used to simulate NO2 concentrations over China, but validation of the simulations with in situ measurements has been extremely limited. Here we use ground measurements obtained from the air quality monitoring network recently developed by the Ministry of Environmental Protection of China to validate modeling surface NO2 concentrations from the CHIMERE regional chemical transport model driven by the satellite-derived DECSO and the bottom-up MIX emission inventories. We applied a correction factor to the observations to account for the interferences of other oxidized nitrogen compounds (NOz), based on the modeled ratio of NO2 to NOz. The model accurately reproduces the spatial variability in NO2 from in situ measurements, with a spatial correlation coefficient of over 0.7 for simulations based on both inventories. A negative and positive bias is found for the simulation with the DECSO (slopeD0.74 and 0.64 for the daily mean and daytime only) and the MIX (slopeD1.3 and 1.1) inventories, respectively, suggesting an underestimation and overestimation of NOx emissions from corresponding inventories. The bias between observed and modeled concentrations is reduced, with the slope dropping from 1.3 to 1.0 when the spatial distribution of NOx emissions in the DECSO inventory is applied as the spatial proxy for the MIX inventory, which suggests an improvement of the distribution of emissions between urban and suburban or rural areas in the DECSO inventory compared to that used in the bottom-up inventory. A rough estimate indicates that the observed concentrations, from sites predominantly placed in the populated urban areas, may be 10-40% higher than the corresponding model grid cell mean. This reduces the estimate of the negative bias of the DECSO-based simulation to the range of -30 to 0% on average and more firmly establishes that the MIX inventory is biased high over major cities. The performance of the model is comparable over seasons, with a slightly worse spatial correlation in summer due to the difficulties in resolving the more active NOx photochemistry and larger concentration gradients in summer by the model. In addition, the model well captures the daytime diurnal cycle but shows more significant disagreement between simulations and measurements during nighttime, which likely produces a positive model bias of about 15% in the daily mean concentrations. This is most likely related to the uncertainty in vertical mixing in the model at night.

NO2 modelling↗
NASA NTRS2014

Investigation of Spiral Bevel Gear Condition Indicator Validation Via AC-29-2C Using Damage Progression Tests

This report documents the results of spiral bevel gear rig tests performed under a NASA Space Act Agreement with the Federal Aviation Administration (FAA) to support validation and demonstration of rotorcraft Health and Usage Monitoring Systems (HUMS) for maintenance credits via FAA Advisory Circular (AC) 29-2C, Section MG-15, Airworthiness Approval of Rotorcraft (HUMS) (Ref. 1). The overarching goal of this work was to determine a method to validate condition indicators in the lab that better represent their response to faults in the field. Using existing in-service helicopter HUMS flight data from faulted spiral bevel gears as a "Case Study," to better understand the differences between both systems, and the availability of the NASA Glenn Spiral Bevel Gear Fatigue Rig, a plan was put in place to design, fabricate and test comparable gear sets with comparable failure modes within the constraints of the test rig. The research objectives of the rig tests were to evaluate the capability of detecting gear surface pitting fatigue and other generated failure modes on spiral bevel gear teeth using gear condition indicators currently used in fielded HUMS. Nineteen final design gear sets were tested. Tables were generated for each test, summarizing the failure modes observed on the gear teeth for each test during each inspection interval and color coded based on damage mode per inspection photos. Gear condition indicators (CI) Figure of Merit 4 (FM4), Root Mean Square (RMS), +/- 1 Sideband Index (SI1) and +/- 3 Sideband Index (SI3) were plotted along with rig operational parameters. Statistical tables of the means and standard deviations were calculated within inspection intervals for each CI. As testing progressed, it became clear that certain condition indicators were more sensitive to a specific component and failure mode. These tests were clustered together for further analysis. Maintenance actions during testing were also documented. Correlation coefficients were calculated between each CI, component, damage state and torque. Results found test rig and gear design, type of fault and data acquisition can affect CI performance. Results found FM4, SI1 and SI3 can be used to detect macro pitting on two more gear or pinion teeth as long as it is detected prior to progressing to other components or transitioning to another failure mode. The sensitivity of RMS to system and operational conditions limit its reliability for systems that are not maintained at steady state. Failure modes that occurred due to scuffing or fretting were challenging to detect with current gear diagnostic tools, since the damage is distributed across all the gear and pinion teeth, smearing the impacting signatures typically used to differentiate between a healthy and damaged tooth contact. This is one of three final reports published on the results of this project. In the second report, damage modes experienced in the field will be mapped to the failure modes created in the test rig. The helicopter CI data will then be re-processed with the same analysis techniques applied to spiral bevel rig test data. In the third report, results from the rig and helicopter data analysis will be correlated. Observations, findings and lessons learned using sub-scale rig failure progression tests to validate helicopter gear condition indicators will be presented.

gears↗
NASA NTRS1971

Development of techniques for measuring pilot workload

An objective method of assessing information workload based on physiological measurements was developed. Information workload, or reserve capacity, was measured using a visual discrimination secondary task and subjective rating of task difficulty. The primary task was two axis (pitch and roll) tracking, and the independent variables in this study were aircraft pitch dynamics and wind gust disturbances. The study was structured to provide: (1) a sensitive, nonloading measure of reserve capacity, and (2) an unencumbering reliable measurement of the psychophysiological state. From these, a measured workload index (MWI) and physiological workload index (PWI) were extracted. An important measure of the success of this study was the degree to which the MWI and PWI agreed across the 243 randomly-presented, four-minute trials (9 subjects X 9 tasks X 3 replications). The electrophysiological data collected included vectorcardiogaram, respiration, electromyogram, skin impedance, and electroencephalogram. Special computer programs were created for the analysis of each physiological variable. The digital data base then consisted of 82 physiological features for each of the 243 trials. A prediction of workload based on physiological observations was formulated as a simultaneous least-squares prediction problem. A best subset of 10 features was chosen to predict the three measures of reserve capacity. The cannonical correlation coefficient was .754 with a chi squared value of 91.3 which allows rejection of the null hypothesis with p of .995.

Spyker, D. A.↗
NASA NTRS1971

Characterization of impulse noise and analysis of its effect upon correlation receivers

A noise model is formulated to describe the impulse noise in many digital systems. A simplified model, which assumes that each noise burst contains a randomly weighted version of the same basic waveform, is used to derive the performance equations for a correlation receiver. The expected number of bit errors per noise burst is expressed as a function of the average signal energy, signal-set correlation coefficient, bit time, noise-weighting-factor variance and probability density function, and a time range function which depends on the crosscorrelation of the signal-set basis functions and the noise waveform. A procedure is established for extending the results for the simplified noise model to the general model. Unlike the performance results for Gaussian noise, it is shown that for impulse noise the error performance is affected by the choice of signal-set basis functions and that Orthogonal signaling is not equivalent to On-Off signaling with the same average energy.

Houts, R. C.↗
NASA NTRS1972

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.↗