How to build a regression equation

The equation of the regression model of dependence of performance from the factors affecting it, expressed in numerical form. The complexity of its construction is that of the variety of functions is necessary to choose the one that most closely describes the studied dependence. This choice is made either on the basis of theoretical knowledge about the studied phenomenon, or the experience of the previous similar study or with a simple search and evaluation functions of different types.

There are various kinds of models of functional dependence. The most common are the linear, hyperbolic, quadratic, power, exponential and exponential.

The source material for the compilation of the equations are values of x and y obtained as a result of observation. Based on them is a table, which reflects some actual factor values and corresponding values of resultant variable y.

The easiest way to build the equation of regression of the pair. It has the form: y = ax+b. The parameter a is the so - called free member. The parameter b is the regression coefficient. It shows the amount by which the average effective changes sign when changing the sign of factor x per unit.

The construction of the regression equation is reduced to the determination of its parameters. They are using the method of least squares, which is a solution of the system of the so-called normal equations. In this case, the parameters of the equation are the formulas: a = khsr – bxср; b=((y×x)SR-SRM×khsr)/((x^2)CP – (khsr)^2).

If it is impossible to ensure the equality of all other conditions in the analysis of the influence of the build equation, the so-called multiple regression. In this case, the selected model is introduced other factor the signs which must meet the following criteria: to be quantifiable and be in functional dependence. Then the function takes the form:y = b+a1x1+a2x2+a3x3...anxn. The parameters of this equation are the same as for the equation pair.