The regression analysis represents search of function which would describe dependence of a variable on a number of factors. The equation received as a result of a research is used for creation of the line of regression.
It is required to you
- - calculator.
Instruction
1. Calculate average values of productive (y) and factorial (x) sign. For this purpose it is necessary to use formulas simple arithmetic and average.
2. Find equation regressions. It reflects dependence between the studied indicator and independent factors which influence it. For a temporary row its schedule will have an appearance of a trend characteristic of some random variable in time.
3. Most often in calculations use the equation of simple pair regression: y = ax+b. But also apply also others: power, exponential and exponential function. The function type in each case can be defined by selection of the line which describes the studied dependence more precisely.
4. Creation of linear regression comes down to determination of its parameters. They are recommended to be counted by means of analytical programs for the personal computer or special financial calculator. The easiest way of finding of elements isapplicationof the function of the classical approach based on a method of the smallest squares. Its essence consists in minimization of the sum of squares of deviations of the actual values of sign from settlement. It represents the solution of a system of the so-called normal equations. In case of linear regression the parameters of the equation are on formulas: a = hsr – bxcp; b=((y×x) ср-yср×xср) / ((x^2) sr – (hsr) ^2).
5. On the basis of the obtained data make regression function. Calculate average values x and y, substitute them in the received equation. By means of it find coordinates of points of the line of regression (xi and yi).
6. In the rectangular system of coordinates on axis x postpone xi values and, respectively, value of the yi variables for axes y. The same it should be noted coordinates of average values. If schedules were constructed truly, then they will be crossed in a point with the coordinates equal to average values.
7. The line of regression reflects the expected values of function at the known values of an argument. The interrelation between sign and factors is stronger, the corner between schedules is less.