Theorem about the sufficient condition for the equality of the estimates of the OLS and Aitken of the leading coefficient of quadratic regression

At the paper in the case of heteroscedastic independent deviations a quadratic regression model is studied. A theorem is formulated that gives a sufficient condition on the variance of deviations for the coincidence of Aitken's estimate of the leading regression coefficient with his estimation of the OLS in the case of an odd number of observation points and a bisymmetric covariance matrix. On the basis of this theorem, in some cases examples of non-unit covariance matrices are constructed for which the indicated estimations of the leading coefficient of the quadratic regression coindcide.

Distribution of Bark Procyanidin Contents in Pinus yunnanensis Populations and Related Species

The distribution of the bark procyanidin contents in 26 populations of Pinus yunnanensis and 8 populations of P. kesiya var. langbianensis and 5 populations of P. densata was determined. The results indicated that genetic and environmental factors commonly affected the procyanidin content in the populations of P. yunnanensis and related species. The procyanidin contents in the three related species followed the order of P. densata (54.72 mg/g) > P. kesiya (43.86 mg/g) > P. yunnanensis (37.95 mg/g). Furthermore, the procyanidin content in P. yunnanensis and related species had high variability. The procyanidin contents in the three related species showed that the procyanidin contents of P. densata distributed in northwest Yunnan and P. kesiya distributed in southern Yunnan were high, the procyanidin content of the population with introgression and hybridization or a heterogeneous habitat was also high, and that of P. yunnanensis distributed in central Yunnan was low. The quadratic regression model of procyanidin content and latitude was Y = 1329.06 -100.52* Latitude +1.95 * Latitude2.

Generation of regression models and multi-response optimization of friction stir welding technique parameters during the fabrication of AZ80A Mg alloy joints

Conventional methodologies employed for the selection of weld process parameters for fabricating sound quality weldments have been found to consume more time and are often unreliable. Therefore, in this paper, an analysis was made to develop a quadratic regression model and empirical relationships by employing response surface methodology between various input parameters of the friction stir welding (FSW) technique including rotational speed of tool, axial force, and traversing speed of tool and five responses of output including percentage of elongation, yield strength, tensile strength, grain size, and microhardness. The discrepancies between the anticipated values and the genuine experimental outcomes are within ±1%, which reveals that the established mathematical quadratic regression model was a good fit to the actual experimental results. The experimental analysis also determined the elite combination of input parameters of the FSW technique for the output parameters.

Production Components and Agricultural Productivity of Corn under Nitrogen Doses and Planting Times

Aims: The objective of this study was to evaluate the best time for planting and nitrogen dose during the dry season that provides better yield to corn crop in the Alagoas Coastal Tablelands region. Study Design: The experimental design was in randomized blocks, in the split plot scheme with four repetitions. Place and Duration of Study: The experiment was developed at the Center of Agrarian Sciences of the Federal University of Alagoas in 2016. Methodology: The plots consisted of 20 lines with seven meters in length and received the four sowing seasons (E1: 28/05/16, E2: 11/06/16, E3: 25/06/16, E4: 22/07/16). The subplots contained 5 lines of 7 meters each and received the nitrogen doses (0, 75, 150 and 225 kg ha-1). The variables analyzed were: Number of grains per ear (NGE), grain mass per ear (GME) and agricultural yield obtained from the weighing of all grains harvested in the useful area of each plot. Results: The variables agricultural productivity and number of grains per ear of corn adjusted to the quadratic regression model, while for the mass of 1,000 grains the linear was better. Grain mass per cob, number of grains per cob, weight of 1,000 grains and yield are influenced by nitrogen rates. The E1 season was the one that provided the highest grain mass per turn (235 g), number of grains per ear (675) and agricultural yield (9.6 t ha-1). For the mass of 1,000 grains, season E2 obtained the highest result (263 g). Conclusion: Maximum corn yield can be achieved by applying 209 kg ha-1 of N, which corresponds to a yield of 9.55 t ha-1 if planted until 06/11/16.