Statistical measure Bivariate regression and correlation

Statistical measure Bivariate regression and correlation

1. This technique allows the analysis and hypothesis in the association and the relationship that exists between two sets of variables, since it helps to determine a value of one variable and know the value of another independently, in addition to knowing its measurements through linear parameters and analysis. of regression.

   • Correlation and regression analysis involves the analysis of sample data to find out how two or more variables in a population are related to each other. (Martinez, 2020, p.95).
     • It can be classified as follows form. (Martinez, 2011, p.570)
       • Unilateral causal dependence: this relationship occurs when one of the variables influences the other, but not the other way around.
       • Interdependence: occurs when the influence between the two variables is reciprocal. It would be a case of two-sided dependency.
       • Indirect dependency: the two variables can show a correlation through a third variable that influences them.
       • Concordance: it is presented in two variables independent to whom it is determined the correlation that may exist.
     • Regression
       • The term regression was originally used by Galton to indicate certain relationships in the theory of biological inheritance, although later it has come to mean the statistical method developed to investigate such relationships. (Martinez, 2011. p570)
       • Simple linear regression is trying to develop a linear or linear mathematical equation that describes the relationship between two variables. (Martinez, 2020, p. 95)
       • For this reason, regression equations allow explaining the values ​​of one variable in terms of the other, its causes and effects through analysis.
       • Regression analysis results in a mathematical equation that describes this relationship.
         • Regression analysis provides help in finding the correlation coefficient. Since your equation can be on a line or curve.
         • It also performs calculations on the measure of dispersion and position.
         • Straight line is used for its simplicity in mathematical calculation
       • Regression coefficient
         • It is the mean change in the response variable for a unit change in the predictor variable while holding the other predictors constant in the model.
       • Method of least squares
         • It is a preferred method of estimation, which the quantities to be estimated are determined, minimizing the sum of the squares of the differences between the observed values ​​(y) and the estimated values ​​of Y. (Martínez, 2011, p.580)
       • Assumptions in regression analysis
         • These are the assumptions that must be made in the regression analysis, among the main
     • Correlation
       • Correlation coefficient allows to know if the data in question are related. That is, when the correlation coefficient is zero, the variables are not related. Likewise if the correlation coefficient is a positive 1 and its variables are correlated.
       • Pearson correlation between “y” and “x”. Measures the degree of covariation between two linearly related variables quantitatively and continues
         • It is the degree of relationship that can exist between the two variables. We obtain this degree of correlation by calculating the Correlation Coefficient
         • The correlation coefficient is a measure of the interdependence of two random variables.
         • The squared correlation coefficient or coefficient of determination measures the proportion of the variance that is explained by the regression equation, which describes the relationship established between the two variables
           • Indicates the percentage of the variations of the dependent variable and attributes to the influence of the independent variable.
       • The covariance allows to measure the linear dependence, it is said that if the covariance is positive there is no standardized measure or a positive slope and the line would be ascending, on the contrary if it is negative the linear would be descending. (Martinez, 2011, p.573)
         • If most of the points fall in the lower left and upper right sections, the covariance is positive.
         • On the contrary, the points are located in the lower right and upper left, it is indicative of a negative covariance
       • Scatter diagrams because it allows an analysis of the realization between two variables its value and function.
         • It is plotted on a pair of coordinate axes. The abscissa axis for the first variable (x,) and the vertical or ordinate axis, for the values ​​of the second variable
           • Also represented on a Cartesian plane, scatter plot, point cloud scatter plot
             • it is presented in a linear, rectilinear, parabolic, exponential or any other type that represents the whole.
       • Correlation Types

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