Bivariate statistical measures regression and correlation

Bivariate statistical measures regression and correlation

1. Bivariate measures are those that study the relationship that may exist between two variables analyzed simultaneously.

   • for this reason it is known as two-dimensional distributions or bivariate data
   • Unlike univariate data, it focuses on the analysis of one variable with independent parameters.

2. Correlation and regression analysis

   • analyzes how two or more quantitative variables in a set of data are related to each other
     • One way in which these analyzes are implemented is to explain how one variable is related in terms of the other.
       • For example when talking about the existing relationship between production and consumption; income and expenses; weight and height
         • The relationship between the variables can be classified into:
           • one-sided causal dependence
             • one of the variables influences the other, but not the other way around
           • interdependence
             • there is an influence between two variables reciprocally
           • direct dependency
             • show a correlation by means of a third variable
           • agreement
             • is presented in two independent variables where a correlation is determined
           • chance covariation
             • correlation between the two variables
         • When interpreting the results, it is important to keep in mind:
           • the correlation coefficient
             • allows to know the degree of correlation between the variables
           • the coefficient of determination
             • measures the reliability of the model
   • Correlation analysis
     • gives a number that summarizes the degree of relationship between the variables
       • the correlation coefficient has two properties which establish the nature of the relationship
         • these are its sign and magnitude
           • when the values ​​are close to -1 or +1 they indicate that the values ​​are close to the line or below it and when the values ​​are close to 0 it suggests a greater dispersion
   • regression analysis
     • Give the mathematical equation that describes the relationship
       • another use of the regression equation is to predict future values ​​for a variable
         • regression analysis allows obtaining ideal knowledge as a regression line, which describes the relationship or dependence between variables
           • where it is necessary to use a measure that is known as the correlation coefficient
             • In addition, it indicates whether the mathematical relationship is linear, parabolic, exponential, etc.
     • • Generally, when we talk about regression analysis, a straight line is used for mathematical calculation.
         • This model indicates that a linear relationship occurs when the value of y is a function of x
   • In these measurements, scatter diagrams are very important since they easily show the relationship between quantitative variables.

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