Cross-correlation analysis of the productivity of sugar beets and factors, that it is formed

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Statistics are social science, which studies the quantitative side of the high-quality certain mass socio-economic phenomena and processes, their structure and distributing, placing in space, direction and speed of time-histories, tendencies and conformities to law of motion, closeness of intercommunications and interdepends.
The quantitative side of any public phenomenon is indissolubly related to his high-quality aspects, because a quantitative dimension does not exist without high-quality definiteness.

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Entry.............................................................................................................................................4
1. An object, task of statistics, its organization, short history of development and connection, is with other sciences........................................................................................................................................ 5
1.1. An object, task of statistics and its connection, is with other sciences..................................5
1.2. Short history of development of statistics..............................................................................7
2. Statistical estimation of indexes of products of stock-raising and factors, that on it influence.......................................................................................................................................9
2.1. System of indexes of statistics of stock-raising and method of their calculation....................................................................................................................................9
2.2. Statistical groupings and their kinds....................................................................................11
2.3. Distributing rows and them graphic image..........................................................................15
2.4. Summarizing the indexes of distributing rows......................................................................21
2.5. Variation of signs and indexes of their measuring...............................................................29
2.6. Verification of accordance of distributing of frequencies of empiric row to distributing
Theoretical..................................................................................................................................36
2.7. Selective method....................................................................................................................37
3. Cross-correlation analysis of the productivity of sugar beets and factors, that it is formed...........................................................................................................................................40
3.1. Grade correlation..................................................................................................................40
3.2. Linear regression. Determination of parameters of connection and them economic interpretation.................................................................................................................................43
3.3. Measuring of intensity of correlation. Coefficient of simple correlation and his maintenance.................................................................................................................................. 48
3.4. Plural correlation...................................................................................................................50
Conclusions....................................................................................................................................56
List of the used literature...............................................................................................................57

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Groups of economies are after the output of calves Amount of economies A middle level  of output of calves is on groups A middle level of yield is on groups
І. 90 – 91,4 6             90,67 34,43
ІІ. 91,4 – 92,8 3                92             35,47
ІІІ.92,8 – 94,2 9 93,44             36,58
IV.94,2 – 95,6 5 95 37,24
V. 95,6 - 97 7 96,43 38,71
In all: 30 467,54 182,43

     Tables are given 4 testify to the presence of direct connection between the probed signs, that with the increase of output of calves the level of yield is increased.

     With the increase of level of output of calves in economies And group as compared to economies ІV groups on 95,44% ( ), the level of yield was increased on 92,45% ( ). 

 

     

     2.3. Distributing rows and them graphic image

     At the statistical grouping of information every group is characterized the system of indexes which have complete connection and interdependence with a groups sign. If the selected groups characterize the not system of indexes, but only by the amount of units which behave to every group, reach distributing rows.

     A distributing row is grouping of units of aggregate on one sign. If an attributive sign is fixed in basis of distributing row, a row is named attributive. If a distributing row is formed on a quantitative sign, he is named variation.

     The variation rows of distributing consist of two elements - variants and frequencies. Variants are name the separate values of групувальної sign.  Frequencies are numbers which show, how many times those are or other variants in the row of distributing. 
 

Table 5 A row is well-organized after the charges of forages on a cow c. of forage units

№ in initial data Charges of forages are on a cow, ö of forage units
1 20 35,4
2 30 36,6
3 5 36,7
4 12 37
5 17 37
6 27 37,1
7 10 37,4
8 25 37,5
9 7 37,6
10 14 37,7
11 24 37,8
12 2 37,9
13 8 38
14 15 38
15 19 38
16 18 38,5
17 3 39,5
18 21 39,7
19 23 39,8
20 16 40
21 9 40,2
22 1 40,4
23 22 40,6
24 26 41,2
25 6 41,3
26 13 41,5
27 29 42
28 4 42,3
29 28 43
30 11 43,1
 
 

     

 
 

Table 6 . An interval variation row of distributing after the charges of forages is on a cow

Charges of forages on a cow c.f.un. Frequencies Middle of interval Frequency is accumulated
35,4 – 36,94 3 36,17 3
36,94 – 38,48 12 37,71 15
  38,48 – 40,02 5 39,25 20
  40,02 – 41,56 6 40,79 26
  41,56 – 43,1 4 42,33 30
Together 30 Х Х
 

Table 7. A row is well-organized after the output of calves on 100 cows

№ in initial data An output of calves is on 100 cows, chairmen
1 20 90
2               25 90
3 12 91
4 14 91
5 18 91
6 21 91
7 3 92
8 24 92
9               27 92
10                2 93
11                4 93
12 6 93
13 15 93
14 29 93
15 5 94
16 17 94
17 23 94
18 30 94
19 1 95
20 8 95
21 10 95
22 19 95
23 26 95
24 7 96
25 13 96
26 16 96
27 22 96
28 9 97
29 11 97
30 28 97
 
 

     

 

Table 8. An interval variation row of distributing is after the output of calves

An output of calves is on 100 cows, chairmen Frequencies Middle of interval Frequency is accumulated
90 – 91,4 6 90,7 6
91,4 – 92,8 3             92,1 9
92,8 –  94,2

 

9 93,5 18
94,2 –  95,6 5             94,9 23
95,6 - 97 7 96,3 30
Together 30 Х Х
 
 

Table 9. A row is well-organized after a yield on a cow

№ п/п № in initial  data yield on a cow, с
1 20                                        31,3
2               27                                         32
3 12                                        32,4
4 14                                        33,7
5 25                                        33,8   
6 30                                        35,2
7 5                                        35,4
8 19                                        35,4
9               2                                        35,9
10               17                                        35,9
11                10                                         36
12 15                                         36
13 24                                         36
14 7                                        36,3
15 8                                        37,3
16 29                                        37,3
17 4                                        37,5
18 21                                        37,5
19 23 37,8
20 18                                        37,9
21 1                                        38,1
22 6                                        38,2
23 22                                        38,2
24               28                                        38,3
25 3                                        38,4
26 11 38,6
27 16                                         39
28 13 39,4
29 26 39,4
30 9 41,2

     

Table 10. An interval variation row of distributing is after a yield on a cow

Yield on a cow, с Frequencies Middle of interval Frequency accumulated
    31,3 – 33,28 3 32,29 3
33,28 –  35,26 3 34,27 6
35,26 –  37,24 8 36,25 14
37,24 –  39,22 13 38,23 27
39,22 –  41,2 3 40,21 30
Together 30 Х Х
 

     Poligon of distributing is built in the rectangular system of co-ordinates, here on wasp of abscissas put aside variant, and on wasp of ordinates is frequency. By the ground of distributing, graphicly represent discrete variation rows. 

     

     For the graphic image of interval variation rows more frequent utillize histograms. The order of construction of this type of the graphs is such: on wasp of abscissas variants put aside the intervals of values. They are bases of rectangles the height of which (ordinate) is proportional frequency of intervals. 

     

     At the image of variation row with the accumulated frequencies the so-called curve of sums turns out in the rectangular system of co-ordinates - Kumulyatu. Kumulyatu apply at comparison of different variation rows, and also in economic researches, in particular for the analysis of concentration of production. 

     

           Like Kumulyatu in the rectangular system of co-ordinates build Ogivu. A difference of the graph is only in that on abscise an axis inflict story frequencies, and on a y-axis - value variant. 
 

       
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

                       2.4. Summarizing the indexes of distributing rows

     In an order to know about distributing of indexes, there is a necessity of calculation of descriptions of statistical rows of distributing. Major description of variation row of distributing is an average.

     An average in statistics is name summarizing description of aggregate of the of the same type phenomena from any variation sign, which shows the level of sign, counted on unit of aggregate. Together with the method of groupings averages in statistics are one of basic methods of working and analysis of mass data.

     Average as category of statistics - it, from one side, an index, which represents objectively existent properties of the public phenomena which middle indexes can be calculated on the basis of, is real; and from the second - in it взаємознищуються individual divergences of many sizes of the same kind.

     A few types of averages are used in statistics. All of them belong to the class of middle of degree, the general formula of which has such kind:                              

      ,

                                   

     If т = 1, middle arithmetic -  ;

     If т = 2, middle quadratic -  ; 

      If т =  -1, middle harmonious  - ;

     If m=0, middle geometrical   - ,

     Where К1, К2, ….Кn – chain coefficients of dynamics.

     Except for the averages of degree, descriptive descriptions of row of distributing of sign are used in statistics — Moda (Мо) and Mediana (Ме).

     An arithmetic average is widely used in statistics.  It is the most widespread type of averages. The middle arithmetic is determined as attitude of sum of separate values of sign toward the amount of units of aggregate. Distinguish middle arithmetic simple and weighed. Middle the arithmetic simple is applied then, when the individual values of avarage sign are known in every unit of aggregate. Middle arithmetic the weighed is calculated, when the separate values of average sign repeat oneself in the probed aggregate different number one times, and weighing in this case conduct after frequencies which show how many times a certain variant repeats oneself. A geometrical average is utillized for determination of middle rates of dynamics of the meaningful phenomena. A quadratic average is used at the study of connections between the probed phenomena and their reasons by the method of correlation analysis but other

     Will apply theoretical material to our project task and will expect simple averages. 
 
 

     Table 11.  Initial and calculation information is for the calculation of simple averages

№ п/п Y X1 X2 1/Y Y2 1/ X1 X12 1/ X2    X22
1 38,1 40,4 95 0,0262 1451,61 0,0248 1632,2 0,0105 9025
2 35,9 37,9 93 0,0279 1288,81 0,0264 1436,4 0,0108 8649
3 38,4 39,5 92 0,0260 1474,56 0,0253 1560,3 0,0109 8464
4 37,5 42,3 93 0,0267 1406,25 0,0236 1789,3 0,0108 8649
5 35,4 36,7 94 0,0282 1253,16 0,0272 1346,9 0,0106 8836
6 38,2 41,3 93 0,0262 1459,24 0,0242 1705,7 0,0108 8649
7 36,3 37,6 96 0,0275 1317,69 0,0266 1413,8 0,0104 9216
8 37,3 38 95 0,0268 1391,29 0,0263 1444 0,0105 9025
9 41,2 40,2 97 0,0243 1697,44 0,0249 1616 0,0103 9409
10 36 37,4 95 0,0278 1296 0,0267 1398,8 0,0105 9025
11 38,6 43,1 97 0,0259 1489,96 0,0232 1857,6 0,0103 9409
12 32,4 37 91 0,0309 1049,76 0,0270 1369 0,0110 8281
13 39,4 41,5 96 0,0254 1552,36 0,0241 1722,3 0,0104 9216
14 33,7 37,7 91 0,0297 1135,69 0,0265 1421,3 0,0110 8281
15 36 38 93 0,0278 1296 0,0263 1444 0,0108 8649
16 39 40 96 0,0256 1521 0,0250 1600 0,0104 9216
17 35,9 37 94 0,0279 1288,81 0,0270 1369 0,0106 8836
18 37,9 38,5 91 0,0264 1436,41 0,0260 1482,3 0,0110 8281
19 35,4 38 95 0,0282 1253,16 0,0263 1444 0,0105 9025
20 31,3 35,4 90 0,0319 979,69 0,0282 1253,2 0,0111 8100
21 37,5 39,7 91 0,0267 1406,25 0,0252 1576,1 0,0110 8281
22 38,2 40,6 96 0,0262 1459,24 0,0246 1648,4 0,0104 9216
23 37,8 39,8 94 0,0265 1428,84 0,0251 1584 0,0106 8836
24 36 37,8 92 0,0278 1296 0,0265 1428,8 0,0109 8464
25 33,8 37,5 90 0,0296 1142,44 0,0267 1406,3 0,0111 8100
26 39,4 41,2 95 0,0254 1552,36 0,0243 1697,4 0,0105 9025
27 32 37,1 92 0,0313 1024 0,0270 1376,4 0,0109 8464
28 38,3 43 97 0,0261 1466,89 0,0233 1849 0,0103 9409
29 37,3 42 93 0,0268 1391,29 0,0238 1764 0,0108 8649
30 35,2 36,6 94 0,0284 1239,04 0,0273 1339,6 0,0106 8836
Together 1099,4 1172,8 2811 0,8219 40445,2 0,7695 45976 0,3203 263521

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