Bivariate statistical measures regression and correlation.

Bivariate statistical measures regression and correlation.

1. 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. Martinez Bencardino, C. (2018, p.591).
     • 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.
         • Linear regression
           • It uses the straight line for its simplicity in mathematical calculations, also, in many real life cases it provides us with sufficient approximations to be accepted. Martinez Bencardino, C. (2018, p.599)
             • multiple regression
               • allows you to work with a variable at the interval or ratio level. In the same way, it is possible to analyze the relationship between two or more variables through equations
                 • Logistic regression
                   • Used to predict the outcome of a categorical variable (a variable that can take on a limited number of categories) over the independent or predictor variables.
                     • regression lines
                       • They are the lines that best fit the cloud of points (or also called a scatter diagram) generated by a binomial distribution.
                         • regression problems
                           • inhomogeneous variance, nonlinear relationship, Correlated errors.

2. Correlation

   • includes the analysis of sample data to find out how two or more variables are related to each other in a population. "correlation" literally means mutual relationship, since it indicates the degree to which the values of one variable are related to the values of another. Matus, R. (2010, p.106).
     • Correlation analysis
       • produces a number that summarizes the degree of relationship between two variables.
         • The correlation coefficient
           • The correlation coefficient numerically expresses both the strength and the direction of the linear correlation. It presents two properties that establish the nature of a relationship between two variables. One is its sign (+ 0 -) and the other is its magnitude.
             • Linear correlation measure
               • commonly used in statistics is the "beloved Pearson's correlation coefficient between "y" and "x'. This amount, denoted by the symbol "r'.
                 • positive correlation
                   • A significant and positive correlation means that the subjects coded with a one have a greater mean in the continuous variable than the subjects coded with a zero; if the correlation is negative, the highest mean in the continuous variable corresponds to the subjects coded with a zero. Matus, R. (2010, p.112).
                     • Negative Correlation.
                       • It occurs when as one of the variables increases, the other decreases or vice versa. Matus, R. (2010, p.112).