Bivariate measures regression and correlation.

Bivariate measures regression and correlation.

1. Correlation: Corresponds to the relationship between two variables or groups of techniques to measure associations between 2 variables that are related change in one is reflected in the other.

2. Pearson's coefficient: Normalizes the covariance with a measure of dispersion for X and Y, if the points have a tendency to line up; It is useful to determine if there is a linear relationship between two variables, but it won't do for (quadratic, logarithmic).

3. Simple linear regression: Assume a chance ratio of variable X (cause) towards a variable AND (effects), studies changes in a variable. This means that when a variable independently exercises influence over a dependent variable, where X is the independent variable, explanatory or exogenous and Y the dependent variable, response or endogenous.

4. Values ​​fitted to the model.

   • Statistical: Allows the incorporation of a random component in the relationship.
   • Deterministic: That, under ideal conditions, the independent variable can be for a mathematical function of variables independent. Linear regress model, it can be used to obtain Y values ​​adjusted to the model using the following formula.
   • Standardized: The slope ¬ẞ 1 gives us indicates whether there is a relationship between two variables.

5. Multiple regression: It is an extension of linear regression and it can extend to use multiple independent variables, the multiple regression model is the extension to (K) variables explanations of the simple regression model, in the particular case in that there are two regressors, K = 2, the model would have the form.

6. Scatter Plot: Also Known as a dot plot XY plot, scatter diagram or scattergram.

7. Bounded measure: Between 1 and -1 when testing is known as the Cauchy-Schwartz inequality for dot product. Limitations of the Pearson coefficient.

8. Regression: Explains the behavior of a variable and predicts the value of a variable based on the given values ​​of the other, called explanatory dependent or endogenous depending on other called independent explanatory or exogenous, a classification can be made into function of the number of explanatory variables of regression and correlation and it is simple if there is a variable explanatory and is multiple, if the number of variables explanations are various.

9. Covariance: Measures change with respect to the mean level of each variable, tells us if the relationship between two variables is direct or inversely, the sign of the covariance tells us that the cloud of points is growing or not but it says nothing about the degree of relationship between variables.

10. Some formulas: Linear regression y = a + bx Logarithmic y = a + bl n (x) Exponential y = ac (bx) Quadratic y = a + bx + cx 2

11. Font: Martínez, C. (2011). Capítulo 2. Distribuciones de frecuencia. En: Estadística y muestreo, 13a ed. [Online]. Ecoe Ediciones. (pp 590 – 677). Martínez, E. (2020) Estadística. ed. Santiago de los Caballeros: Universidad Abierta para Adultos (UAPA). (pp 106-138).