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A joint determination of horizontal and vertical movement of water through porous medium is addressed in this study through fast multi-output relevance vector regression (FMRVR). To do this, an experimental data set conducted in a sand box with 300 × 300 × 150 mm dimensions made of Plexiglas is used. A random mixture of sand having size of 0.5-1 mm is used to simulate the porous medium. Within the experiments, 2, 3, 7, and 12 cm walls are used together with different injection locations as 130.7, 91.3, and 51.8 mm measured from the cutoff wall at the upstream. Then, the Cartesian coordinated of the tracer, time interval, length of the wall in each setup, and two dummy variables for determination of the initial point are considered as independent variables for joint estimation of horizontal and vertical velocity of water movement in the porous medium. Alternatively, the multi-linear regression, random forest, and the support vector regression approaches are used to alternate the results obtained by the FMRVR method. It was concluded that the FMRVR outperforms the other models, while the uncertainty in estimation of horizontal penetration is larger than the vertical one.

Based on data collected from 2054 saplings of Larix gmelinii forest in 55 fixed plots in 2018-2019 in Cuigang Forestry Station, Daxing'anling area, we classified the stand density index (SDI) into four classes, i.e ., Class Ⅰ (SDI 1 <1863 plants·hm -2 ), Class Ⅱ (1863 plants·hm -2 ≤SDI 2 <2155 plants·hm -2 ), Class Ⅲ (2155 plants·hm -2 ≤SDI 3 <2459 plants·hm -2 ) and Class Ⅳ (SDI 4 ≥2459 plants·hm -2 ) by using the quartile method. We constructed a dummy variable model and quantile regression model for the height-breast diameter of saplings of L. gmelinii with dummy variable method introduced SDI. The results showed that among the five selected representative non-linear tree height curve models, the Richards model fitted the best, with R , RMSE and MAE of 0.7637, 0.8250 m and 0.5696 m. The dummy variable model including the SDI constructed based on the Richards model showed a 1.3% increase in a 2 , RMSE and MAE of 0.7637, 0.8250 m and 0.5696 m. The dummy variable model including the SDI constructed based on the Richards model showed a 1.3% increase in R a 2 compared with the base model, while RMSE, MAE, and AIC decreased by 2.1%, 1.5%, and 11.2%, respectively. When the quantile τ was 0.5, R a 2 of quantile regression model was the maximum, and RMSE, MAE, AIC was the minimum, being 0.7612, 0.8294 m, 0.5657 m, and -767.19, respectively. Compared with SDI 1 , sapling height in SDI 2 -SDI 4 was increased by 5.6%, 5.6%, and 11.3%, suggesting reasonable that regulation of stand density was conducive to increase the height growth of saplings in regeneration.

Based on data from 56 plots of natural Larix gmelinii forest in Cuigang Forest Farm of Daxing'anling Mountains, we constructed the height to diameter ratio (HDR) model of L. gmelinii with exponential decay function as the base model. We used the tree classification as dummy variables and the method of reparameterization. The aim was to provide scientific evidence for evaluating the stability of different grades of L. gmelinii trees and stands in Daxing'anling Mountains. The results showed that except for diameter at breast height, the dominant height, dominant diameter, individual tree competition index all had significant correlations with the HDR. The involvement of these variables significantly improved the fitted accuracy of the generalized HDR model, with the adjustment coefficients, root mean square error and mean absolute error being 0.5130, 0.1703 m·cm -1 and 0.1281 m·cm -1 , respectively. When the tree classification as a dummy variable was added to parameters  0 and  2 of the generalized model, the fitting effect of the model was further improved. The three above-mentioned statistics were 0.5171, 0.1696 m·cm -1 and 0.1277 m·cm -1 , respectively. Through comparative analysis, the generalized HDR model with tree classification as dummy variable had the best fitting effect, which was superior to the basic model, and had higher prediction precision and adaptability.

Carbon dioxide has a significant impact on global climate change due to its natural greenhouse effect. The objective and credible forecast of carbon emissions is very important for the government to formulate and implement the corresponding emission reduction targets. For controlling the growth of carbon emissions, Chinese government has put forward the low-carbon pilot policy and carbon trading policy. However, the existing grey models cannot measure the impact of policies and their interactions. In order to remedy the defect, a novel grey multivariable model based on dummy variables and their interactions is established. Two kinds of grey multivariable models and back propagation neural network model are chosen as comparison models to highlight that the introduction of dummy variables and their interactions plays an important part in improving the model performance. To verify the effectiveness, these four models are selected to simulate and predict the carbon emissions generated from primary energy consumption in Guangdong Province of China. The empirical results indicate that the mean absolute percentage errors of the novel model are 2.87% and 0.86%, respectively, which is significantly better than these three competing models. Finally, based on the outstanding performance of the novel model, it is chosen to forecast the fluctuating tendency of carbon emissions in the next 5 years., (© 2022. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

This paper has been empirically investigated the existence of the day-of-the-week effect by using closing daily data for Nifty 50, Nifty 50 Midcap, Nifty 100, Nifty 100 Midcap, Nifty 100 Smallcap, and Nifty 200 for before and during the COVID-19 health crisis. This study used secondary data for all indices over the period 1 April 2005-14 May 2020. The present study used both dummy variable regression and the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model. The total study period is divided into two sub-periods, that is, during and before the COVID-19 health crisis. A negative return is found for Mondays when the during-COVID-19 health crisis period is examined; in contrast, it was positive for the before COVID-19 period. Tuesday's effect on index return is found statistically significant and positive for all indices during the COVID-19 crisis., (© 2021 John Wiley & Sons, Ltd.)

With the commonly used variable-exponent taper models developed by Kozak (1988), Muhairwe (1999), Lee (2003) and Kozak (2004), we aimed to develop taper functions of diameter outside bark (DOB), heartwood diameter (HD), sapwood width (SW), and bark thickness (BT) based on the data of 2977 discs from 103 sample trees of Pinus koraiensis plantations under different conditions in Mengjiagang Forest Farm, Dongjingcheng and Linkou Forestry Bureau in Heilongjiang Province. We selected the optimal basic model after comparison. By using seemingly unrelated regression (SUR) method in the PROC MODEL of SAS software, we established an additive model system for the taper equations of DOB, HD, SW and BT. By introducing the region as a dummy variable, the models were evaluated by coefficient determination ( R adj 2 ), root mean square error (RMSE), Akaike information criterion (AIC) and Bayesian information criterion (BIC). The results showed that the taper model developed by Kozak (2004) was the optimal one for the DOB, HD, SW and BT. When satisfying the additivity of each component and total amount, the additivity model system got better prediction effect, with a prediction precision of more than 98%. The additive model system with dummy variables improved the prediction ability to varying degrees, especially the prediction precision of HD and SW models. Minor differences existed in DOB and BT among different regions, while enormous differences in HD and SW. The additive model system with dummy variables not only had high prediction accuracy but also satisfied the additive logic of DOB, HD, SW and BT, which provided a basis for accurate estimation of heartwood, sapwood and bark volume of P. koraiensis .

The outbreak of coronavirus disease 2019 (COVID-19) has been spreading rapidly in China and the Chinese government took a series of policies to control the epidemic. Therefore, it will be helpful to predict the tendency of the epidemic and analyze the influence of official policies. Existing models for prediction, such as cabin models and individual-based models, are either oversimplified or too meticulous, and the influence of the epidemic was studied much more than that of official policies. To predict the epidemic tendency, we consider four groups of people, and establish a propagation dynamics model. We also create a negative feedback to quantify the public vigilance to the epidemic. We evaluate the tendency of epidemic in Hubei and China except Hubei separately to predict the situation of the whole country. Experiments show that the epidemic will terminate around 17 March 2020 and the final number of cumulative infections will be about 78 191 (prediction interval, 74 872 to 82 474). By changing the parameters of the model accordingly, we demonstrate the control effect of the policies of the government on the epidemic situation, which can reduce about 68% possible infections. At the same time, we use the capital asset pricing model with dummy variable to evaluate the effects of the epidemic and official policies on the revenue of multiple industries., (© Shanghai Jiao Tong University and Springer-Verlag GmbH Germany, part of Springer Nature 2020.)

This study were estimated the contribution of carcass traits to unit price, to analyze the marbling score as a categorical variable rather than a numerical variable, and to develop an optimal model that also includes the holiday effect and the raising period. The data for this study were acquired from the Quality Evaluation of the Korea Institute for Animal Products, and consisted of the trading records of 1,613,699 heads at 12 wholesale markets from 2010 to 2014. The unit price of a cow was estimated from the following parameters: -52.50 Won/mm, 8.93 Won/cm 2 , 7.20 Won/kg, and -1.04 Won/day for backfat thickness, eye muscle area, carcass weight, and raising period, respectively. Parameters for the dummy variables of marbling scores varied from 0 to 8328.74 Won/kg, which means that each marbling score grade had a different price value. The unit price of a steer was estimated from the following parameters: -92.12 Won/mm, 20.22 Won/cm 2 , 1.30 Won/kg, and -1.72 Won/day for backfat thickness, eye muscle area, carcass weights, and raising period, respectively. Parameters for dummy variables of marbling scores varied from 0 to 7338.80 Won/kg, which means that the grades of each marbling score had different price values. The unit price of sales during traditional holidays was significantly higher (827.71 Won/kg for cows, and 645.15 Won/kg for steers) than during non-holidays.We conclude that the use of categorical values for marbling scores would be needed to evaluate the price of Hanwoo beef using multiple regression analysis based on carcass traits and environmental factors.

In the first article in this series we explored the use of linear regression to predict an outcome variable from a number of predictive factors. It assumed that the predictive factors were measured on an interval scale. However, this article shows how categorical variables can also be included in a linear regression model, enabling predictions to be made separately for different groups and allowing for testing the hypothesis that the outcome differs between groups. The use of interaction terms to measure whether the effect of a particular predictor variable differs between groups is also explained. An alternative approach to testing the difference between groups of the effect of a given predictor, which consists of measuring the effect in each group separately and seeing whether the statistical significance differs between the groups, is shown to be misleading., (© The Author 2013. Published by Oxford University Press on behalf of the British Society for Rheumatology. All rights reserved. For Permissions, please email: journals.permissions@oup.com.)