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Empirical Data and Statistical Analysis
Published in We-Min Chow, Assembly Line Design, 2020
Their correlation is measured by their covariance and correlation coefficient, respectively: Cov[X,Y]=E[X,Y]−E[X]E[Y]ρ(X,Y)=Cov[X,Y]SD[X]SD[Y]
Multivariate Distributions
Published in Norman Matloff, Probability and Statistics for Data Science, 2019
Suppose that typically when X is larger than its mean, Y is also larger than its mean, and vice versa for below-mean values. Then (X − EX) (Y − EY) will usually be positive. In other words, if X and Y are positively correlated (a term we will define formally later but keep intuitive for now), then their covariance is positive. Similarly, if X is often smaller than its mean whenever Y is larger than its mean, the covariance and correlation between them will be negative. All of this is roughly speaking, of course, since it depends on how much and how often X is larger or smaller than its mean, etc.
Sampling error correlated among observations: origin, impacts, and solutions
Published in Applied Earth Science, 2020
Victor Miguel Silva, João Felipe Coimbra Costa Leite
The true statistics cannot be directly measured from observations in real-world problems because available data are always affected by errors. Bivariate statistics naively inferred from these observations measure the association between observations but not the variance, covariance, and correlation between the underlying true processes of interest. Two situations in geosciences in which the covariance plays a relevant role in parameter estimation were used to show how the true statistics may be estimated using the developed equations and what needs to be done after we measure shared and non-shared errors and estimate the correct associations between variables Extending the proposed solution to other statistical applications is straightforward.
Condition monitoring with defect localisation in a two-dimensional structure based on linear discriminant and nearest neighbour classification of strain features
Published in Nondestructive Testing and Evaluation, 2020
R. Janeliukstis, S. Rucevskis, A. Chate
Linear discriminant classifiers have the option of regularisation – finding an optimum set of parameters and that lead to an effective predictive model. The amount of regularisation is responsible for regularising the covariance and correlation matrices of data as
Handbook of Regression Modeling in People Analytics: With Examples in R and Python,
Published in Technometrics, 2022
Chapter 3, “Statistics Foundations,” reviews topics of descriptive statistics, distributions, and hypothesis testing, with illustrations on numerical examples run by R codes for sample mean, variance and standard deviation, covariance and correlation, random variables and histograms, t-distribution and confidence intervals, testing for a difference in means, for a nonzero correlation, and Chi-square test for a difference in frequency distribution. Foundational statistics in Python is also considered.