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The application of correlation models for the analysis of market risk factors in KGHM capital group
Published in Christoph Mueller, Winfred Assibey-Bonsu, Ernest Baafi, Christoph Dauber, Chris Doran, Marek Jerzy Jaszczuk, Oleg Nagovitsyn, Mining Goes Digital, 2019
Łukasz Bielak, Paweł Miśta, Anna Michalak, Agnieszka Wyłomańska
After visual inspection, we propose to quantify the relationship between the selected market risk factors. We propose to take under consideration three different measures of dependence. The first one is the classical Pearson correlation coefficient [1]. In statistics, the Pearson correlation coefficient is a measure of the linear relation between two variables X and Y. According to the Cauchy–Schwarz inequality it has a value between +1 and −1, where 1 is total positive linear correlation, 0 is no linear correlation, and −1 is total negative linear correlation. This is the most classical dependence measure and its empirical version for two time series x = (x1, x2, …, xn) and y = (y1, y2, …, yn) is defined as follows [13]: () ρxy=σxy2σxxσyy,
2
Published in Eric W. Harmsen, Megh R. Goyal, Flood Assessment, 2017
The Pearson correlation coefficient measures the strength of the linear relationship between the X and Y variables on a probability plot (The value close to 1 indicates that the relationship is highly linear). Almost all graphs present Pearson correlation coefficient values above 0.93. The event that presents the lowest was August 28, 2008 (Figure 7.15A) for peak flows with 0.875 coefficient of determination. Additional information such as mean and standard deviation of the ensemble are shown in Figures 7.12–7.16. The lowest extreme values in peak and runoff depth did not have good agreement with the PDF, and was produced by low initial soil saturation values (0.25) in combination with high hydraulic conductivities. In general, the ensemble means and standard deviation decreased with increasing rain resolution input or increase of model resolution.
Energy Analysis Techniques
Published in Clive Beggs, Energy: Management, Supply and Conservation, 2010
The regression analysis method described in Section 6.5.1 enables a best-fit straight line to be determined for a sample data set. However, in some circumstances the sample data points may be very scattered with the result that the derived equation may be meaningless. It is therefore important to determine how well the best-fit line correlates to the sample data. This can be done by calculating the Pearson correlation coefficient [3], which gives an indication of the reliability of the line drawn. The Pearson correlation coefficient is a value between 1 and 0, with a value of 1 representing 100% correlation. The Pearson correlation coefficient (r) can be determined using eqn (6.4): r=∑(x−x¯)(y−y¯)[∑(x−x¯)2∑(y−y¯)2]
A prediction model of the friction coefficient of asphalt pavement considering traffic volume and road surface characteristics
Published in International Journal of Pavement Engineering, 2023
Miao Yu, Shikang Liu, Zhanping You, Zhi Yang, Jue Li, LiMing Yang, Geng Chen
First, SPSS software was used to analyze the correlation between the micro-texture parameters and the dynamic friction coefficient of the three groups of asphalt mixture specimens. The common Pearson correlation method was used to calculate the correlation between the texture characteristic parameters and the dynamic friction coefficient. The range of Pearson correlation coefficient is between −1 and 1. Generally, |r| ≥ 0.8 indicates a very strong correlation between variables; 0.6 ≤ |r| < 0.8 indicates a strong correlation between variables; 0.4 ≤ |r| < 0.6 indicates a moderate correlation between variables; 0.2 ≤ |r| < 0.4 indicates a weak correlation between variables; and |r| < 0.2 indicates a very weak correlation between variables. It can be seen in the Table 7 correlation analysis results that the absolute value of the linear correlation coefficient between the surface texture feature parameters of coarse aggregate and the road friction coefficient is not larger than 0.544, indicating that the correlation between the texture feature parameters and the road friction coefficient was not obvious in this study.
Energy simulation and variable analysis of refining process in thermo-mechanical pulp mill using machine learning approach
Published in Mathematical and Computer Modelling of Dynamical Systems, 2021
B. Talebjedi, T. Laukkanen, H. Holmberg, E. Vakkilainen, S. Syri
On the other hand, it is not possible to use the Pearson correlation coefficient or other similar methods to detect influential refining variables for refining motor load simulation. The use of the Pearson correlation coefficient has assumptions, the violation of which leads to erroneous and unreliable results. Normality, linearity, and no outliers are among the most vital hypotheses that do not apply to the measured data from the studied mills. In this regard, Figure 4 shows the relationship between the first- and second-stage refining dilution water (in mill 2) after the outlier discarding process. As it is clear from Figure 4, two assumptions, linearity and no outlier, are not satisfied even after massive outlier detection and removal. The obtained correlation coefficient between these variables is 0.7; nevertheless, this value does not correspond to the scatter plot where no linear correlation is found. This is also true for the correlation between other refining variables received from studied mills.
Demonstration of the Advanced Dynamic System Modeling Tool TRANSFORM in a Molten Salt Reactor Application via a Model of the Molten Salt Demonstration Reactor
Published in Nuclear Technology, 2020
M. Scott Greenwood, Benjamin R. Betzler, A. Lou Qualls, Junsoo Yoo, Cristian Rabiti
In this study, the Pearson correlation coefficient was also estimated to gain an understanding of the relationship between the selected input and output parameters. The Pearson correlation coefficient is a test statistic to measure the statistical relationship between the two variables.50 To determine whether the relationship is statistically significant, a statistical hypothesis test was employed, along with the estimated values of Pearson’s correlation coefficients. Specifically, the two-tailed t-test was performed with a null hypothesis stating that “there is no statistical relationship between the two parameters.” To implement this approach, the t-statistic t must be calculated as shown in Eq. (16):