In the study of a phenomenon or process is often necessary to find out whether there is a relationship between the factors (variables) and the response function (dependent variables) and how close is their interaction.Make it allows regression analysis, which is carried out in several stages.
One of the main stages of the regression analysis is to calculate the mathematical relationship between the factors and the response function, which allows you to quantify the existing relationship between them.This relationship is called the regression equation.Formally, the basic analytical method for the determination of this equation is the method of least squares, as this method is optimal and allows smooth point correlation field.In practice, to find such a function can be difficult, because you have to rely on theoretical knowledge about the phenomenon under study, the experience of his predecessors in the field of science or by the method of "trial and error" to make a simple search and evaluation of the various functions.In case of success will be obtained regression equation adequately assess the impact of various factors on the response function, that is, to find the expected value of the response function (the dependent variable) for certain values of factors (dependent variables).
The initial data for the regression analysis of the values of x and factor corresponding values of the response function Y, obtained by carrying out the experimental part of the work.For clarity and easier perception of these values are presented in tabular form.
linear regression equation, as a rule, has the form Y = a + b ∙ X.It includes constant coefficient (constant) a, and the regression coefficient (the slope) b, multiplied by the variable factor H. The coefficient b indicates the average change in the response function when the value factor by one unit.When plotting the regression equation using the coefficient b can also determine the angle of a straight line to the abscissa.It should be noted that this ratio has certain properties:
· b may have different values;
· b is not symmetric, ie changes its value when studying the effect of Y on X;
· unit of measurement of the correlation coefficient is the ratio of units of the response function Y of the unit of measurement of variables X;
· in case of change of units of measurement variables X and Y value of the regression coefficient also changes.
In most cases, the observed values are rarely located exactly on the line.Almost always, you can watch some scatter of the experimental data on the regression line, which forms the predicted values.Deviation from a particular point of the regression line from its theoretical or predicted value is called the remainder.
Very often in practice is determined by sampling the regression equation, the basic method of calculating the coefficients of which is the least squares method.The coefficients are calculated from the initial data representing the sample values of a variable factor and the response function.
At first glance it may seem that the calculation of the value of the coefficients in the regression equation is rather complicated and time-consuming.But it is not.It offers researchers numerous software packages (the easiest is Microsoft Excel), which according to your original data is not only to calculate all the factors included in the equation, will be able to establish the extent of the relationship between the variables and the dependent variables, but will represent the values obtained in graphical form.
