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1

Zheng, Qi, and James H. Matis. "Correlation Coefficient Revisited." American Statistician 48, no. 3 (August 1994): 240. http://dx.doi.org/10.2307/2684726.

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2

Sedgwick, P. "Intraclass correlation coefficient." BMJ 346, mar22 1 (March 22, 2013): f1816. http://dx.doi.org/10.1136/bmj.f1816.

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3

Sedgwick, P. "Pearson's correlation coefficient." BMJ 345, jul04 1 (July 4, 2012): e4483-e4483. http://dx.doi.org/10.1136/bmj.e4483.

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4

Zheng, Qi, and James H. Matis. "Correlation Coefficient Revisited." American Statistician 48, no. 3 (August 1994): 240–41. http://dx.doi.org/10.1080/00031305.1994.10476066.

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5

M. Tratz, Christine, Patton L. Fast, and Donald G. Truhlar. "Improved coefficients for the scaling all correlation and multi-coefficient correlation methods." PhysChemComm 2, no. 14 (1999): 70. http://dx.doi.org/10.1039/a908207g.

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6

Shieh, Gwowen. "Improved procedures and computer programs for equivalence assessment of correlation coefficients." PLOS ONE 16, no. 5 (May 28, 2021): e0252323. http://dx.doi.org/10.1371/journal.pone.0252323.

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The correlation coefficient is the most commonly used measure for summarizing the magnitude and direction of linear relationship between two response variables. Considerable literature has been devoted to the inference procedures for significance tests and confidence intervals of correlations. However, the essential problem of evaluating correlation equivalence has not been adequately examined. For the purpose of expanding the usefulness of correlational techniques, this article focuses on the Pearson product-moment correlation coefficient and the Fisher’s z transformation for developing equivalence procedures of correlation coefficients. Equivalence tests are proposed to assess whether a correlation coefficient is within a designated reference range for declaring equivalence decisions. The important aspects of Type I error rate, power calculation, and sample size determination are also considered. Special emphasis is given to clarify the nature and deficiency of the two one-sided tests for detecting a lack of association. The findings demonstrate the inappropriateness of existing methods for equivalence appraisal and validate the suggested techniques as reliable and primary tools in correlation analysis.
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7

Bradley, Christopher. "The Absolute Correlation Coefficient." Mathematical Gazette 69, no. 447 (March 1985): 12. http://dx.doi.org/10.2307/3616441.

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8

Novak, S. Y. "On Gebelein's correlation coefficient." Statistics & Probability Letters 69, no. 3 (September 2004): 299–303. http://dx.doi.org/10.1016/j.spl.2004.06.026.

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9

MIMOTO, Tomoaki, Hiroyuki YOKOYAMA, Toru NAKAMURA, Takamasa ISOHARA, Masayuki HASHIMOTO, Ryosuke KOJIMA, Aki HASEGAWA, and Yasushi OKUNO. "Privacy-Preserving Correlation Coefficient." IEICE Transactions on Information and Systems E106.D, no. 5 (May 1, 2023): 868–76. http://dx.doi.org/10.1587/transinf.2022dap0014.

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10

LYU, JIANHUA, CHENG GUAN, XIANWEI LI, and MING CHEN. "EFFECTS OF STAND DENSITY ON TURPENTINE TERPENE COMPONENTS AND RESIN DUCT MORPHOLOGICAL STRUCTURE OF PINUS MASSONIANA." WOOD RESEARCH 66(4) 2021 66, no. 4 (September 9, 2021): 643–56. http://dx.doi.org/10.37763/wr.1336-4561/66.4.643656.

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The influence of stand density on the resin duct morphological structure and terpene components of Pinus massonianawere studied. The resin duct morphological characteristics and the relative content of the terpene components were investigated by microscopyand gas chromatography-mass spectroscopy, respectively. The experimental results revealed that there was a specific correlation between thestand density andresin duct area, resin duct diameter, and the relative contents of main terpene components in the turpentine extracts. Additionally, the relative contents of β-pinene and (+)-camphene were positively correlated with stand density, with correlation coefficients of 0.8208and 0.5539, respectively.In contrast, the relative contents of(+)-longifolene and (+)-longicyclene were negatively correlated with stand density, with correlation coefficients of -0.5750and -0.7726, respectively, andα-pinene, β-caryophyllene, and (+)-α-longipinene had no correlation with stand density. The relative content of (+)-α-pinene was negatively correlated with the relative contents of both (+)-longifolene and (+)-longicyclene,with correlation coefficients of-0.8770 and -0.8914, respectively. There were positive correlations between the relative contents of (+)-longifolene and (+)-longicyclenewith correlation coefficient of0.9718, (+)-longifolene and (+)-α-longipinenewith correlation coefficient of0.8399,β-caryophyllene and (+)-α-longipinenewith correlation coefficient of0.9360, and (+)-longicyclene and (+)-α-longipinenewith correlation coefficient of0.8626.
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11

Domínguez, Marisela. "Mixing coefficient, generalized maximal correlation coefficients, and weakly positive measures." Journal of Multivariate Analysis 43, no. 1 (October 1992): 110–24. http://dx.doi.org/10.1016/0047-259x(92)90111-r.

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12

Wu, Berlin, and Chin Feng Hung. "Innovative Correlation Coefficient Measurement with Fuzzy Data." Mathematical Problems in Engineering 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/9094832.

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Correlation coefficients are commonly found with crisp data. In this paper, we use Pearson’s correlation coefficient and propose a method for evaluating correlation coefficients for fuzzy interval data. Our empirical studies involve the relationship between mathematics achievement and other projects.
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13

YAMAMOTO, Fujio, Ari-isa WADA, Xiang-Qun SONG, Yuichi MURAI, Masa-aki ISHIKAWA, and Manabu IGUCHI. "Discussion on Cross-Correlation Coefficient." Journal of the Visualization Society of Japan 17, Supplement1 (1997): 129–32. http://dx.doi.org/10.3154/jvs.17.supplement1_129.

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14

Chambers, Ll G. "73.52 Spearman's Rank Correlation Coefficient." Mathematical Gazette 73, no. 466 (December 1989): 331. http://dx.doi.org/10.2307/3619313.

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15

I. C. A, Oyeka, and Nwankwo Chike, H. "Ties Adjusted Rank Correlation Coefficient." IOSR Journal of Mathematics 10, no. 5 (2014): 09–17. http://dx.doi.org/10.9790/5728-10530917.

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16

Okamoto, Yasuharu. "Predictive assessment and correlation coefficient." Proceedings of the Annual Convention of the Japanese Psychological Association 84 (September 8, 2020): PC—017—PC—017. http://dx.doi.org/10.4992/pacjpa.84.0_pc-017.

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17

Bryc, Wlodzimierz, Wlodzimierz Bryc, Amir Dembo, Amir Dembo, Abram Kagan, and Abram Kagan. "On the maximum correlation coefficient." Teoriya Veroyatnostei i ee Primeneniya 49, no. 1 (2004): 190–97. http://dx.doi.org/10.4213/tvp246.

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18

Bryc, W., and A. Dembo. "On the Maximum Correlation Coefficient." Theory of Probability & Its Applications 49, no. 1 (January 2005): 132–38. http://dx.doi.org/10.1137/s0040585x97980968.

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19

Lord, Nick. "Properties of the correlation coefficient." Teaching Statistics 13, no. 2 (June 1991): 42–43. http://dx.doi.org/10.1111/j.1467-9639.1991.tb00162.x.

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20

Burghes, David N. "Teaching Spearman's Rank Correlation Coefficient." Teaching Statistics 15, no. 3 (September 1993): 68–69. http://dx.doi.org/10.1111/j.1467-9639.1993.tb00658.x.

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21

Becker, Gilbert, and Robert L. Thorndike. "The Biserial-Phi Correlation Coefficient." Journal of Psychology 122, no. 5 (September 1988): 523–26. http://dx.doi.org/10.1080/00223980.1988.10542957.

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22

Krehbiel, Timothy C. "Correlation Coefficient Rule of Thumb." Decision Sciences Journal of Innovative Education 2, no. 1 (January 2004): 97–100. http://dx.doi.org/10.1111/j.0011-7315.2004.00025.x.

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23

Guedes, E. F., A. A. Brito, F. M. Oliveira Filho, B. F. Fernandez, A. P. N. de Castro, A. M. da Silva Filho, and G. F. Zebende. "Statistical test forΔρDCCAcross-correlation coefficient." Physica A: Statistical Mechanics and its Applications 501 (July 2018): 134–40. http://dx.doi.org/10.1016/j.physa.2018.02.148.

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24

Zebende, G. F., and A. M. da Silva Filho. "Detrended Multiple Cross-Correlation Coefficient." Physica A: Statistical Mechanics and its Applications 510 (November 2018): 91–97. http://dx.doi.org/10.1016/j.physa.2018.06.119.

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25

Asuero, A. G., A. Sayago, and A. G. González. "The Correlation Coefficient: An Overview." Critical Reviews in Analytical Chemistry 36, no. 1 (January 2006): 41–59. http://dx.doi.org/10.1080/10408340500526766.

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26

Yu, Yaming. "On the maximal correlation coefficient." Statistics & Probability Letters 78, no. 9 (July 2008): 1072–75. http://dx.doi.org/10.1016/j.spl.2007.10.006.

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27

Wilcox, Rand R. "The percentage bend correlation coefficient." Psychometrika 59, no. 4 (December 1994): 601–16. http://dx.doi.org/10.1007/bf02294395.

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28

Bedrick, Edward J., and Frederick C. Breslin. "Estimating the polyserial correlation coefficient." Psychometrika 61, no. 3 (September 1996): 427–43. http://dx.doi.org/10.1007/bf02294548.

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29

Emerson, Robert Wall. "Causation and Pearson's Correlation Coefficient." Journal of Visual Impairment & Blindness 109, no. 3 (May 2015): 242–44. http://dx.doi.org/10.1177/0145482x1510900311.

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30

Abdullah, Mokhtar Bin. "On a Robust Correlation Coefficient." Statistician 39, no. 4 (1990): 455. http://dx.doi.org/10.2307/2349088.

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31

González, A. Gustavo, M. Ángeles Herrador, Agustín G. Asuero, and Ana Sayago. "The correlation coefficient attacks again." Accreditation and Quality Assurance 11, no. 5 (May 18, 2006): 256–58. http://dx.doi.org/10.1007/s00769-006-0153-5.

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32

Liao, Jason J. Z. "An improved concordance correlation coefficient." Pharmaceutical Statistics 2, no. 4 (2003): 253–61. http://dx.doi.org/10.1002/pst.52.

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33

Ahn, Sojin, and Dae-Heung Jang. "Applications of Chatterjee correlation coefficient." Korean Journal of Applied Statistics 36, no. 3 (June 30, 2023): 261–69. http://dx.doi.org/10.5351/kjas.2023.36.3.261.

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34

H.O., Etaga, Okoro I., Aforka K.F., and Ngonadi L.O. "Methods of Estimating Correlation Coefficients in the Presence of Influential Outlier(s)." African Journal of Mathematics and Statistics Studies 4, no. 3 (December 20, 2021): 157–85. http://dx.doi.org/10.52589/ajmss-llnzxuoz.

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Correlation methods are indispensable in the study of the linear relationship between two variables. However, many researchers often adopt inappropriate correlation methods in the study of linear relationships which usually leads to unreliable results. Recurrently, most researchers ignorantly employ the Pearson method in a dataset that contained outliers, instead of more appropriate correlation methods such as Spearman, Kendall Tau, Median and Quadrant which might be suitable in the calculation of correlation coefficient in the presence of influential outliers. It is noted that the accuracy of estimation of correlation coefficients under outliers has been a long-standing problem for methodological researchers. This is due to low knowledge of correlation methods and their assumptions which have led to inappropriate application of correlation methods in research analysis. Five different methods of estimating correlation coefficients in the presence of influential outlier (contaminated data) were considered: Pearson Correlation Coefficient, Spearman Correlation Coefficient, Kendall Tau Correlation Coefficient, Median Correlation Coefficient and Quadrant Correlation Coefficient.
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35

Cao, Guangxi, Cuiting He, and Wei Xu. "Effect of Weather on Agricultural Futures Markets on the Basis of DCCA Cross-Correlation Coefficient Analysis." Fluctuation and Noise Letters 15, no. 02 (June 2016): 1650012. http://dx.doi.org/10.1142/s0219477516500127.

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This study investigates the correlation between weather and agricultural futures markets on the basis of detrended cross-correlation analysis (DCCA) cross-correlation coefficients and [Formula: see text]-dependent cross-correlation coefficients. In addition, detrended fluctuation analysis (DFA) is used to measure extreme weather and thus analyze further the effect of this condition on agricultural futures markets. Cross-correlation exists between weather and agricultural futures markets on certain time scales. There are some correlations between temperature and soybean return associated with medium amplitudes. Under extreme weather conditions, weather exerts different influences on different agricultural products; for instance, soybean return is greatly influenced by temperature, and weather variables exhibit no effect on corn return. Based on the detrending moving-average cross-correlation analysis (DMCA) coefficient and DFA regression results are similar to that of DCCA coefficient.
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36

Dong, Keqiang, Hong Zhang, and You Gao. "Modeling Complex System Correlation Using Detrended Cross-Correlation Coefficient." Mathematical Problems in Engineering 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/230537.

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The understanding of complex systems has become an area of active research for physicists because such systems exhibit interesting dynamical properties such as scale invariance, volatility correlation, heavy tails, and fractality. We here focus on traffic dynamic as an example of a complex system. By applying the detrended cross-correlation coefficient method to traffic time series, we find that the traffic fluctuation time series may exhibit cross-correlation characteristic. Further, we show that two traffic speed time series derived from adjacent sections exhibit much stronger cross-correlations than the two speed series derived from adjacent lanes. Similarly, we also demonstrate that the cross-correlation property between the traffic volume variables from two adjacent sections is stronger than the cross-correlation property between the volume variables of adjacent lanes.
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37

Balakrishna, P., Rajasekhar Pinnamaneni, KV Pavani, and RK Mathur. "Correlation and Path Coefficient Analysis in Indian Oil Palm genotypes." Journal of Pure and Applied Microbiology 12, no. 1 (March 30, 2018): 195–206. http://dx.doi.org/10.22207/jpam.12.1.25.

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38

Chen, Chia-Cheng, and Huiman X. Barnhart. "Assessing agreement with intraclass correlation coefficient and concordance correlation coefficient for data with repeated measures." Computational Statistics & Data Analysis 60 (April 2013): 132–45. http://dx.doi.org/10.1016/j.csda.2012.11.004.

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39

Adler, Jeremy, and Ingela Parmryd. "Quantifying colocalization by correlation: The Pearson correlation coefficient is superior to the Mander's overlap coefficient." Cytometry Part A 77A, no. 8 (March 30, 2010): 733–42. http://dx.doi.org/10.1002/cyto.a.20896.

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40

Zebende, G. F. "DCCA cross-correlation coefficient: Quantifying level of cross-correlation." Physica A: Statistical Mechanics and its Applications 390, no. 4 (February 2011): 614–18. http://dx.doi.org/10.1016/j.physa.2010.10.022.

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41

Gui-zhi, Ju, and Zhao Ya-qun. "Correlation degree and correlation coefficient of multi-output functions." Wuhan University Journal of Natural Sciences 10, no. 1 (January 2005): 195–98. http://dx.doi.org/10.1007/bf02828648.

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42

Du, Wen Sheng. "Correlation and correlation coefficient of generalized orthopair fuzzy sets." International Journal of Intelligent Systems 34, no. 4 (November 2, 2018): 564–83. http://dx.doi.org/10.1002/int.22065.

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43

Sangngam, Prayad. "Ratio Estimators Using Coefficient of Variation and Coefficient of Correlation." Modern Applied Science 8, no. 5 (August 5, 2014): 70. http://dx.doi.org/10.5539/mas.v8n5p70.

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This paper introduces ratio estimators of the population mean using the coefficient of variation of study variable and auxiliary variables together with the coefficient of correlation between the study and auxiliary variables under simple random sampling and stratified random sampling. These ratio estimators are almost unbiased. The mean square errors of the estimators and their estimators are given. Sample size estimation in both sampling designs are presented. An optimal sample size allocation in stratified random sampling is also suggested. Based on theoretical study, it can be shown that these ratio estimators have smaller MSE than the unbiased estimators. Moreover, the empirical study indicates that these ratio estimators have smallest MSE compared to the existing ones.
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44

Wang, Gang-Jin, Chi Xie, Shou Chen, Jiao-Jiao Yang, and Ming-Yan Yang. "Random matrix theory analysis of cross-correlations in the US stock market: Evidence from Pearson’s correlation coefficient and detrended cross-correlation coefficient." Physica A: Statistical Mechanics and its Applications 392, no. 17 (September 2013): 3715–30. http://dx.doi.org/10.1016/j.physa.2013.04.027.

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45

Kader, Gary, and Christine Franklin. "The Evolution of Pearson's Correlation Coefficient." Mathematics Teacher 102, no. 4 (November 2008): 292–99. http://dx.doi.org/10.5951/mt.102.4.0292.

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Studying the relationship between two quantitative variables is a standard topic in statistics. In high school and introductory college-level statistics, Pearson's correlation coefficient, r, is typically included as a measure of the direction and strength of the linear relationship between two quantitative variables. This article describes an activity that aids an intuitive development of the formula for r and its interpretation. Exploring scatter plots allows students to develop an intermediate measure of association called the quadrant count ratio (QCR), investigate properties of the QCR, and develop Pearson's r to address some of the QCR's shortcomings.
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46

Broumi, Said, and Florentin Smarandache. "Correlation Coefficient of Interval Neutrosophic Set." Applied Mechanics and Materials 436 (October 2013): 511–17. http://dx.doi.org/10.4028/www.scientific.net/amm.436.511.

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47

Dembo, Amir, Abram Kagan, and Lawrence A. Shepp. "Remarks on the Maximum Correlation Coefficient." Bernoulli 7, no. 2 (April 2001): 343. http://dx.doi.org/10.2307/3318742.

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48

Korol, A. M., P. Foresto, M. Darrigo, and O. A. Rosso. "Diabetic Erythrocytes Test by Correlation Coefficient." Open Medical Informatics Journal 2, no. 1 (October 9, 2008): 105–11. http://dx.doi.org/10.2174/1874431100802010105.

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49

KAYA, Mehmet Onur, Yunus GÜRAL, and Mehmet GÜRCAN. "Entropy, Information and Entropy Correlation Coefficient." Turkiye Klinikleri Journal of Biostatistics 12, no. 1 (2020): 83–88. http://dx.doi.org/10.5336/biostatic.2020-74305.

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50

Bundala, Ntogwa Ng’habi. "Homo-Hetero Pairing Effect Correlation Coefficient." International Journal of Business, Management and Economics 3, no. 3 (July 11, 2022): 213–56. http://dx.doi.org/10.47747/ijbme.v3i3.706.

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The study aimed to examine the pairing relationship between economic growth and psychological human behavior (psychological well-being) of the individuals by application of the homo-hetero pairing effect correlation coefficient technique. The cross-sectional data were used. The data were collected from 211 individuals randomly sampled from two regions in Tanzania. The data were analysed by homo-hetero pairing effect correlation coefficient and the results were compared to that of the Pearson correlation coefficient and simple regression model. The study found that economic growth and psychological well-being are positively changing in pairs, and the psychological well-being of the individual is the true enabler (optimal independent) of the linear modelling. The study concluded that the improvement of the psychological well-being of individuals significantly improves economic growth and not vice versa. Therefore, the paper recommended that psychological well-being-based initiatives should be established and encouraged in society as found to have a positive impact on economic growth. Moreover, the study specifically, recommends the application of the homo-hetero pairing correlation coefficient in studies of cardiology, neurology, epidemiology, psychology, economics, anthropology, sociology and other fields of the social sciences.
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