Bivariate statistics regression and correlation

Bivariate statistics regression and correlation

1. REGRESSION ANALYSIS

   • is used to derive an equation that relates the criterion variable to one or more predictor variables
   • Standard error of the estimate Term used in regression analysis to refer to the absolute value of the variation in the criterion variable, which is left unexplained, or not counted, in the fitted regression equation.
   • determination coefficient Term used in regression analysis to denote the relative proportion of the total variation in the criterion variable that can be explained by the fitted regression equation.
   • This type of statistical analysis allows mathematical classification through different questions such as: What factors matter the most? What factors can be ignored? How do these factors interact with each other? And finally, how confident do you feel about all these factors?
     • The process of running a regression allows you to confidently determine which factors are most important, which ones can be ignored, and how they influence each other.
       • These factors are called variables which are classified as:
         • Dependent variable(s): It is the most important factor, which is trying to understand or predict.
         • Independent variable(s): This is the factor that you think can impact your dependent variable.
   • Types of regression analysis
     • Simple linear regression model
       • Simple linear regression is the most widely used technique, it is a way to model a relationship between two sets of variables. The result is an equation that can be used to make projections or estimates on the data.
         • This model is considered a predictor x and a dependent variable or response Y. Imagine that the true relationship between Y and x is a straight line and that the observation Y at each level x is a random variable.
     • Multiple linear regression model
       • Multiple linear regression is a statistical technique that is responsible for analyzing situations that involve more than one variable. This method makes it possible to identify which independent variables are the ones that can explain an independent variable, check the causes and predict the values ​​approximately.
     • Modelo de regresión no lineal
       • Nonlinear regression is a more complicated process where it may happen that the number of parameters does not coincide with the number of explanatory variables.

2. CORRELATION ANALYSIS

   • measures the closeness of the relationship between two or more variables, considering the joint variation of the two measurements, neither of which is subject to restriction by the experimenter.
   • There is nothing in correlation analysis or any other mathematical procedure that can be used to establish causality.
   • Correlation coefficient Term used in regression analysis to designate the strength of the linear relationship between the criterion and predictor variables.
   • To determine the degree of correlation between the variables, it is not enough to calculate the variance , since there is the coefficient of determination or squared correlation coefficient; however, a rectilinear correlation coefficient is frequently used, r this being a value between -1 and 1.
     • If the correlation coefficient r is equal to or less than one, it tells us that both the covariance and the angular coefficients are negative and therefore the line will be descending, as the slope is negative. In addition, if it is equal to -1, it indicates that there is a perfect correlation, in other words, each value of the variable must be exactly equal to the estimate, and therefore the residual variance equal to zero, and the explained variance equal to the total variance.
   • is calculated with the correlation coefficients
     • Correlation coefficients are numbers that vary between +1 and -1. Its magnitude indicates the degree of association between the variables, if it is 0 it indicates that there is no relationship and the extreme values ​​+1 and -1 indicate a perfect positive or negative correlation, respectively.

3. BIVARIATE STATISTICAL MEASURES

   • Coefficient of determination R2
   • SIMPLE LINEAR CORRELATION
   • positive and negative correlation
   • scatter diagrams
   • regression
   • simple regression
   • multiple regression