LINEAR REGRESSION

In statistics the linear fit linear regression is a mathematical method that models the relationship between a dependent variable Y, independent variables Xi and a random term .This model can be expressed as: Where is the intersection or 0 term “constant”, the respective parameters i are each independent variable, p is the number of independent parameters to be considered in the regression.The linear regression can be contrasted with the nonlinear regression. The linear regression model 1.The linear model relating the dependent variable and with K explanatory variables Xk (k 1, … K), or transforming them, which generate a hyperplane k unknown parameters: 2. where is the random disturbance that reflects all those factors not controllable or observable reality and therefore are associated with chance, and is what gives the model its stochastic character.In the simplest case of two explanatory variables, the hyperplane is a line: 3. The regression problem is to choose certain values for the unknown parameters k, so the equation is completely specified. This requires a set of observations. In an observation anyone ith (i 1, …I) records the simultaneous behavior of the dependent variable and the explanatory variables (random shocks are assumed unobservable). 4. The chosen values as estimators of the parameters are the regression coefficients, without being able to secure matching actual parameters of the generative process.

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