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Statistics
Published in Paul L. Goethals, Natalie M. Scala, Daniel T. Bennett, Mathematics in Cyber Research, 2022
Both correlation and regression analysis quantify the relationship between two variables. One distinct difference between correlation and regression is that a correlation analysis produces a quantitative statistical value (correlation coefficient), whereas a regression analysis produces a quantitative equation, known as a regression model. Generally, a regression model can be represented as: yi=f(xi,β)+εi
Advances in development appraisal simulation
Published in Peter Byrne, Risk, Uncertainty and Decision-Making in Property, 2002
A perfect positive correlation between two variables, A and B, gives a correlation coefficient of + 1. As A increases so B increases in exact linear step with A. In contrast, a correlation coefficient of -1 implies a perfect negative correlation between two variables, A and B. That is, as A increases so B decreases in linear step with A, and vice versa. Intermediate values of the coefficient, suggest that the relationship is not as strong. For example, -0.5 indicates that when the value of A is high, the value of B will tend to be low, but not always. Thus, if two variables are strongly positively correlated then a high value in one should be matched by a high value in the other. This is what @RISK attempts to do during the sampling operation.
Multivariate Methods
Published in Shayne C. Gad, Carrol S. Weil, Statistics and Experimental Design for Toxicologists, 1988
Correlation. Although covariances are useful for many mathematical purposes, they are rarely used as descriptive statistics. If two variables are related in a linear way, then the covariance will be positive or negative depending on whether the relationship has a positive or negative slope. But the size of the coefficient is difficult to interpret because it depends on the units in which the two variables are measured. Thus the covariance is often standardized by dividing by the product of the standard deviations of the two variables to give a quantity called the correlation coefficient. The correlation between variables Xi and Xj will be denoted by rij, and is given by
A Novel Hybrid Machine Learning Model for Analyzing E-Learning Users’ Satisfaction
Published in International Journal of Human–Computer Interaction, 2023
Sulis Sandiwarno, Zhendong Niu, Ally S. Nyamawe
On the other hand, we examined the correlation results between our proposed algorithm and common feature extraction techniques on the machine learning classifiers using Pearson Correlation Coefficient (PCC) algorithm. PCC is an important algorithm to assess the correlation between variables (Adler & Parmryd, 2010; Benesty et al., 2009). Generally, the PCC algorithm denotes the value between [−1, 1]. When the correlation coefficient values near equals 1 depicts a perfect positive relationship, −1 represents a perfect negative relationship, and 0 denotes the blank relationship absence between variables. Generally, the PCC method is defined as: where, represents the mean of variables and is defined as the mean of variable. Moreover, the deep learning parameter settings in the experiment are shown in Table 1.
Artificial neural networks for predicting the demand and price of the hybrid electric vehicle spare parts
Published in Cogent Engineering, 2022
Wafa’ H. AlAlaween, Omar A. Abueed, Abdallah H. AlAlawin, Omar H. Abdallah, Nibal T. Albashabsheh, Esraa S. AbdelAll, Yousef A. Al-Abdallat
Statistical correlation analysis was executed between the vehicle types and the SPs-related variables and the demand and the price of the HEV SPs. In general, the correlation coefficient, as a statistical tool, indicates the strength of the association between two variables. The output values range from −1 to 1, indicating a negative or positive association, respectively. A correlation value of 1 or −1, or closer to them, indicates a strong linear relationship between the two variables, whereas a value of zero, or closer to zero, means a weak linear relationship between the two variables. Table 2 summarizes the correlation coefficient values. It is noticeable that the vehicle types and the SPs-related variables have different effects on both the demand and price of the HEV SPs. To illustrate, the correlation coefficient, for instance, that represents the strength of the linear relationship between the SP variable and the demand is smaller than the one that represents the strength of the linear relationship between the same variable and the price, in other words, the former linear relationship is weaker than the latter one. It is also apparent that some variables have different nature of the relationships. For example, the relationship between the FR and the demand is a direct one, whereas the relationship between the FR and the price is inverse.
Grit, motivational belief, self-regulated learning (SRL), and academic achievement of civil engineering students
Published in European Journal of Engineering Education, 2022
Hector Martin, Renaldo Craigwell, Karrisa Ramjarrie
The Pearson product-moment or bivariate correlation expresses the strength of the relationship between two variables (George and Mallery 2011). Correlation values range from −1 to +1, where the magnitude of the value indicates the strength of the relationship and the direction (negative or positive) reflects the relationship’s nature. A correlation coefficient of zero indicates no relationship between the variables at all. The assumption of using this method is that the two measured variables are approximately normally distributed (George and Mallery 2011). The Durbin-Watson statistic is used to test the remainder of the assumptions for sample suitability for parametric evaluation and to ensure the residuals are independent (or uncorrelated). This statistic can vary from 0 to 4, with the optimal being 2. All values were within the range of 1 and 3, rendering the analysis valid (Stevens 2012). Cook’s Distance statistic for each participant was determined. No value was over 1 to indicate significant outliers, which may place undue influence on the model. Scatter plots were also examined.