The basics of determining the coefficients of a linear correlation

2020 ◽  
Vol 65 (6) ◽  
pp. 69-87 ◽  
Author(s):  
Zbigniew Śleszyński
Keyword(s):  
Correlation Coefficient ◽  
Linear Correlation ◽  
Partial Correlation ◽  
Least Squares Method ◽  
Pearson Correlation ◽  
Coefficient Of Determination ◽  
Regression Equations ◽  
Multivariate Correlation ◽  
Mutual Relations ◽  
Partial Correlation Coefficient

The aim of the paper is to present the basic measures related to the analysis of relationships between quantitative variables used in econometric modelling and their selected applications. The following measures are discussed: the Pearson correlation coefficient, the multivariate correlation coefficient, coefficient of determination, partial correlation coefficient and semi-partial correlation coefficient. A homogeneous approach is applied to the measures presented. Each is defined as a linear correlation coefficient of relevant vectors derived from regression equations. Additionally, mutual relations between the coefficients are described. Bordered matrices have been applied to the calculations, which significantly simplified the process, while the Statistica 13.3 PL program was used to verify the correctness of the calculations. The issue is illustrated in the model of regression of salary growth in Poland in the years 2001–2019 with four covariates, estimated using the least squares method.

scholarly journals FOREST COVERAGE AND STREAMFLOW OF WATERSHEDS IN THE TROPICAL ATLANTIC RAINFOREST

2018 ◽  
Vol 42 (2) ◽  
Author(s):  
Natalia Gomes de Souza Mendes ◽  
Roberto Avelino Cecílio ◽  
Sidney Sara Zanetti
Keyword(s):  
Linear Regression ◽  
Multiple Linear Regression ◽  
Correlation Coefficient ◽  
Partial Correlation ◽  
Forest Cover ◽  
Regression Equations ◽  
Tropical Atlantic ◽  
Forest Coverage ◽  
Partial Correlation Coefficient ◽  
Forest Biome

ABSTRACT The present study analyzed the average and minimum streamflow behavior of 11 watersheds located in the Atlantic Forest Biome, relating them to the changes in forest cover. The average minimum flow with seven days of duration (Q7), the average annual flow (Qave), the total annual precipitation (Pa) and the percentage of forest cover (FC) for each watershed were determined. The joint correlation between the FC and the Pa with the flow for each watershed were analyzed by adjusting multiple linear regression equations. The partial correlation coefficient was also used to analyze whether the variation in the FC influenced the water flow when the effects of Pa are fixed. This study allowed us to identify significant associations between FC and Pa with Q7 or Qave in only two of the watersheds. Disregarding the effects of Pa, the increase in the FC tended to result in a reduction in the Qave, and in turn increased the Q7 in these two watersheds.

scholarly journals Pengaruh Kecemasan Matematika dan Motivasi Belajar terhadap Prokrastinasi Akademik

2020 ◽  
Vol 3 (1) ◽  
pp. 42
Author(s):  
Nanda Mellenia Amin Putri ◽  
Ika Kurniasari
Keyword(s):  
Correlation Coefficient ◽  
Mathematics Anxiety ◽  
Partial Correlation ◽  
Mathematics Learning ◽  
Multiple Correlation Coefficient ◽  
Learning Motivation ◽  
Coefficient Of Determination ◽  
Academic Procrastination ◽  
Negative Effects ◽  
Partial Correlation Coefficient

Abstrak — Prokrastinasi adalah penundaan yang disengaja dalam mengerjakan suatu pekerjaan. Efek dari prokrastinasi dapat berakibat negatif pada emosi, mengakibatkan stress, dan akan mengganggu kegiatan sehari-hari. Jenis prokrastinasi yang berhubungan dengan kerja akademik adalah prokrastinasi akademik. Dengan mengingat pentingnya matematika dalam sehari-hari, peserta didik diharapkan dapat meminimalisir perilaku prokrastinasi akademik yang berefek negatif pada keoptimalan kerja akademik dan efikasi akademik pada matematika. Faktor-faktor yang dapat mempengaruhi tinggi rendahnya prokrastinasi akademik adalah kecemasan matematika dan motivasi belajar. Kecemasan matematika adalah kecemasan yang disebabkan oleh peristiwa yang berhubungan dengan matematika yang akan terjadi di masa yang akan datang. Sedangkan motivasi belajar adalah dorongan-dorongan yang membuat seseorang melakukan kegiatan belajar. Tujuan penelitian ini adalah untuk mengetahui pengaruh dari kecemasan matematika dan motivasi belajar terhadap prokrastinasi akademik. Dengan sampel 31 peserta didik SMAN 1 Krian, data dikumpulkan dengan menggunakan angket kecemasan matematika, angket motivasi belajar, dan angket prokrastinasi akademik. Pengaruh kecemasan matematika dan motivasi belajar terhadap prokrastinasi akademik dicari dengan menggunakan koefisien korelasi dan koefisien penentu. Koefisien korelasi berganda kecemasan matematika dan motivasi belajar dengan prokrastinasi akademik adalah 0,451 dengan koefisien penentu berganda 20,3%. Kemudian koefisien korelasi parsial kecemasan matematika dengan prokrastinasi akademik apabila motivasi belajar dikontrol adalah 0,423 dan koefisien penentu parsial sebesar 17,89%. Koefisien korelasi parsial motivasi belajar dengan prokrastinasi akademik apabila kecemasan matematika dikontrol adalah -0,141 dan koefisien penentu parsialnya adalah sebesar 1,98%.Kata Kunci: kecemasan matematika, motivasi belajar, prokrastinasi akademik. Abstract — Procrastination is an intentional delay in doing activities. Procrastination can cause negative effects on emotions, stress, and interfering with everyday life. Procrastination type that related to academic work is academic procrastination. On a more important note, we need to keep in mind how important mathematics is in our lives and students are expected to minimalize academic procrastination behavior that could make academic works less optimal and negative effects on academic efficacy on mathematics learning. Many factors could contribute to academic procrastination levels. Two of them are mathematics anxiety and learning motivation. Mathematics anxiety is an anxious feeling caused by events related to mathematics that will happen in the future. Whilst learning motivation is the stimulus that drives a person to learn. The aim of this research is to find out the relationship between mathematics anxiety and learning motivation with academic procrastination. Using 31 students of SMAN 1 Krian as the sample, the data is gathered with a mathematics anxiety questionnaire, learning motivation questionnaire, and academic procrastination questionnaire. The multiple correlation coefficient of mathematics anxiety and learning motivation with academic procrastination is 0,451 while the coefficient of determination is 20,3%. The partial correlation coefficient of mathematics anxiety with academic procrastination is 0,423 while the coefficient of determination is 17,89%. Lastly, the partial correlation coefficient of learning motivation with academic procrastination is -0,141 while the coefficient of determination is 1,98%.Keywords: mathematics anxiety, learning motivation, academic procrastination.

IMBALAN DAN GAYA KEPEMIMPINAN PENGARUHNYA TERHADAP KEPUASAN KERJA KARYAWAN DI BALAI BESAR INDUSTRI HASIL PERTANIAN BOGOR

2018 ◽  
Vol 1 (01) ◽  
pp. 17
Author(s):  
Ramlan Ruvendi
Keyword(s):  
Job Satisfaction ◽  
Multiple Regression ◽  
Correlation Coefficient ◽  
Analysis Of Variance ◽  
Partial Correlation ◽  
Multiple Correlation Coefficient ◽  
Multiple Correlation ◽  
Average Value ◽  
Partial Correlation Coefficient

The study was carried out to find out whether there were influence and correlation bet-ween : a) Reward received by the IRDABI’s employees on their job satisfaction. b) style of the leader-ship on the job satisfaction. c) Reward together with style of leadership on the job satisfaction of IR-DABI’s employees.The result of the study showed that there was significant correlation and influence between the reward on the job satisfaction with was shown by the value of partial correlation coefficient of 0.6185 and coefficient of multiple regression for reward variable (β1) of 0.412. The influence of variable for style of leadership on the job satisfaction was also significant with the partial correlation coefficient of 0.5495 and coefficient of multiple regression (β2) of 0.355.In the test of Analysis of Variance (ANOVA) on the equation of multiple regression show that F-value was bigger that F-table (F = 58.97 > F-table = 3.098) or the Probability Value smaller than 0.05. At showed that there was significant correlation and influence between reward variables all together with style of leadership on the job satisfaction of employees. The value of multiple correlation coefficient (R) was 0.751 and R Square (R2) was 0.564. Value of R Square (0.564) meant that 56.5% of variation pro-portion total of job satisfaction can be eliminated of equation of multiple regression was used as the es-timator rather than using average value of job satisfaction as the estimator.

scholarly journals Synovial fluid but not plasma interleukin-8 is associated with clinical severity and inflammatory markers in knee osteoarthritis women with joint effusion

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
María García-Manrique ◽  
Joan Calvet ◽  
Cristóbal Orellana ◽  
Antoni Berenguer-Llergo ◽  
Silvia Garcia-Cirera ◽  
...  
Keyword(s):  
Synovial Fluid ◽  
Knee Osteoarthritis ◽  
Correlation Coefficient ◽  
Inflammatory Markers ◽  
Partial Correlation ◽  
Statistical Significance ◽  
Clinical Severity ◽  
Joint Effusion ◽  
Cross Sectional ◽  
Partial Correlation Coefficient

AbstractSeveral cytokines and adipokines are related to clinical severity and progression in knee osteoarthritis. The aim of this study was to evaluate the associations of IL-8 with clinical severity and with local and systemic adipokines and cytokines. This is a Cross-sectional study including 115 women with symptomatic primary knee osteoarthritis with ultrasound-confirmed joint effusion. Age, symptoms duration and body mass index were collected. Radiographic severity was evaluated according to Kellgren–Lawrence. Pain and disability were assessed by Lequesne and Knee injury and Osteoarthritis Outcome Score pain, symptoms and function scales. Three inflammatory markers and five adipokines were measured by ELISA in serum and synovial fluid. Partial correlation coefficient (PCC) and corresponding 95% confidence interval were used to evaluate association. Synovial fluid IL-8 was significantly associated with clinical severity scales. After controlling for potential confounders, associations measured by a Partial Correlation Coefficient (PCC) remained essentially unaltered for Lequesne (PCC = 0.237), KOOS pain (PCC = − 0.201) and KOOS symptoms (PCC = − 0.209), KOOS function (PCC = − 0.185), although the later did not reach statistical significance. Also in synovial fluid samples, associations were found between IL-8 and TNF (PCC = 0.334), IL6 (PCC = 0.461), osteopontin (PCC = 0.575), visfatin (PCC = 0.194) and resistin (PCC = 0.182), although significance was not achieved for the later after statistical control for confounders. None of these associations were detected in serum. In conclusion, IL-8 was associated with clinical severity, inflammatory markers and adipokines in synovial fluid, but not in blood. Although the reported associations are weak to moderate in magnitude, these findings reinforce the notion that local and not systemic inflammation is more relevant to clinical severity in knee OA women with joint effusion.

Thyroid function in hyperemesis gravidarum

1989 ◽  
Vol 120 (2) ◽  
pp. 155-160 ◽  
Author(s):  
R. Swaminathan ◽  
R. K. Chin ◽  
T. T. H. Lao ◽  
Y. T. Mak ◽  
N. S. Panesar ◽  
...  
Keyword(s):  
Correlation Coefficient ◽  
Partial Correlation ◽  
Hyperemesis Gravidarum ◽  
Zinc Content ◽  
Normal Pregnancy ◽  
Uncomplicated Pregnancy ◽  
Wide Variability ◽  
Molecular Variant ◽  
Tissue Marker ◽  
Partial Correlation Coefficient

Abstract. Plasma total T4 (TT4), T3 (TT3), free T4 (FT4), free T3 (FT3), thyroxine binding globulin, hCG, and erythrocyte zinc content were measured in 43 women with uncomplicated pregnancy and in 71 patients admitted with hyperemesis gravidarum. Plasma concentration of thyroid hormones in hyperemesis subjects showed wide variability and 32% of subjects had high TT4 (higher than mean +2 sd of normal pregnant subjects), 33% had high FT4, 20% had high TT3, and 20% had high FT3. Red cell zinc content, a tissue marker of thyroid status, in the hyperthyroxinemic subjects was not different from that of normothyroxinemic hyperemesis subjects or of subjects with uncomplicated pregnancy. The elevated TT4 concentration decreased spontaneously in all but two of the hyperemesis subjects to normal pregnant levels. The plasma FT4 concentration at presentation correlated with plasma hCG in hyperemesis gravidarum (partial correlation coefficient r = 0.411, P< 0.01), but not in normal pregnancy (partial correlation coefficient r = 0.043) after allowing for the effect of gestational age. We conclude that approximately one third of hyperemesis subjects show transient hyperthyroxinemia and suggest that hCG or a molecular variant of hCG may stimulate the thyroid gland.

scholarly journals Operational Risk Aggregation Based on Business Line Dependence: A Mutual Information Approach

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Wenzhou Wang ◽  
Limeng Shi ◽  
Xiaoqian Zhu
Keyword(s):  
Mutual Information ◽  
Correlation Coefficient ◽  
Linear Correlation ◽  
Risk Estimation ◽  
Pearson Correlation ◽  
Operational Risk ◽  
Random Variable ◽  
Data Set ◽  
Risk Aggregation ◽  
Business Line

The dependencies between different business lines of banks have serious effects on the accuracy of operational risk estimation. Furthermore, the dependencies are far more complicated than simple linear correlation. While Pearson correlation coefficient is constructed based on the hypothesis of a linear association, the mutual information that measures all the information of a random variable contained in another random variable is a powerful alternative. Based on mutual information, the generalized correlation coefficient which can capture both linear and nonlinear correlation can be derived. This paper models the correlation between business lines by mutual information and normal copula. The experiment on a real-world Chinese bank operational risk data set shows that using mutual information to model the dependencies between business lines is more reasonable than linear correlation.

scholarly journals Simultaneous Measurement of Ear Canal Movement, Electromyography of the Masseter Muscle and Occlusal Force for Earphone-Type Occlusal Force Estimation Device Development

Sensors ◽  
2019 ◽  
Vol 19 (15) ◽  
pp. 3441
Author(s):  
Kurosawa ◽  
Taniguchi ◽  
Momose ◽  
Sakaguchi ◽  
Kamijo ◽  
...  
Keyword(s):  
Correlation Coefficient ◽  
Masseter Muscle ◽  
Partial Correlation ◽  
Force Estimation ◽  
Ear Canal ◽  
Basic Study ◽  
Occlusal Force ◽  
Absolute Value ◽  
The Absolute ◽  
Partial Correlation Coefficient

We intend to develop earphone-type wearable devices to measure occlusal force by measuring ear canal movement using an ear sensor that we developed. The proposed device can measure occlusal force during eating. In this work, we simultaneously measured the ear canal movement (ear sensor value), the surface electromyography (EMG) of the masseter muscle and the occlusal force six times from five subjects as a basic study toward occlusal force meter development. Using the results, we investigated the correlation coefficient between the ear sensor value and the occlusal force, and the partial correlation coefficient between ear sensor values. Additionally, we investigated the average of the partial correlation coefficient and the absolute value of the average for each subject. The absolute value results indicated strong correlation, with correlation coefficients exceeding 0.9514 for all subjects. The subjects showed a lowest partial correlation coefficient of 0.6161 and a highest value of 0.8286. This was also indicative of correlation. We then estimated the occlusal force via a single regression analysis for each subject. Evaluation of the proposed method via the cross-validation method indicated that the root-mean-square error when comparing actual values with estimates for the five subjects ranged from 0.0338 to 0.0969.

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