# Regresion lineal

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SIMPLE LINEAR REGRESSION

Regression and correlation are two statistical techniques that can be used to solve common problems in business.
Many studies are based on the belief that it is possibleto identify and quantify any functional relationship between two or more variables, where a variable depends on another variable.
One can say that Y depends on X, where X and Y are two variables inany simple regression model.
"And it is a function of X"
Y = f (X)
Since Y depends on X,
Y is the dependent variable, and
X is the independent variable.
In the regression model is very importantto identify which is the dependent variable and what is the independent variable.
In the Simple Regression Model states that Y is a function of only one independent variable, which is why it iscalled bivariate regression also because there are only two variables, one dependent and one independent and looks like this:
Y = f (X)

"And it's coming back for X"

The dependent variable is thevariable to be explained, predicted. Also called back or response variable.
The independent variable x is called the regressor or explanatory variable and is used to explain y.

Now assume that ifthere is a causal variable X (cause) to the variable Y (effect). In addition, we know that this relationship is linear within the range of data.
Establish a model to explain the (Y) in terms of effect(X), the following type:
Y = a + bX + e
For i = 1,2 ,..., n
In a and b are two fixed amounts (model parameters) and i are random quantities that represent the differences between what the modelposits a + bx and what is actually observed, y. For this reason and to call them "mistakes" or "random errors". Is assumed to have expected value 0 and standard deviation σ common.
Our problem is toestimate the parameters a, b σ2 to identify the model.
To estimate b using the least squares method, which is to find those values ​​of a and b that make minimum the sum of the squares of the...