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A correlation coefficient is a numerical measure of some type of linear correlation, meaning a statistical relationship between two variables. [ a ] The variables may be two columns of a given data set of observations, often called a sample , or two components of a multivariate random variable with a known distribution .
This term is distinct from multivariate linear regression, which predicts multiple correlated dependent variables rather than a single dependent variable. [2] In linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters are estimated from the data.
Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.
Furthermore, if the data are represented by a mixture model of simple relationships, these relationships will be visually evident as superimposed patterns. [citation needed] The scatter diagram is one of the seven basic tools of quality control. [8] Scatter charts can be built in the form of bubble, marker, or/and line charts. [9]
The response variable may be non-continuous ("limited" to lie on some subset of the real line). For binary (zero or one) variables, if analysis proceeds with least-squares linear regression, the model is called the linear probability model. Nonlinear models for binary dependent variables include the probit and logit model.
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Knowing the values of n-1 variables, the value of the unknown variable can be found, or by fixing the values of some variables, the relationship between the unfixed ones can be studied. The result is obtained by laying a straightedge across the known values on the scales and reading the unknown value from where it crosses the scale for that ...
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