l Bivariate statistical measures regression and correlation

l Bivariate statistical measures regression and correlation

1. Bivariate analysis is a statistical method that examines how two different things are related. The bivariate analysis aims to determine if there is a statistical link between the two variables and, if so, with what intensity and in which direction.

   • CORRELATION
     • In the most general sense, it means the interdependence between quantitative or qualitative data, and can be extended to more than two random variables. We often refer to the relationship between random variables or between ranges.
       • YACHT CORRECTION: Also known as continuity correction, adjustment proposed by Yates (1934) in the calculation of Chi-square in "2x2" contingency tables.
         • CURVILINEAR CORRELATION: Expression to denote the correlation in bivariate data (two variables) when the regressions are not linear. Some do not agree, since the correlation is given by a number and not by a function that admits curvature.
           • RANK CORRELATION: Measures the intensity of the correlation between two sets of rankings and the degree of correspondence between them. The best known are those of Kendall (1938) and Spearman (1904).
             • DIRECT CORRELATION: See Correlation coefficient.
               • LINEAR CORRELATION: This expression is not advisable, used very frequently in linear functions of the observations.
     • The relationship that can exist between two variables can be classified as follows:
       • • Unilateral causal dependence. This relationship occurs when one of the variables influences the other, but not vice versa.
         • • Interdependence. It occurs when the influence between the two variables is reciprocal. It would be a case of bilateral dependency.
           • • Indirect dependency. Two variables can show a correlation through a third variable that influences them.
             • • Concordance. It is presented in two independent variables to which the correlation that may exist is determined.
               • • Chance covariation. When the correlation that occurs between the two variables is completely random or accidental.
     • The correlation analysis describes the degree or strength with which this relationship occurs, for this we will use a measure known as the correlation coefficient or Pearson correlation. Just as the correlation analysis allows to measure the strength of the association between two variables, the regression analysis allows the prediction, that is, the estimation of a value or average of a so-called dependent variable, based on a value or average supposedly known for the other. variable, called independent
   • Regression:
     • The term regression was originally used by Galton to indicate certain relationships in the theory of biological inheritance, although it has later come to mean the statistical method developed to investigate such relationships.
       • The regression analysis gives rise to a mathematical equation that allows us to describe the relationship between two variables. That is, to obtain an "ideal" line known as the regression line, which describes the relationship or dependency between two variables.

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