Correlated in the context of Polycarpic

The g factor is a construct developed in psychometric investigations of cognitive abilities and human intelligence. It is a variable that summarizes positive correlations among different cognitive tasks, reflecting the assertion that an individual's performance on one type of cognitive task tends to be comparable to that person's performance on other kinds of cognitive tasks. The g factor typically accounts for 40 to 50 percent of the between-individual performance differences on a given cognitive test, and composite scores ("IQ scores") based on many tests are frequently regarded as estimates of individuals' standing on the g factor. The terms IQ, general intelligence, general cognitive ability, general mental ability, and simply intelligence are often used interchangeably to refer to this common core shared by cognitive tests. However, the g factor itself is a mathematical construct indicating the level of observed correlation between cognitive tasks. The measured value of this construct depends on the cognitive tasks that are used, and little is known about the underlying causes of the observed correlations.

The existence of the g factor was originally proposed by the English psychologist Charles Spearman in the early years of the 20th century. He observed that children's performance ratings, across seemingly unrelated school subjects, were positively correlated, and reasoned that these correlations reflected the influence of an underlying general mental ability that entered into performance on all kinds of mental tests. Spearman suggested that all mental performance could be conceptualized in terms of a single general ability factor, which he labeled g, and many narrow task-specific ability factors. Soon after Spearman proposed the existence of g, it was challenged by Godfrey Thomson, who presented evidence that such intercorrelations among test results could arise even if no g-factor existed.

Quantum entanglement is the phenomenon wherein the quantum state of each particle in a group cannot be described independently of the state of the others, even when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between classical physics and quantum physics: entanglement is a primary feature of quantum mechanics not present in classical mechanics.

Measurements of physical properties such as position, momentum, spin, and polarization performed on entangled particles can, in some cases, be found to be perfectly correlated. For example, if a pair of entangled particles is generated such that their total spin is known to be zero, and one particle is found to have clockwise spin on a first axis, then the spin of the other particle, measured on the same axis, is found to be anticlockwise. This behavior gives rise to seemingly paradoxical effects: any measurement of a particle's properties results in an apparent and irreversible wave function collapse of that particle and changes the original quantum state. With entangled particles, such measurements affect the entangled system as a whole.

In statistics, linear regression is a model that estimates the relationship between a scalar response (dependent variable) and one or more explanatory variables (regressor or independent variable). A model with exactly one explanatory variable is a simple linear regression; a model with two or more explanatory variables is a multiple linear regression. This term is distinct from multivariate linear regression, which predicts multiple correlated dependent variables rather than a single dependent variable.

In linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters are estimated from the data. Most commonly, the conditional mean of the response given the values of the explanatory variables (or predictors) is assumed to be an affine function of those values; less commonly, the conditional median or some other quantile is used. Like all forms of regression analysis, linear regression focuses on the conditional probability distribution of the response given the values of the predictors, rather than on the joint probability distribution of all of these variables, which is the domain of multivariate analysis.