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

Project task №79

before a term paper from statistics on a theme: „Statistical study of the productivity of cows” 

the Project task is given out a student __ to the course __ groups _________(Date) To give a term paper to defence       (Date)

Scientific leader       /doc.Krayevskiy V.M.

                                                     /аs. Ganaba M.D. 

PLAN 
 

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 
 
 
 

       Entry

     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.

     The task of statistical research consists in searching for of summarizings indexes establishment of conformities to law of public life, which appear only in a certain plural.

     The phenomena of public life are dynamic, inherent continuous changes and development them. The sizes of the phenomena, correlation and proportion change during a certain period. All of it means that the quantitative side of the public phenomena of statistician studies in the concrete terms of space and time.

     Given a term paper is dedicated to the study of the productivity of cows and factors, that on it influence.  So come forward the objects of my research: hopes, charges of forage and output of calves. The purpose of this course project is to rotin dependence of yield on the charges of forage on cows and output of calves. The quantitative reflection of intercommunication through the system of statistical indexes appears the task of this course project.   
 
 
 
 
 
 
 

1. An object, task of statistics, its organization, short history of development and connection, is with other sciences

1.1. An object, task of statistics and its connection, is with other sciences 

     A word «statistics» (from lat. status is the state of affairs) is  
a synonym of aggregate of facts, certain information about the socio-economic phenomena and processes. The determining line of such information is quantitative description. Name statistics also science which unites principles and methods of work with mass numeric data.

     Consequently, the objects of statistical analysis can be the most various phenomena and processes of public life. The article of statistics are sizes and quantitative between’s by the mass public phenomena, conformities to law of their forming, development, intercommunication.

     In the resulted determination of object statisticians are underlined two of principle his features. At first, statistics study the quantitative side of the public phenomena, and secondly, it studies the not single, but mass phenomena.

     Studying the quantitative side of the phenomena, statistician represents it in the numbers-indexes and exactly characterizes the concrete measure of the phenomena these, sets general properties, finds out a germination and difference of separate lines, unites elements in groups, finds out the certain types of the phenomena.

     Will notice that the study of quantitative side of the public phenomena is indissolubly related to their high-quality maintenance. In fact a quantitative dimension does not exist without high-quality definiteness. Yes, at grouping of population on age of statistician selects excellent contingents high-quality: preschool age, school, capable of working, pension. However before to figure on, it is necessary to define high-quality properties and limits of every contingent.

     The phenomena of public life are dynamic, they continuously change and develop. The sizes of the phenomena, correlation and proportion change in course of time. Their values are different for separate objects, regions and others like that. And consequently the quantitative side of the public phenomena of statistician must study in the concrete terms of space and time.

     Other  feature of the article of statistics is related to mass character of the public phenomena. Statistics study the phenomena which repeat oneself in space or in time.

     For the mass phenomenon characteristic participating in him of certain plural of elements substantial properties of which are alike. Yes, the shareholders of firm are united by a proper, managers, unlike shareholders, regulate businesses of firm, workers execute production functions are certain. The presence of any properties at a separate, single element - a chance. Barely only the far of elements unites in one unit, the combined action of chances gives a result, practically independent of case. Generally known, that the market of equities is related to the risk. Propensity to the risk among a population as a potential investor different. One are ready to risk, other do not present a risk without guarantees or avoid it at any terms. On the whole, propensity to the risk among young people considerably higher, than among people a summer, and too years old. A risk investor is young.

     Examining the public phenomena as mass and leaning on the account of all aggregate of facts which belong to these phenomena, statistics by numbers show a degree to their development, direction and speed of changes, closeness of intercommunications and взаємозалежностей. All of it grounds to assert that statistics are a mighty mean of cognition of difficult public life.

     Statistics are the diversified science, it consists of separate sections or industries which, being it by independent parts, closely associated between itself. To four component parts of statistics are this day selected:

     1) theory of statistics, which examines the categories of statistical science, and also general for any mass phenomena methods and facilities  
of analysis;

     2) economic statistics, which studies the phenomena and processes which take place in an economy, develop the system of economic indicators and methods of study of economy of country or region as one whole;

     3) of a particular branch statisticians (industrial, financial, social infrastructure and ò. other) develop maintenance and methods calculations of indexes, which remove the features of every separate industry;

     4) social statistics, the article of which is a study of social terms and character of labour, standard of living, incomes, consumption of material welfares and services to the populations.

     However much social science of statistician can develop separately from theoretical sciences about society, in particular economic theory and sociology. Leaning on essence, high-quality nature of the phenomena, through generalization of mass information of statistician studies character and operate basic laws in the real life. Assuming that complex of terms and factors which form the proper conformities to law, in future will remain unchanging, statistics do prognosis calculations, very necessary for the ground of directions of economic policy. 
 
 
 
 
 
 
 

     The primary form of statistics was an economic account appearance of which behaves to the deep remoteness and related to formation of the states. For a government information is needed was about the quantity of population, composition of earths, population of cattle, state of shipping et al. Already there were the developed systems of state and administrative account in the countries of the Ancient world, that got a reflection in the sacred books of different people. Yes, Konfutsiy in the book of «Shu-king» alludes to information of census of population of China in 2238 to í. it is. In Bible, in the Fourth book of Moses «Chisla» told about the account of masculine population, able to carry arm or weapons.

     The ancient world was changed by character of economic account. An account on initiative of bankers, merchants, proprietors of workshops appears except for a state account, where slaves worked, and латифунцій. With expansion of connections and pictures of the world there were descriptions of the states. Aristotle described 157 cities and the states at one time.

     In ancient Rome the first statistical organ - qualification was formed for enumerating of free citizens. A considerable impulse to development got the account of private economies.

     From dark Ages to our times the unique report of information of the general landed census of England was saved «Book of doomsday». Development of cities resulted in appearance of municipal account.

     Exactness and authenticity of economic account were low. In everyday life people used comparative charts «anymore - less than» and only as a last resort - by quantitative measuring devices. Renaissance age gave to the world Luke Pacheli, which in the fundamental encyclopaedic labour «Sum of arithmetic, geometry, studies about proportions and relations» (1494) pawned bases of record-keeping.

     Development book-keeping account and primary registration of facts, accumulation of mass information about the public phenomena and necessity of their generalization, increase of demand in relation to the quantitative measuring of the phenomena and conformities to law of public life, development of such fundamental sciences, as philosophy and mathematics, which helped to realize value of statistics as mean of social cognition, - here incomplete list of terms due to which from the XVII item forming of statistics became inevitable. At the beginning of this process two was selected directions: stateknowing and political arithmetic.

     Stateknowing is often named descriptive school of statistics. Its representatives considered the systematized description of those facts which determine a grandeur and power of the state the basic tasks of statistics. However much verbal descriptions prevailed through narrow-mindedness of digital data, and mathematical methods of cognition are underestimated. Without regard to all of it, it follows to consider the aggregate of the developed indexes indisputable achievement of stateknowing creation of the special system of capture of statistical data about the mass phenomena.

     School of political arithmeticers at the study of the social phenomena gave advantage to quantitative descriptions. Founder of it V.Petti used the new method of leading to. In place of verbal comparisons, praise and abstract arguments he expressed the opinions the language of numbers, weight, measures.

     Political arithmeticers on the whole right defined essence of statistics, its task and value as to the method of social cognition. Their lamps indissoluble connection handed on the with practical, political and economic activity. The representatives of this school (A. Graunt, P. Zyusmil'kh but other) brought in a ponderable contribution to development of demography, entered tables and graphic arts in a scientific turn. In the XVIII item the first steps were done also on a way to the study of dynamics of prices by indexes (Dyuto, Charles).

     Thus, stateknowing and political arithmetic - two directions of gradual development of economic account, for them one object of research is society, but different methods are description and measuring.

     In the XIX item the volumes of official information and quantitative descriptions grew gradually ousted text descriptions. Statistics acquired a «quantitative tint». Its subsequent development required perfection of methods of collection, treatment, generalization of mass information. The founder of theory of statistics was become by A.Ketle. His labours, foremost «Social physics», is beginning of search of philosophical foundations of statistics. A. Ketle considered that the article of statistics is a «man in society», and by methodological basis is principle of mass character, later adopted by the law of large numbers. Exactly this principle stipulated the necessity of calculation of averages as summarizings descriptions of aggregate.

     In Russia in the XIX item statistics of politically economic were formed straight. To it works testify K. F. Herman, K. I. Arsen'eva, V. P. Androsova, D.P. Zhuravskogo but other However much intensive development of mathematical statistics at the end of age pressed political economy its direction. In this connection two conceptions were selected in relation to scientific maintenance of statistics:

1. statistics as method of cognition (I. I. Chuprov, I. I. Kaufman,          N.A. Kablukov, N.K. Druzhinin and ін);
2. statistics are science, the article of research of which are the mass phenomena and processes (Þ. It is. Yanson, And. Ô. Fortunatov, In. Ñ. Nimchinov, Y. S. Paskhaver but other).

     Each of conceptions represented one side of statistics only, as statistics simultaneously are and science, and method. Expansion of statistical methods in the different areas of knowledges resulted in the protracted discussion in relation to the article of statistics. One considered that statistics studied any mass phenomena, other  limited the article of study of public life the phenomena. A discussion was completed by confession of statistics by social science. 
 

2. Statistical estimation of indexes of products of stock-raising and factors, that on it influence 

2.1. System of indexes of statistics of stock-raising and method of their calculation

       Statistics of agriculture are one of the special areas of statistical science. Before to give determination of the article of statistics of agriculture, it follows to specify on the existent different concept of this science. Some statisticians in determination of object apply the known formulation of statistics as science which studies quantitative description of the mass public phenomena in indissoluble connection with their high-quality description, and mechanically bind this formulation to the estimations of the phenomena in an agricultural production. Other consider that statistics study the phenomena and processes of recreation of material welfares and public relations in agriculture in their high-quality expression, giving the proper digital description to them. An idea deserves the special attention, that the article of agricultural statistics is the system of objective statistical indexes of the state to development of agricultural production.

       So, Statistic of agriculture - one of basic sectorial statistician, which develops maintenance and methods of calculation and analysis of statistical indexes which characterize the state and development of agriculture. 

       The products of stock-raising are divided into two groups:

       1) products of normal vital functions of animals, realization of which for the use outside a stock-raising is unconnected with the coalface of animals (milk, wool, eggs, honey and others like that). In creation of this products animals come forward in quality facilities of labour;

       2) products of issue and increase, or products of growing of animals. Realization of this products outside a stock-raising offers the coalface of animals. The use of this products of growing of animals for the recreation of herd is related to his subsequent abandonment in the sphere of stock-raising. Thus, animals which grow or get fat come forward as the articles of labour constrained in a production, or differently, uncompleted production of meat contingent, and also animals of basic herd. Grown grown man cattle, pedigree, is the complete prepared products which is used in a role of facilities of labour.

       To the completed products of stock-raising, cattle got as a result of growing, take:

       1) animals, grown for pedigree aims (completing of basic herd);

       2) animals, grown for exploitation in quality draft force;

       3) animals, grown for a coalface on meat;

       4) increase of living weight of grown man animals which are put on fattening.

         It follows notices, that if not to take into account the increase of living weight of grown man cattle and precocity of types of animals, then the prepared products of stock-raising (in the type of adults, pedigree, workings and appointed to the coalface meat animals) created during more or less great while (1,5 - 3 years). In this connection to the end of year, when determine the products of all industries considerable part of population is in a state of the uncompleted production. However very specific this uncompleted production is through the features of the natural form, as: a) possible realization of part of such cattle on a side for the subsequent growing on a tribe or coalface; b) possibly comparatively in largenesses change of time of transmission of cattle for a coalface (though economic cattle of that or other age and setting or to the uncompleted production, whether to functionings facilities of labour, at certain terms this cattle can be also hammered in on meat).

       As a result of the noted circumstances in quality the prepared products of stock-raising of agricultural  enterprises all cattle of the pedigree and meat setting realized outside an economy appears, at first, including unfinished a production in general (sapling), secondly, cattle which is grown for addition to the herd and for a внутрігосподарського coalface. But cattle, realized on a side, and a cattle, leave on a tribe for itself or hammered on meat, is a result of production of not alone year (in any event this period of production goes out outside a calendar year). Moreover, realized after fattening cattle and bought cattle contains part of products, which was taken into account for other periods or in other economies. Therefore products this year can be defined only by a calculation way in two forms: in money and in living weight.

       1. In a money form. In this case from the cost of cattle on the end of year and cost of the realized hammered cattle calculate the cost of cattle, which is on beginning of year and purchased.

       2. In living weight. Determination of products of stock-raising in living weight has the known economic value from two grounds: 1) growing on a tribe and meat, and also fattening of cattle is characterized by the change  of living weight; 2) all cattle of the meat setting, and also (during the proper period) and the cattle of basic herd presents complex raw material for the production of meat, fat, skin and others like that. At the same time it is necessary to mark, that this index of living weight is very rough and inexact, as: a) living weight of cattle of different kinds, which differs the output of meat and his quality, is summarized (calorie content, taste qualities, et cetera); b) living weight considerably hesitates regardless of for slaughter weight through one state of animal; c) the taken into account products of living weight can be forgotten at to the next underfeeding of cattle. 

       The first failing can be in a certain measure liquidated by the count of living weight on for slaughter. However, in relation to growing of pedigree cattle it does not give  the special advantage. The second failing can not be overcame by a normative count by for slaughter weight. For this purpose it is necessary to define for slaughter weight of animals, that needs the special skills and to carry  out only on purveying points. The third failing, unfortunately, presents specific difficulty of account of unjustified losses of production. Information about motion of total number of livestock of cattle and bird in the agricultural enterprises of area is resulted in addition 1. 

       2.2. Statistical groupings and their kinds

     A statistical report is the scientific working of primary materials of statistical supervision for description of aggregate by the generalized indexes.

     Primary purpose and maintenance of statistical report - to generalize material, full and objectively to describe all aggregate of facts, expose conformities to law of mass processes which are fixed in indexes.

     Grouping is the major stage of statistical report. It is a method of research of the mass public phenomena by the association of units of aggregate in homogeneous groups after substantial signs. It enables to dissociate substantial lines from unimportant in primary statistical material, to feel passing of quantitative changes to high-quality, in many chances to find out a necessity as those or other conformities to law of the investigated phenomenon.

     In addition, the method of grouping creates terms for scientific application of other statistical methods of analysis: to the method of, relative averages, index method and others like that. An important value has a table of contents of groupings in sociallegal researches, as enables: to find out high-quality homogeneous aggregates, types of the phenomena; to describe the structure of aggregate and structural changes; to investigate intercommunication between legally dependent indexes. In accordance with these tasks a statistician is applied by three basic types of groupings:typological, structural and analytical.

     Under the типологічним grouping understand distributing of the investigated aggregate on the high-quality homogeneous types of the phenomena and processes. (Grouping of enterprises is after the patterns of ownership; population - after community groups; crimes - after forms and types of guilt - intentional, careless and after the categories of weight; personalities guilty - minor, adults, засуджені, justified; criminals after - by the articles of the Criminal code and others like that.)

     The structural grouping is characterized by distributing high-quality of homogeneous aggregate on groups on a certain sign with the purpose of study of structure (to composition) typically homogeneous groups of cultures. Consequently, the типологічне grouping is preceded structural.

     The analytical grouping is done by possible by the exposure of intercommunication of the investigated phenomena and processes. Two signs are fixed in basis of the analytical grouping at least: factor and effective. The factor is name such sign, which other sign which is named effective changes under act of.

     At grouping after signs which have direct quantitative expression, it is necessary to untie a question about the amount of groups and about the choice of interval of grouping after a formula:

     where Xmax and Xmin -  accordingly most and the least value of sign; n - is a number of groups.

       If aggregate - N<30 of units, then the amount of groups (n) will be evened three. In our project task of N=30, that is why will select 5 groups.

     Determination of influencing of charges of forages on yield:

     So , using a formula to our aggregate of information, will define that an interval will be evened 0,77 c.f.un.

     Knowing the size of interval and amount of groups, build the limits of groups: 

     1. 35,4 - 36,94

     2. 36,94 - 38,48

     3. 38,48 - 40,02

     4. 40,02 - 41,56

     5. 41,56 - 43,1 

     Erect all calculations in a table 1.

  Table 1. Influencing of expense  of forages on hopes              

     For to information of auxiliary table 1, will build a basic table 2: 

Table 2. Influencing of middle  is charges  of forages on yield

     Tables are given 2 testify to the presence of direct connection between the probed signs, that with the increase  of charges of forages on a cow  the level of yield is increased.

     With the increase of level of charges of forages in economies And group as compared to economies   ІV groups on 88,65% ( ), the level of yield was increased on 86,92% ( ).

     Determination of influencing of output of calves on yield:

     So, using   formula to our aggregate of information, will define that interval approximately 1,4 chairmen.

     Knowing the size of interval and amount of groups, build the limits of groups:

1. 90 – 91,4
2. 91,4 – 92,8
3. 92,8 – 94,2
4. 94,2 – 95,6
5. 95,6 - 97

     Erect all calculations in a table 3: 
 
 
 
 
 

Table 3. Influencing of output of calves on yield

     For to information of auxiliary table 3, will build a basic table 4:

Table 4. Influencing of middle output of calves  on the level of yield