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"Independent variables"
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Energy Efficiency Modeling of Integrated Energy System in Coastal Areas
Yang, C.; Gao, F., and Dong, M., 2020. Energy efficiency modeling of integrated energy system in coastal areas. In: Yang, Y.; Mi, C.; Zhao, L., and Lam, S. (eds.), Global Topics and New Trends in Coastal Research: Port, Coastal and Ocean Engineering. Journal of Coastal Research, Special Issue No. 103, pp. 995–1001. Coconut Creek (Florida), ISSN 0749-0208. In order to overcome the problem of large energy consumption cost in the traditional energy efficiency modeling method of integrated energy system, the energy efficiency modeling method of integrated energy system in coastal area is proposed to reduce the energy consumption cost of integrated energy system in coastal area. Based on the energy network of the integrated energy system, the energy conversion relationship of the integrated energy system is analyzed, and a group of independent variables in the energy network is selected to calculate the complexity of the energy network. The time-varying energy network equation of the comprehensive energy system is established by establishing the difference matrix of the strength at both ends of the branch. Combined with the process of energy efficiency modeling of integrated energy system in coastal areas, the cost of energy efficiency modeling of integrated energy system is improved, and the energy efficiency modeling of integrated energy system is realized. The simulation results show that the proposed energy efficiency modeling method has lower energy consumption cost in the process of energy efficiency modeling.
Journal Article
Approximated Uncertainty Propagation of Correlated Independent Variables Using the Ordinary Least Squares Estimator
For chemical measurements, calibration is typically conducted by regression analysis. In many cases, generalized approaches are required to account for a complex-structured variance–covariance matrix of (in)dependent variables. However, in the particular case of highly correlated independent variables, the ordinary least squares (OLS) method can play a rational role with an approximated propagation of uncertainties of the correlated independent variables into that of a calibrated value for a particular case in which standard deviation of fit residuals are close to the uncertainties along the ordinate of calibration data. This proposed method aids in bypassing an iterative solver for the minimization of the implicit form of the squared residuals. This further allows us to derive the explicit expression of budgeted uncertainties corresponding to a regression uncertainty, the measurement uncertainty of the calibration target, and correlated independent variables. Explicit analytical expressions for the calibrated value and associated uncertainties are given for straight-line and second-order polynomial fit models for the highly correlated independent variables.
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The multicollinearity illusion in moderated regression analysis
Numerous papers in the fields of marketing and consumer behavior that utilize moderated multiple regression express concerns regarding the existence of a multicollinearity problem in their analyses. In most cases, however, as we show in this paper, the perceived multicollinearity problem is merely an illusion that arises from misinterpreting high correlations between independent variables and interaction terms.
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Dimension-Free Estimators of Gradients of Functions with(out) Non-Independent Variables
This study proposes a unified stochastic framework for approximating and computing the gradient of every smooth function evaluated at non-independent variables, using ℓp-spherical distributions on Rd with d,p≥1. The upper-bounds of the bias of the gradient surrogates do not suffer from the curse of dimensionality for any p≥1. Additionally, the mean squared errors (MSEs) of the gradient estimators are bounded by K0N−1d for any p∈[1,2], and by K1N−1d2/p when 2≤p≪d with N the sample size and K0,K1 some constants. Taking max2,log(d)
Journal Article
Straight Line Fitting and Predictions
Even in the simple case of univariate linear regression and prediction there are important choices to be made regarding the origins of the noise terms and regarding which of the two variables under consideration that should be treated as the independent variable. These decisions are often not easy to make but they may have a considerable impact on the results. A unified probabilistic (i.e., Bayesian with flat priors) treatment of univariate linear regression and prediction is given by taking, as starting point, the general errors-in-variables model. Other versions of linear regression can be obtained as limits of this model. The likelihood of the model parameters and predictands of the general errors-in-variables model is derived by marginalizing over the nuisance parameters. The resulting likelihood is relatively simple and easy to analyze and calculate. The well-known unidentifiability of the errors-in-variables model is manifested as the absence of a well-defined maximum in the likelihood. However, this does not mean that probabilistic inference cannot be made; the marginal likelihoods of model parameters and the predictands have, in general, well-defined maxima. A probabilistic version of classical calibration is also included and it is shown how it is related to the errors-in-variables model. The results are illustrated by an example fromthe coupling between the lower stratosphere and the troposphere in the Northern Hemisphere winter.
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Machine Learning-Based Modeling of Air Temperature in the Complex Environment of Yerevan City, Armenia
Machine learning (ML) was used to assess and predict urban air temperature (Tair) considering the complexity of the terrain features in Yerevan (Armenia). The estimation was performed based on the Partial Least-Squares Regression (PLSR) model with a high number (30) of input variables. The relevant parameters include a newly purposed modification of spectral index IBI-SAVI, which turned out to strongly impact Tair prediction together with land surface temperature (LST). Cross-validation analysis on temperature predictions across a station-centered 1000 m circular area revealed quite a high correlation (R2Val = 0.77, RMSEVal = 1.58) between the predicted and measured Tair from the test set. It was concluded the remote sensing is an effective tool to estimate Tair distribution where a dense network of weather stations is not available. However, further developments will include incorporation of additional weather parameters from the weather stations, such as precipitation and wind speed, as well as the use of non-parametric ML techniques.
Journal Article
Multidimensional regular C-fraction with independent variables corresponding to formal multiple power series
In the paper the correspondence between a formal multiple power series and a special type of branched continued fractions, the so-called ‘multidimensional regular C-fractions with independent variables’ is analysed providing with an algorithm based upon the classical algorithm and that enables us to compute from the coefficients of the given formal multiple power series, the coefficients of the corresponding multidimensional regular C-fraction with independent variables. A few numerical experiments show, on the one hand, the efficiency of the proposed algorithm and, on the other, the power and feasibility of the method in order to numerically approximate certain multivariable functions from their formal multiple power series.
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Investigation of ensemble methods in terms of statistics: TIMMS 2019 example
In this study, it is aimed to determine the factors affecting the mathematics achievements of eighth-grade students through trends in international mathematics and science study 2019 and compare the classification performances according to sample sizes and the number of independent variables of Bagging and Adaboost methods. Firstly, the most important factors affecting mathematics skills were obtained by using feature selection methods. Then, the performances of the methods were examined according to the sample size and the number of variables. As a result of the analysis carried out, no obvious difference was found between the performances of the methods according to the number of independent variables. On the other hand, the performances of methods of this study varied according to sample sizes, and it was seen that Bagging method showed better classification performance than Adaboost method in all sample sizes, and the performance of both methods approached each other when a sample of 3000 units was used.
Journal Article
Identification of Independent Variables to Assess Green-Building Development in China Based on Grounded Theory
Background: Development of green building as future buildings has become a trend and played a significant role in changing the general direction of building development and creating an environment for sustainable development ’People-centric’ explores the relationship between people and building development. From the perspective of users, what are the influencing factors of green building? What is the relationship between independent variables? The authors link this issue to the development of green building and gaining a clearer understanding and direction. Methods: The authors applied grounded theory and intensity sampling to analyse the relationships of independent variables. Results: The findings of this study reveal the four core factors affecting how independent variables get to learn about green building, which are ‘personal perception elements’, ‘social elements’, ‘organisational elements’, and ‘architectural properties’. Conclusions: The authors also analysed the relationships between the independent variables to explore construction theory for helping green building better respond to people’s demand and pushing forward its development. In this case, the ’people-centric’ green building further improves the urban living environment.
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Misleading Heuristics and Moderated Multiple Regression Models
Moderated multiple regression models allow the simple relationship between the dependent variable and an independent variable to depend on the level of another independent variable. The moderated relationship, often referred to as the interaction, is modeled by including a product term as an additional independent variable. Moderated relationships are central to marketing (e.g., Does the effect of promotion on sales depend on the market segment?). Multiple regression models not including a product term are widely used and well understood. The authors argue that researchers have derived from this simpler type of multiple regression several data analysis heuristics that, when inappropriately generalized to moderated multiple regression, can result in faulty interpretations of model coefficients and incorrect statistical analyses. Using theoretical arguments and constructed data sets, the authors describe these heuristics, discuss how they may easily be misapplied, and suggest some good practices for estimating, testing, and interpreting regression models that include moderated relationships.
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