Bivariate statistical measures regression and correlation.

Bivariate statistical measures regression and correlation.

1. regression theory tries to explain the behavior of a variable, called explained (dependent or endogenous), based on another or others, called explanatory (independent or exogenous)

   • You can set a first classification
     • simple if there is only one explanatory variable
     • Multiple if number of variables explanatory are several.
   • Types regression
     • Type I
       • will only provide estimates of Y for the values of X contained in the distribution of frequencies.
     • Type II
       • This function will be chosen in such a way that best fit the observations, resulting in great utility for these purposes graphical representation of it

2. The linear correlation coefficient is the ratio between the covariance and the product of the standard deviations of both variables.

3. Correlation Ratio

   • In statistics, the correlation ratio is a measure of the relationship between the dispersion statistics between individual categories and the dispersion between the sample or population complete.
     • Correlation
       • Correlation tries to establish the relationship or dependency between the two variables that are involved in a two-dimensional distribution.
         • Types of Correlation
           • Correlation direct
             • The direct correlation is gives when to increase one of the variables the other increases.
           • Correlation reverse
             • the inverse correlation is gives when increasing a of the variables the other decreases
           • null correlation
             • The null correlation is given when there is no dependency of any kind between variables
         • Degree of Correlation
           • Strong correlation
             • The correlation will be strong when the closer the points are straight
           • Weak Correlation
             • The correlation will be weak when the farther apart the points are of the straight
           • null correlation
             • there is no pattern or relationship between them
         • Linear Correlation Coefficient
           • The coefficient of linear correlation is expressed through the letter R.

4. regression analysis

   • study the relationship between two Quantitative variables
   • Statistical technique used to derive a equation relating a criterion variable with one or more predictor variables.
   • Study the strength of the association through a measure of association called correlation coefficient

5. Problems with regression

   • Inhomogeneous variance.
   • nonlinear relationship
   • Correlated errors

6. Linear regression

   • Pearson linear correlation coefficient
     • If the points have a tendency to be arranged in line
     • r is useful to determine if there is a linear relationship between two variables. but it won't work for( quadratic, logarithmic
     • It has the same sign as Sxy
   • Covariance of two random variables X and Y
     • Between two variables, Sxy, tells us if the relationship between two variables is direct or reverse
     • The sign of the covariance tells us that the cloud of the points is increasing or not but does not say nothing about the degree of the relationship between variables.

7. regression model simple linear

   • And the ŷ since it is rarely that match no matter how good it is regression model to quantity "-e Y-ŷ" is called the residual error.
   • We found a very simple function of X - Linear, which allows approximation by means of -ŷ=b0+ b1X

8. Regression analysis model

   • Statistical: Allows the incorporation of a random component in the relationship.
   • Standardized: the slope β1 gives us indicates whether there is a relationship between two variables.
   • Deterministic: that under ideal conditions, the independent variable can be for a mathematical function of variables independent.

9. statistical measures bivariate

   • Regression and correlation
   • Dispersion diagram
   • simple linear regression
     • simple linear regression is a model linear regression with a single variable explanatory.
   • Correlation
   • Multiple Regression