bivariate statistical measures

bivariate statistical measures

1. linear correlation

   • tries to establish the relationship or dependency that exists between the two variables that intervene in a two-dimensional distribution, that is, it determines if the changes in one of the variables influence the changes in the other, in case it happens we will say that the variables are correlated or that there is a correlation between them
     • correlation types
       • direct correlation
         • When one of the variables increases, the other increases, the line corresponding to the cloud of points of the distribution is a growing line
       • inverse correlation
         • occurs when one of the variables increases the other decreases, the line corresponding to the cloud of points of the distribution is a decreasing line
       • null correlation
         • occurs when there is no dependency of any kind between the variables, in this case it is said that the variables are uncorrelated and the cloud of points has a rounded shape
     • degree of correlation
       • strong correlation
         • it will be stronger the closer the points are to the line
       • weak correlation
         • will be weaker the further apart the points are on the line
       • null correlation
         • there is no correlation
         • positive correlation
         • high positive correlation

2. linear regression

   • regression tries to explain the behavior of a variable called dependent or endogenous based on another variable called dependent or exogenous
     • regression analysis model
       • deterministic: it assumes that under ideal conditions the behavior of the dependent variable can be fully described by a mathematical function of the independent variables, that is, under ideal conditions the model allows predicting the value of the dependent variable without error
       • Statistical: allows the incorporation of a Random Component in the relationship. Consequently, the predictions obtained through statistical models will have an associated prediction error
       • Standardized: the slope &1 indicates the relationship between the two variables, its sign indicates the positive or negative relationship, the reason is that its numerical value depends on the units of measurement of the two variables, a change of units is one of them can produce a drastic change in the value of the slope
     • linear regression coefficient
       • quantity that results from a multiple analysis that indicates the average change in a criterion variable per unit change in a predictive variable in equal circumstances in all as a correction variable
     • regression analysis
       • statistical technique to derive an equation that relates a criterion variable with one or more predictor variables, when a predictor variable is used the regression analysis is multiple
     • simple linear regression
       • linear function is one that satisfies the properties; active property exists and which is a polynomial function whose representation is in the Cartesian plane is a straight line
     • linear coefficient of determination
       • once the rectilinear function has been chosen to represent the dependency relationship of Y on X, and its parameters a and b have been estimated, the linear determination coefficient is computed with the aim of measuring degrees of dependency a y on x under the estimated linear regression function

3. multiple regression

   • regression can be linear and curvilinear or non-linear
     • regression coefficient
       • the regression coefficient can be
         • indicates the number of units in which the variable Y is modified due to the effect of the change of the independent variable X or vice versa in a unit of measure
           • positive
           • negative
           • null
   • coefficient of determination R2
     • determines the degree of correlation between the variables the coefficient of determination also called R square that reflects the goodness of the fit of a model to the variable