Measures Bivariates of regression and correlation.

Measures Bivariates of regression and correlation.

1. REGRESSION

   • simple linear regression
     • We try to explain the relationship exists between the response variable Y and a single explanatory variable X. Y=a+bX +C
   • multiple regression
     • Allows you to work with a variable at the level of interval or ratio. 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 value that can be adopt a limited number of categories) as a function of the independent variables or predictors.
   • REGRESSION OF TYPE 1
     • It is assigned to each value of the explanatory variable (or set of values ​​of the explanatory variables, in the multiple case) the mean of the explained variable conditional on such value(s) of the variable(s) explanatory(s). Therefore, it will only provide estimates of Y for the values ​​of X contained in the frequency distribution.
   • REGRESSION OF TYPE 2
     • It is assumed that the function y = f(x) or y = f(x1, x2, …, xp) that links the explained variable with the explanatory one (or explanatory) has a parametric form, that is, Y is related to X through a series of coefficients or parameters. Consequently, provides estimates of Y for any value of X, whether it is contained in the distribution or not

2. CORRELATION

   • MISTAKE STANDARD OF THE ESTIMATE
     • Even though the line seems to fit reasonably good on points, there is still deviation from these in I turn to her The magnitude of your deviation measures the fit. it's possible calculate a numerical measure of the variation of the points around the line, similar to the calculation of the standard deviation of a distribution of frequencies.
   • INFERENCES ABOUT THE SLOPE COEFFICIENT
     • Before continuing, it should be noted that the estimators of squares minimum of the parameters of the original population are the best unbiased linear estimators of population parameters true, regardless of the shape of the distribution of the term of mistake. It is enough that the previous assumptions are satisfied. This is a remarkable result of the Gauss-Markov theorem. are required assumptions of errors with normal distribution only if it is intended draw statistical inferences about the coefficients of regression.
   • COEFFICIENT OF CORRELATION
     • Up to this point, we have analyzed the relationship function of Y with X. Suppose that we are also interested the intensity of the linear relationship between these two variables, which leads to the concept of coefficient of correlation. Two additional assumptions were made when analyzing the correlation model. First, that Xi is a random variable. An observation sample allows obtaining values ​​of Xi and Yi. The second, that the observations come from a normal distribution of two variables, that is, one in which the variable X has a normal distribution, same as the variable Y.