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Statistics
Published in Paul L. Goethals, Natalie M. Scala, Daniel T. Bennett, Mathematics in Cyber Research, 2022
An important application of statistics is to be able to estimate the relationship between two or more quantitative variables. This can fundamentally be achieved by correlation and regression analysis. The strength of the relationship between two quantitative variables can be estimated through a correlation analysis. A high correlation indicates that the two variables have a strong relationship, whereas a low correlation is associated with a weak relationship between the two variables. A correlation is often assumed to follow a linear line. Thus, correlation analysis is often related to linear regression analysis (Franzese & Iuliano, 2019). Regression analysis is a statistical approach that involves predicting the value of a dependent variable (response) based on the known value of one or more independent variables. Both correlation and regression analysis are part of the fundamental methods behind modern machine learning algorithms.
Methods to Predict the Performance Analysis of Various Machine Learning Algorithms
Published in K Hemachandran, Shubham Tayal, Preetha Mary George, Parveen Singla, Utku Kose, Bayesian Reasoning and Gaussian Processes for Machine Learning Applications, 2022
M. Saritha, M. Lavanya, M. Narendra Reddy
R square is a metric for how well a model can explain variation in a predictor variable. It is named R Square since it is the square of the Correlation Coefficient (R) (Regression Analysis: How Do I Interpret R-Squared and Assess the Goodness-of-Fit?, n.d.). The sum of the squared error rate scaled by the entire sum of the square, which replaces the computed forecast with mean, yields R square. The value of R square ranges from 0 to 1, with a higher value indicating a better match between the forecast and the actual value. R2=1−SSRegressionSSTotal=1−∑(y−y′)2∑(y−y′)2
Development of Precision Additive Manufacturing Processes
Published in Richard Leach, Simone Carmignato, Precision Metal Additive Manufacturing, 2020
Ahmed Elkaseer, Amal Charles, Steffen G. Scholz
Statistical analysis is a methodology for systematically examining DoE results in order to categorise the most significant process parameters, to evaluate the effect of these parameters on the process responses and to identify the proper process parameters for optimal responses (Baturynska 2018, Grasso et al. 2018). Among statistical analysis techniques, regression is an effective methodology, utilising the least-squares method for determining the degree of correlation between process parameters and process responses, or the experimental results–based model. The proposed model can be used for process prediction and as an objective function in the optimisation of the process in a later step. Simple regression analysis is applied when a process response depends on a single process parameter, while multiple regression analysis is used in the case of dependence on multiple process parameters (Noryani et al. 2019). Regression analysis is developed based on a pre-defined relationship between the process parameters and process responses (Stulp and Sigaud 2015), such as linear, logarithmic and polynomial.
Evaluation of seawater intake discharge coefficient using laboratory experiments and machine learning techniques
Published in Ships and Offshore Structures, 2023
Mahmood Rahmani Firozjaei, Seyed Taghi Omid Naeeni, Hassan Akbari
Data-mining techniques and statistical analyses can be used to discover the relationships between different variables. Various techniques have been applied to solve these engineering problems. Two models, regression analysis and model tree (MT), were used to evaluate each model’s accuracy in predicting the discharge coefficient (Cd). These methods are briefly discussed below. More details can be found in the related references. The two major parts of supervised learning methods are classification and regression problems. There are different types of Regression analysis, and linear and nonlinear analyses are commonly used for regression. Nonlinear regression is sometimes more applicable than linear regression and can describe the relationship between variables properly.
AI Privacy Opinions between US and Chinese People
Published in Journal of Computer Information Systems, 2023
Yunfei Xing, Wu He, Justin Zuopeng Zhang, Gaohui Cao
A regression analysis combined with content analysis was used to identify driving factors for opinion polarization.37 Regression analysis is a predictive modeling technique that studies the relationship between dependent and independent variables. This technique is commonly used for predictive analysis, time series modeling, and finding causal relationships between variables. First, we randomly collected 300 comments from Twitter datasets and 300 comments from Weibo datasets. Then, based on the cultural identity theory and 600 sample texts, the corresponding response variables were retrieved and sorted into three main classes (security concerns, national development, and AI technologies), shown in Table 1. The security concerns include variables: security, ethics, and systems. National development includes technology, economics, and society. AI technologies include applications, algorithms, and machine learning. The polarity was classified into positive (supporting), neutral, and negative (opposing) groups. Finally, the whole datasets (8845 tweets and 10924 Weibo posts) were analyzed based on the coding framework. All the response variables are composed of dichotomous variables, i.e., a classification is coded as 1 when identified in the sample and 0 if it is not. In the coding process, when a response variable is mentioned in a tweet, we coded it as 1 under that response variable and 0 otherwise.
Modelling and optimisation of hardness in citrate stabilised electroless nickel boron (ENi-B) coatings using back propagation neural network – Box Behnken design and simulated annealing – genetic algorithm
Published in Transactions of the IMF, 2021
M. Vijayanand, R. Varahamoorthi, P. Kumaradhas, S. Sivamani
Regression analysis is a mathematical modelling technique that is used to generate a relation among independent variables, and between independent and dependent variables.37Table 2 shows the input factors and the levels used in the present study. In this study, the Box–Behnken design (BBD) was selected for performing regression analysis using Design-Expert 11.0 from Stat-Ease Inc., USA. The number of experiments performed for ‘m’ factors and ‘cp’ centre points is given by the relation n = 2m(m − 1) + cp. Table 3 shows the BBD matrix for independent and dependent variables (experimental values). As per the principle of the BBD, the experimental values were fitted into the second-order model as given in Equation (8), and the model coefficients were evaluated using Equation (9).38