Audit and economical analysis

Integral method. M is composed of mixed models with ultilative, square and mixed-additive.

Integral method chain method allows for more accurate results when calculating the effects of factors on absolute and relative differences.

The algorithms for computing the effects of factors for different models are as follows.

Table 18

Integral method models

Models	Determination of the effects of factors
f=xy	fx+fy=f
Impact of X factor	fx= xy0+^1/2xy, or fx=^1/2x(y0+y1)
It is the factor effect	f=yx0 + ^1/2xy, or fy=^1/2y(x0+x1)
f=xyz.	fx+fy+fz = f
Impact of X factor	fx=^1/2x(y0z1+y1z0)+ /xyz;
The effect of that factor	fy=^1/2y(x0z1+x1z0)+ xyz;
Z effect	fz=^1/2z(x0y1+x1y0)+ xyz.
f=xyzq	fx+fy+fz+fq=f
Impact of X factor	fx=1/6x*[3q0*y0*z0+y1*q0(z1+z)+q1*z0(y1+y)+z1*y0(q1+q)]+x*y*z*q/4;
The effect of that factor	1/6y*[3q0*x0*z0+x1*q0(z1+z)+q1*z0(x1+x)+z1*x0(q1+q)]+x*y*z*q/4;
z effect	fz=1/6z* [3q0*x0*y0+x0*q1(y1+y)+y1*q0(x1+x)+x1*y0(q1+q)]+x*y*z*q/4;
q repellent effect	1/6q*[3z0*x0*y0+x0*z1(y1+y)+y1*z0(x1+x)+x1*y0(z1+z)]+x*y*z*q/4.

 

The impact of the factors on the result can be reviewed in the following examples.

Table 19

An analysis of the impact of productivity changes on the number of workers and their productivity

Indicators	Last year	In fact	Difference (+ ;-)
Number of Employees, Person (X)	144	152	+8
Products manufactured by a worker, thous. UZS (Um)	1235	1207	-28
Product volume, thous. UZS (F)	177840	183464	+5624

O is performed to calculate the effect of moving the following:

F = X * Y

1. 
   Fx = (8 * 1235) + ½ (8 * (- 28)) = 9880 + (- 112) = + 9768 .0
   

2. Fy = (- 28 * 144) +1/2 (-28 * 8) = - 4032+ (-112) = - 4144 .0

D F = D Fx + D Fy = 9768 + (-4144) = 5624 .0

The increase in the number of employees to 8 people increased the volume of production by 9,768,000 UZS. Decrease in the output of one worker by 28,000 UZS decreased production volume by 4,144,000 UZS.

Table 20

Product changes in the size of the average number of employees, and appropriate analysis of the impact on the volume of product a day

Indicators	Last year	In fact	Difference (+ ;-)
Number of Employees, Person ( X )	203	212	+9
The average size of a worker to finish the day, one day (U)	278	270	-8
Average product volume per day, thous. UZS ( Z )	104	111	+7
Product volume, thous. UZS (F )	5869136	6353640	484504

 

F = X * Y * Z

1. Fx = _(1/2 * (9) * 278 * 111 + 270 * 104) + _1/3 * 9 * (8) * 7 = + 265053

2. Fy = _(1/2 * (8) * (203) * 111 + 104 * 212)) + _1/3 * 9 * (8) * 7 = -178492

3. FZ = _(1/2 * (7) * 203 * 270 + 212 * 278) + _1/3 * 9 * (8) * 7 = + 397943

DF = DFx + DFy + DFz = 265053 + (-178492) + 397943 = + 484504

Table 21

Arrays and mixed models

Modular model shape	H account the influence of factors-book

Logarithm method. The logarithm method is used to calculate the effects of factors on multipolar models.

In contrast to the integral method, logorifism is not an absolute increase in indicators , but rather their incremental index.

Using the table data, we count growth of productivity by factor number ( X ), number of days worked by one employee ( U ) and average daily production ( Z ).

Table 22

An analysis of the product size change, the number of employees, the average day of production and the impact of product per day

Indicators	Last year	In fact	Difference (+ ;-)
Number of Employees, Person (X)	120	100	+20
On average, the day when a worker conforms to a person,	208	200	-8
Average product volume per day, thous. UZS (Z)	24	20	+4
Product volume, thous. UZS (F )	600,000	400 . 000	200,000

∆Qumum=∆Qx+∆Qy+∆Qz = 89.9 + 20.2 + 89.9=200 million. UZS.
Correliation (stochastic) ligation . This is an incomplete, concise link between the indicators that appear only in many observations. Usually, jft and large correlation are different. Couples correlation - is one factor, among other indicators resulting bond. The correlation of the final indicators of the maximum amount ofinteraction with a number of factors.

Korrelyatsion analysis or under the influence of several factors used to determine the resulting changes in the indicators (m Should size), each factor to determine the final figure indi Forage us.

Table 23

The labor productivity ( Y ) depends on the age of the worker ( x )

X	y	x /10	xy	x2	x2y	x3	x4	yx
20	4.2	2.0	8.4	4.00	16.8	8.0	16	3.93
25	4.8	2.5	12.0	6.25	30.0	15.62	39	4,90
30	5.3	3.0	15.9	9.00	47.7	27,00	81	5.55
35	6.0	3.5	21.0	12.25	73.5	42.87	150	5.95
40	6.2	4.0	24.8	16.00	99.2	64.00	256	6.05
45	5.8	4.5	26.1	20.25	117.4	91.13	410	5,90
50	5.3	5.0	26.5	25,00	132.5	125,00	625	5,43
55	4.4	5.5	24.2	30.25	133.1	166.40	915	4.78
60	4.0	6.0	24.0	36,00	144.0	216.00	1296	3,70
Total	46.0	36.0	183.0	159.00	794.0	756,00	3788	46.00

As can be seen from the table, the labor productivity of workers increases to 40 and then decreases. So, which many workers in the 30-40-year-old company, that the company's labor unumdorli would be higher. This factor should be taken into account when planning labor productivity and calculating its incremental stocks.

In the economic analysis, hyperlinks are often used to write a slanted link

To determine its parameters, you need to solve the following equations system:       

Hyperbola describes the following links between the two indicators . A train and a variable exceeds the value of the other, and then grow to a certain extent, for example, a decline in productivity growth fertilizer is inserted, the productivity of their animals fed several times depend on the size of the production cost of the products, etc.

Correlation coefficients are used to measure the susceptibility to acute and conclusive relationships . In the case of a direct linear relationship between the indicators being studied , it is derived from the following formula:

                                                       

The table data in the formula is formulated  and   we can deduce the value of the value from 0.66.

The correlation coefficient can range from 0 to 1. The closer the value to 1, the closer the relationship to the case being investigated, and the contrary. The correlation coefficient was higher ( r = 0.66). From this we can conclude that the quality of the land is one of the main factors that depend on the level of crop yield in the area.

If we increase the correlation coefficient to a second, the coefficient of determining ( d = 0,436). This indicates that 43.5% of the indicators are dependent on the remaining factors, 56.5% on the main factor .

The linear correlation coefficient is used to measure the relationship between the curvature of a straight line and this correlation approach is as follows:                                                                     

This formula is universal. The formula for calculating the correlation coefficient can communicate in any form Foya. However, first of all, it is necessary to solve the regression equation and to calculate the correct value of the resultant ( Yx ) for each trace and the square of the real value from the average and corrected level.

Table 24

Calculation of starting data for correlation relations in the inverse linear connection