Multiple Linear Regression
Marcello Pagano, Kimberlee Gauvreau, Heather Mattie in Principles of Biostatistics, 2022
In the regression model that contains gestational age, preeclampsia, and the interaction between the two, preeclampsia and the gestational age–preeclampsia interaction are highly correlated. In fact, the Pearson correlation coefficient quantifying the linear relationship between these two variables is . This model and the model that did not include the interaction term are contrasted in Table 18.1. When the interaction term is included in the equation, the estimated coefficient of preeclampsia doubles in magnitude. In addition, its standard error increases by a factor of 12. In the model without the interaction term, the coefficient of preeclampsia is significantly different from 0 at the 0.05 level; when the interaction term is present, it no longer achieves statistical significance. The coefficient of determination does not change when the interaction is included. It remains 65.3%. Furthermore, the adjusted R2 decreases slightly. These facts taken together indicate that the inclusion of the gestational age – preeclampsia interaction term in the regression model does not explain any additional variability in the observed values of head circumference, beyond that which is explained by gestational age and preeclampsia alone. The information supplied by this term is redundant.
Skin image analysis granulation tissue for healing assessment of chronic ulcers
Ahmad Fadzil Mohamad Hani, Dileep Kumar in Optical Imaging for Biomedical and Clinical Applications, 2017
In order to measure the relationship between the system's detection and dermatologists’ tracings of the granulation tissue, the Pearson correlation coefficient is used. The Pearson correlation coefficient, which is denoted as r, was used to calculate the linear dependency between two measures or variables. It is described as the covariance of the variables divided by the outcome of their standard deviation. Given two samples X and Y, the Pearson correlation coefficient is calculated as follows: where n is the number of data points in the sample and and are the sample means. The value of the correlation coefficient ranges from 0 to (+)1 or (−)1 with values near (+)1 and (−)1 indicating strong correlation. In this study, the Pearson correlation coefficient was calculated using Equation 2.2. The correlation value obtained is 0.961 indicating a strong positive relationship and similarity between the amount of the granulation tissue detected by the system and the amount traced by the dermatologists.
Investigating links between diet and health outcomes
Geoffrey P. Webb in Nutrition, 2019
When correlating two variables (x and y) then a perfect positive correlation (increase in x leads increase y) yields a Pearson correlation coefficient (usually symbolised by the letter r) of +1 and perfect negative correlation (increase in x leads to decrease in y) yields an r value of −1. If you plot these two variables on a graph then you get perfect straight lines, sloping upwards (+1) or downwards (−1). If there is no relationship between x and y, the graph would yield a horizontal line and the correlation coefficient would be 0. Once again, it is highly unlikely that if you correlated even two completely unrelated variables, the correlation coefficient would be exactly zero or 1/−1 for associated variables; correlation coefficients almost always lie somewhere between 0 and +1 or −1.
2D-QSAR, 3D-QSAR, molecular docking and ADMET prediction studies of some novel 2-((1H-indol-3-yl)thio)-N-phenyl-acetamide derivatives as anti-influenza A virus
Published in Egyptian Journal of Basic and Applied Sciences, 2022
Mustapha Abdullahi, Adamu Uzairu, Gideon Adamu Shallangwa, Paul Andrew Mamza, Muhammad Tukur Ibrahim
In addition, the population sample was set to 10,000, the maximum generation was set to 1000, and the number of top equations was set to 1 for an effective model convergence [19]. The descriptor matrix of the built model was initially subjected to the Y-Randomization test as a measure to attest to the quality of the model before being exported to Molegro Data Modeler (MDM) for the development of the multi-linear regression (MLR) and the non-linear regression model version based on artificial neural network (ANN) analysis [18,20]. The predictive ability of the GFA-MLR and GFA-ANN models generated was examined using the following internal validation parameters as follows: The Pearson correlation coefficient (r): is a measure of the correlation of two variables x and y. It is mathematically defined as:
Postoperative cognitive dysfunction and the possible underlying neurodegenerative effect of anaesthesia
Published in International Journal of Neuroscience, 2019
Mona Hussein, Wael Fathy, Tamer Nabil, Rehab Abd Elkareem
The data were coded and entered using: the statistical package for social science version 18 (SPSS v 18). Sample size calculation was conducted using G*Power version 3.1.9.2 Software, based on our pre-trial pilot study on 10 patients. The probability of type I error (α) was 5%, and the effect size was 0.3543726. A total number of 50 participants were required to achieve statistical power of the study (1–β) 80%. Descriptive statistics were reported as mean ± SD and number (%) for categorical variables. Paired sample t-test was used for comparison between means of two paired groups of quantitative variables. Mixed ANOVA test was used for comparing paired data in two unpaired groups. The Pearson correlation coefficient (r) was used to describe the degree of relationship between two variables. The sign of correlation coefficient (+, –) defines the direction of the relationship, either positive or negative. The probability/significance value (p value) ≥ .05 is not statistically significant and <.05 is statistically significant.
Self-practice among patients with psoriasis: University hospital experience
Published in Journal of Dermatological Treatment, 2022
Shaimaa Ismail Omar, Moustapha Ahmed Ramadan
The following tests were used:Chi-square test. This test was performed to compare unpaired categorical variables between different groups.Monte Carlo correction. Correction for chi-square test was performed when one or more of the test preconditions are not fulfilled.Pearson correlation coefficient. This test was conducted to correlate two normally distributed quantitative variables.F-test (ANOVA). This test was performed to compare normally distributed quantitative variables between more than two groups.
Related Knowledge Centers
- Standard Deviation
- Stigler'S Law of Eponymy
- Expected Value
- Sampling
- Standard Score
- Null Hypothesis
- P-Value
- Sampling Distribution
- Percentile
- Studentization