REGRESSION ON THE EFFECT OF FEED TO THE TOTAL NUMBER OF EGGS PRODUCE BY LAYERS (A CASE STUDY OF CHICK-TECH FARM LIMITED KASARAWA, SOKOTO STATE)

SUBMITTED TO THE DEPARTMENT OF MATHEMATICS, STATISTIC UNIT IN PARTIAL FULFULMENT OF THE REQUIMENTS FOR THE AWARD OF THE BACHELOR OF SCIENCE DEGREE IN STATISTICS,
USMAN DANFODIYO UNIVERSITY, SOKOTO


















NOVEMBER, 2017
CERTIFICATION
This project by AbdulkareemAbdullahi Admission Number: 1210311096 have been read approved and met the partial requirements for the award of Bachelor of Science Degree in Statistics (B sc. Statistics) of the Department of Mathematics, Faculty of Science, UsmanuDanfodio University, Sokoto.


_________________ ________________________
Dr.Shamsu Suleiman         Date
Supervisor

________________ ________________________
Prof. A. Danbaba          Date
Head of Department

_________________ ________________________
External Examiner         Date









DEDICATION
This research project is dedicated to my parents AlhajiAbdullahi S kamarawa, HajiyaMaimuna Sani In addition, I also dedicated toall my sibling.

































ACKOWLEDGEMENTS
In the name of Allah, the most Beneficent, the most merciful, master of the Day of Judgment. Glory is unto Allah He who has bestowed on me the strength and the knowledge to carry out this project work successfully. It is by his grace and not by anybody’s that I was able to carry out this research work with ease.
May the peace and blessing of Allah be upon the noble prophet Muhammad (S.A.W), his companions, his household and the entire Muslim ummah.
My profound appreciation goes to my kind and humble supervisor Mal. HussainiLawal who despite his tight schedules devoted all his effort and knowledge to read carefully through line and every line and word of this write up making necessary corrections and contribution which led to the success of this research work. May Allah shower his blessing and Mercy upon you and your family (Amin).
My appreciation and thanks goes to our H.O.D Prof. A.Danbaba and also Prof. S.U Gulumbe, Dr Umar Usman, Dr. Yakubu Musa, Dr. Shamsudeen Suleiman, Mal. A.B. Zoramawa, Mal. Audu Ahmed, Mal. NasiruDauran and all staff and lecturers in Mathematics department for their caring advice and knowledge impacted to me. 
At this point my appreciation goes my parents Dr. Ibrahim HussainiAliero and Habiba Ibrahim who has been sponsoring me from primary school up to level I am today in my educational career, I say big thank you for the love and care.
I also have to appreciate the effort of my siblings Mukhtar Ibrahim Hussaini and his wife RashidaAbubakar Saleh, Ahmad Ibrahim, Hassan Ibrahim, Hussaini Ibrahim, Ismaila Ibrahim, Musa Ibrahim, Abubakar Ibrahim for their moral, financial support and caring towards my success in university. May Allah reward you abundantly.
My acknowledgement cannot be complete if I refuse to mention my friends, class mate, colleaques who have been assisting me both inside and outside school: Usman Ibrahim Namaki, Bashir Saidu (Bash pdf), Jibrilmagaji (Last value), Hassan Haruna, Abba Ladan Giro, Ibrahim UbaKallamu, BasiruHaruna, Muhammad zayyanu, RilwanuMamuda, Abubakar Ibrahim, Usman Muhammad Mabera, BuhariAliyu (Boasting), Abba Liman, Ridwanu Musa Hassan who contributed towards the success of this project very big thanks to you all. For those that are not mentioned thank you for understanding.
My acknowledgment is incomplete without saying a big thanks to (B1 Family), Usman Ibrahim,IbrahimSaidu (Baba), Ibrahim Muhammad (bomb), Mustapha Muhammad, MusadiqHaruna, Bello Abdulkadir, NasiruAlhasan, Aliyu Muhammad, Aminu Ibrahim, Zayyanu Muhammad, ShafiuHarunaJibrilAliyu,and lastly Muhammad Zayyanu Ibrahim for their support, caring and advice since the day we met toward the success of my academic pursuit. Thank you and May Allah grant all your wishes. (Amin).




















TABLE OF CONTENT
Title Page                                                                    i
Certification                                                                                        ii
Dedication                                                                              iii
Acknowledgment                                                                                                    v
Table of Contents                                                                                                      vi
List of Tables ix
List of figures x
Abstract                                                                                    xi
CHAPTER ONE: INTRODUCTION
1.0 Introduction 1
1.1 History of Background of the Chick-tech Limited Farm 3
1.3 Statement of the Problem                                41.4 Aim and Objectives                                                                            4
1.5 Scope and Limitation of the Study 5
1.6 Significances of the Study 5
CHAPTER TWO: LITERATURE REVIEW
2.0 Introduction                                                                        6
2.1 Possible Uses of Linear Regression Analysis 7
2.2 Assumption of Linear Regression Analysis 8
2.3 Correlation 10
2.4 Factor Affecting Poultry Production 11
2.5 Guidelines for Improving Household Poultry Production 15
CHAPTER THREE: MATERIAL AND METHODOS
3.0 Introduction 26
3.1 Software Used 26
3.2 Source of Data 26
3.3 Methodology 26
3.3.1 Least Square 27
3.3.2 Estimated Variance 28
3.3.3 Hypothesis Tests of Intercept and Slope 28
3.3.4 Confidence Intervals of the Intercept and Slope 29
3.3.5 Confidence Interval of Y given X 29
3.3.6 Confidence Interval of X given Y 30
3.3.7 R- Squared (Percent of variation Explained) 31
3.3.8 Rbar _ Squared (Adjusted R- Squared) 33
3.4 The correlation Coefficient 33
3.4.1 Facts about the Correlation Coefficient 35
3.4.2 Hypothesis Test for the Correlation 36
3.4.3 Confidence Intervals for the correlation 36
3.5 Independent Errors 36
3.6 Durbin – Watson Test 37
3.7 Definition Used in Residual Diagnostics 38
CHAPTER FOUR: RESULTS AND DISCUSSION
4.0 Introduction      39
4.1 Scatter Plot Section 41
CHAPTER FIVE: SUMMARY, CONCLUSION AND RECOMMENDATION
5.1 Summary  495.2 Conclusion  50
5.3 Recommendation 50
References    51
Appendix  54





















LIST OF TABLES
Table 4.1 Descriptive Statistics 44
Table 4.2 Correlation 44
Table 4.3 Variables entered/removed 45
Table 4.4 Model Summary 45
Table 4.5 Anova 46
Table 4.6 Coefficients 47
Table 4.7 Residual statistics 47
















LIST OF FIGURES
Figure 4.1 Histogram of Number of Eggs 39
Figure 4.2 Probability Plot 40
 Figure 4.3 Age of Hen Vs Total Number of Eggs 41
 Figure 4.4 average weight of hen vs total number of eggs 42
Figure 4.5 Feed Vs Total Number of Eggs 43

















ABSTRACT
Multiple Regression Analysis refers to a set of techniques for studying the straight line relationship among two or more variables. In this research work, the relationship between total number of eggs (dependent variable) and total number of hen, age, feed and average weight (independent variables) was analyzed, significant differences between the data was determined using Rawlings (1973) regression methodology and the range of a possible prediction (forecast) for total numbers of egg production was obtained from the analysis. The final analysis has revealed there is a desirable correlation between the independents and the dependent variables, there is also a strong relationship between the model and the dependent variable. The strength of the relationship between the model and the dependent variable. R(0.922) is the multiple correlation coefficient which indicate the linear correlation between the observed and model- predicted value of the dependent variable, it shows a strong relationship R-square of 85% (0.850), considering the standard deviation error of the estimate (243.50774)compared to the standard deviation of the total egg reported in the descriptive statistic table (596.07912) to measure the strength of the model fit for linear regression model. The Durbin –Watson test is used to test for first order serial correlation in regression data taken over time, since Durbin-Watson estimate (0.825) is less than 1, we conclude the data is not serially correlated. The data was obtained from Chick-Tech farm limited and SPSS was used to carry out the analysis.









CHAPTER ONE
1.0 INTRODUCTION
WITH the exception of urban areas in northern and southern Africa, most poultry production in Africa is undertaken through an extensive system at village or family level. Almost every village household keeps domestic fowl (on average between 5 and 20 birds) and it is estimated that village fowl make up more than 80% of the total fowl population in Africa estimated at 1068 million in 1995 (Guèye 1998). Under these circumstances, poultry provides a good source of protein and ready cash for villagers, which in turn helps to sustain the village economy and contributes to the prevention of urban migration. The benefits from family poultry production go directly to the rural poor, in most cases to the women who are the principal caretakers.
This review outlines the main findings reported in the literature on preferences of laying hens for facilities that may be provided in laying housing systems. Where possible we give indications of how relatively important these are to the birds.  Much of the evidence for this comes from small scale experimental studies using ‘consumer demand theory’ to determine how much the birds are prepared to work for access to the resource or facility. It is important to realise that on farms, the hens are in a more complex environment, where social and other factors in colonies and large commercial flocks may alter their preferences and the relative motivational strength for enrichment components. 
The United Nations Food and Agriculture Organization (FAO) estimated poultry population in Nigeria to be in the range of 175,000,000 in 1987 and 200,000,000 in 2002. These figures reveal a very slow growth rate of nation’s poultry industry. The imports of chilled and frozen poultry meats into Nigeria for the years 2000 to 2005 shows that the total import of poultry products over the five-year period is 11,045,522 kg. The import figures declined from 421,569kg in 2003 to 2,235kg in 2005, (Due to review of import policy which is unfavorable for local production). Thus, indicating a declining contribution of poultry imports to poultry products consumption in Nigeria.
It is expected that in the next ten years, the meat sector as a whole will continue the upward production trend driven by world population growth, particularly in developing countries.
The poultry industry in Nigeria had been rapidly expanding in past years, increasing from 185,300 MT in 2001 to 268,000 MT in 2011. Very high input costs in 2008 and 2010, caused flock expansion to effectively cease in 2008 and in 2011.
In 2011 Nigerian hen egg production totaled 636,000 MT and was valued at $527.49 million, ranking 19th in world hen egg production and the top producer in Africa. (FAO Statistics 2013)
According to Moreki (2001) family-kept chickens are rarely the sole means of livelihood for the family but are one of a number of integrated and complementary farming activities contributing to the overall well-being of the household. The local chicken sector constitutes a significant contribution to human livelihood and contributes significantly to food security of poor households and can be considered an initiative enterprise owing to its low cost ( Gondwe, 2004; Abdelqader, 2007).
 Poultry and poultry by-products can be sold to provide an income. Eating poultry meat and eggs is important especially for children and expectant mothers. Poultry can make a significant contribution in areas where child malnutrition is common. Enhanced nutrition improves growth, mental development, school performance and labour productivity and reduces the likelihood of illness. In many countries, poultry farming is regarded as the responsibility of the women. Women produce poultry to care for their families by selling chickens and eggs to buy other food.
In addition, rural poultry that scavenge for their feed can help to control pests such as cattle ticks while chicken manure can be used to fertilize crops and vegetables. Poultry projects are underway in South Africa to assist families affected by HIV/ AIDS (FAO, 2004). Households which lost loved ones from this disease and afterwards headed by children or elderly people raise poultry for sale and home consumption. In general, rural poultry plays a significant role in cultural and social life of rural people in the following ways: as gifts for relatives and for religious ceremonies, cocks as alarm clocks, to cure a sick person, starting capital for youth and a treat for special guests (Muhiye, 2007).
1.1 HISTORICAL BACKGROUND OF CHICKTECH LIMITED FRAM
The historical back ground of chick tech farm Nig. Ltd. Is a limited company incorporated in February 2008, through the farm was formed belong to Marina Farm, which major focus was poultry production of all type of birds and sale of poultry product.
The chick tech farm limited target on mainly egg production trying to work with the present government policies on reviving the agriculture system of the country.   
The company office is located at kasarawa along Bodinga road, Sokoto state.
The farm is on 100hectares of land compressing of poultry operation
The farm presently has about 19,000 commercial layer birds and day old chick (D.O.C) production
The company currently has 11 staffs made up of experts, professional and junior workers. 


1.2 STATEMENT OF PROBLEM:
We intend to make a statistical analysis on the data collected on Egg production considering Total Number of Eggs as the dependent variable and Total Number of Hen, Age, Feed and Average Weight as the independent variable using multiple regression as the statistical techniques.
For this, the data was grouped and sorted into two groups in order to make the analysis simpler and easier
1.3 AIM AND OBJECTIVES
The aimis to test whether there is significance differences between the total number of eggs and total hen, feed, and average weight. This can be achieved by the following objectives;
To test whether there exist relationships between the total number of the eggs and total number of hen, age, feed and average weight.
To be able to determine whether production of eggs is dependent of age, feed and average weight.
To be able to conduct F-test to make statistical inferences if the multiple regression model is appropriate for the data.
Finally, to be able to know the range of predictable values of Total Number of Eggs (dependent  variable) and also forecasting by using a new value of X (independent variable)


1.4 LIMITATION OF THE RESEARCH
Owing to some factors such as: time, energy and unavailability of other resources, the data employed in this research is a secondary data. Since it is a secondary data, the quality of collecting procedure cannot be controlled and error might have come in during the time of collecting its primary data. Also there is possibility of misappropriation of some data in the process of recording. The research make use of references and journals.
1.5 SIGNIFICANCES OF THE STUDY
This research work attempts to study relationship between the rate total number of egg production and total hen, age, feed and their average weight. This will go a long way in helping the company “Chick Tech Farm” to know the effect of the afore-mentioned factors on total number of egg production.
The appropriate statistical analysis is used to obtain valid conclusion and to give a good recommendation to the farm in order to make higher profit on the production of their eggs.






CHAPTER TWO
                                              LITERATURE REVIEW
2.0 INTRODUCTION
The rate of egg production is the most important trait in layers because it ultimately determines the number of egg produced in a giving period of time. Other traits, such as egg weight, shell integrity, and internal egg quality, are also important because they contribute to the economic value of the salable eggs produced and their market value. However, no other trait has the importance of egg production rate as a single indicator of the egg layer efficiency. With this in mind, major emphasis must be placed on selecting for the rate of egg production in pure lines which is basically attained by fitting a regression model. In this regard, one of the main concern for the poultry breeder is how to best define egg production rate as a trait for selection (Anang, et al., 2002).
 carotenoids are not inert substances. In the metabolism of animals, they may undergo
a large number of transformations. A number
of these compounds have vitamin A activity.
Those that have high vitamin A activity
usually have fairly low pigmenting properties.
Generally only monohydroxy- and
monoketocarotenoids are converted into
vitamin A. Generally plants synthesize
optically active carotenoids. The laying hen is
not able to transform all carotenoid
configurations so that they can be used to
increase egg pigmentation. Feed carotenoids
occur in natural compounds in about 60 to
90% trans and 10 to 30% cis form. The trans
form is a more effective pigment because of
the redder hue and greater stability. Either
the hen has the ability to convert some of the
trans form into the cis form, or this
transformation occurs in the egg yolk. The
saponification process improves the
digestibility of certain xanthophyll
preparations. The efficiency of fat absorption
in the hen also influences the deposition rate.
The rate of egg production changes over time, and be represented in terms of a “production curve”. T shape of the curve is defined by the following stages:
Sexual maturity (which make the onset of production), followed by a stage of increasing production to the maximum, or
A production peak, followed by a steady decline in egg production, or
Persistency of production. In modern layers, the production rate almost reaches its maximal biology potentials (i.e., 1 egg/hen per day) during peak production; therefore, hardly any variation exist among birds at this stage. What differ among birds is how long they can maintain a high rate of lay and at what rate production decreases after the peak. (kranis, et al 2007).
The rate of egg production is the most important trait in layers as it ultimately determines the number of eggs produced in a giving period of time. One of the main concern for the poultry breeder is how to best define egg production as a trait for selection (i.e. one egg per hen per day) during peak production; therefore there is hardly any variation among birds at this stage. What differ among birds is how long they can maintain a high rate of lay and at what rate production decreases after the peak, however this can be achieved by use of regressional analysis which define a model for future prediction and relationship between factors through correlation. (Yalcin 2006).
The domestic supply shortfall is estimated at 25,000 metric ton per annum. Despite the supply shortfall, the Government of Nigeria imposed a ban on legal poultry import in July 2002. Given the fact that Nigeria faced with a great challenge as far as the inadequacy of the livestock sub-sector is concerned, it then becomes imperative to quantitatively measured the current level of and determinants of efficiency and policy options available for raising the present level of efficiency given the fact that efficiency of production is directly related to the overall productivity of the agricultural sector vis-à-vis the poultry sub-sector. From the foregoing, there is a crucial need to raise agricultural productivity as such growth is the most efficient means of archieving food security and alleviating poverty (Amos TT 2006).
2.1 POSSIBLE USES OF LINEAR REGISTRATION ANALYSIS
Montgomery (2006) outlines the following four purposes for running a regression analysis
Description
   The analyst is seeking to find an equation that describes or summarized the relationship between two variables. This purpose makes the fewest assumptions.
Coefficient Estimation
This is a popular reason for doing regression analysis. The analyst may have a theoretical relationship in mind, and the regression analysis will confirm this theory. Most likely, there is specific interest in the magnitudes and signs of the coefficients. Frequently, this purpose for regression overlaps with others.
Prediction
The prime concern here is to predict the response variable, such as sales, delivery time, efficiency, occupancy rate in a hospital, reaction yield in some chemical processes, or strength of some metal. These predictions may be very crucial in planning, monitoring, or evaluating some processes or system. There are many assumptions and qualifications that must be made in this case. For instance, you must not extrapolate beyond the range of the data. Also, interval estimates require that normality assumptions to hold.
Control
Regression models may be used for monitoring and controlling a system. For example, you might want to calibrate a measurement system or keep a response variable within certain guidelines. When a regression model is used for control purposes, the independent variable must be related to the dependent variable in casual way. Furthermore, this functional relationship must continue over time. If it does not, continual modification of the model must occur.
2.2   ASSUMPTIONS OF LINEAR REGRESSION ANALYSIS
Linearity: linear regression models the straight-line relationship Y and X. Any curvilinear relationship is ignored. This assumption is most easily evaluated by using a scatter plot. This should be done early on in your analysis. Nonlinear patterns can also show up in residual plot. A lack of fit test is also provided.
Constant Variance: the variance of the residuals is assumed to be constant for all values of X. This assumption can be detected by plotting the residuals versus the independent variable. If these residuals plots show a rectangular shape, we can assume constant variance. On the other hand, if a residual plot shows an increasing or decreasing wedge or bowtie shape, non-constant variance(heteroscedasticity) exists and must be corrected.
The corrective action for non-constant variance is to use weighted linear regression or to perform either Y or X in such a way that variance is more nearly constant. The most popular variance stabilizing transformation is to take the logarithm of Y.
Special Causes: It is assumed that all species causes, outliers due to one-time situations, have been removed from the data. If not, they may cause non-constant variance, non-normality, or other problems with the regression model. The existence of outliers is detected by considering scatter plots of Y and Xas well as the residuals versus X. Outliers show up as points that do not follow the general pattern.
Normality:When hypothesis test and confidence limits are to be used, the residual are assumed to follow the normal distribution.
Independence: the residuals are assumed to be uncorrelated with one another, which implies that the Y’sare also uncorrelated. This assumption can be violated in two ways: model misspecification or time sequenced data’
1modelmisspecification. If an important independent variable is omitted or if an incorrect functional form is used, the residual may not be independent. The solution to this dilemma is to find the proper functional form or to include the proper independent variable and use multiple regressions.
2 timesequenceddata. Whenever regression analysis is performed on data taken over time, the residual may be corrected. This correlation among residual is called serial correlation.Positive serial correlation means that the residual in time period j tends to have the same sign as the residual in time period (j - k), where k is the lag in time periods. On the other hand, negative serial correlation means that the residual that the residual is in time period jtends to have the opposite sign as the residual in time period (j – k).
The presence of serial correlation among the residuals has several negative impacts.
1 The regression coefficients remain unbiased, but they are no longer efficient, i.e. minimum variable estimates.
2 With positive serial correlation, the mean square error may be seriously underestimated. The impact of this is that the standard errors are underestimated, the t-test are inflated (show significance when there is none), and the confidence intervals are shorter than they should be.
3 any hypothesis tests or confidence limits that require the use of the t or F distribution are invalid. You could try to identify these serial correlation patterns informally, eith the residual plots versus time. A better analytical way would be to use the Durbin-Watson test to assess the amount of serial correlation.
2.3 CORRELATION
Once the intercept and the slope have been estimated using least squares, variation indices are studied to determine the reliability of this estimate. One of the most popular of these reliability indices is the correlationcoefficient. The correlation coefficient, or simply the correlation, is an index that ranges from 1 to 1. When the value is near zero, there is no linear relationship. As the correlation gets closer to plus or minus one, the relationship is stronger. A value of one (or negative one) indicates a perfect linear relationship between two variable.
Actually, the strict interpretation of the correlation is different from that given in the last paragraph. The correlation is a parameter of the bivariate normal distribution. This distribution is used to describe the association between two variables. This association does not include a cause and effect statement. That is, the variables are not labeled as dependent and independent. One does not depend on the other. Rather, they are considered as two random variables that seem to vary together. The important point is that in linear regression, Y is assumed to be a random variable and X is assumed to be a fixed variable. In correlation analysis, both Y and X are assumed to be random variables.
2.4 Factor affecting poultry production
Feeding as a factor
Feeding is the first factor to be considered, generally when flock are fed with feed of high nutritive value, they will surly produced good eggs of good quality. The quality of the eggs depends largely on the green feed and the yellow corn or maize present in the feed. The amount of thick and thin albumen an egg contains at the time it is laid is an inherited characteristic and is not influenced by the feed. Clean and cool water must always be available to avoid heat stress. Lack of water results in reduced egg production. The amazing part of this is that, they will not eat much when the feed has no taste. For maximum production of eggs, make feed available at all time for the birds.

Quality of feed intake is one of the factors affecting eggs production in layers
You cannot just be feeding your birds with any how feed and think they will produce eggs to your expectation, if this is your opinion, my dear you totally wrong. Make available to your birds feed of high quality not quantity. There are some essential elements that must be present in the feed, if they are absent you will not achieved the maximum result from them. The provision of adequate dietary minerals and vitamins is essential for good eggshell quality. Similarly, as water quality varies from country to country and region to region, the role of drinking water in mineral and trace elements supply should not be under rated.

Management issues is another factors affecting eggs production in layers
Management of the poultry compound is very important and contributes greatly to eggs production in the farm.  If the compound or the entire place it dirty, this will surly welcome some agent that will have negative influenced on the birds.  These agents include reptiles, outbreak of diseases among others. Another thing is to make light available at all time, change the bulb if they are not functioning, bird cannot eat in the darkness as this will result in low eggs production. Chickens are to be expose to light so that they will produce more eggs and they reach maturity age early when they have more light than less light.

Genetic factors of the breed birds as factors affecting eggs production in layers
Maximum production of high quality eggs starts with a closely controlled breeding program emphasizingfavorable genetic factors. Sex Links are the most productive brown egg layers because they are a mix of two high productive breeds. If you were to breed a very low productive chicken with a high productive chicken, the next generation would not be nearly as productive as their high productive parent. But if you were to cross a high productive breed with another high productive breed the next generation would be just as productive as or more productive than their parents. So when selection you pullet for commercial eggs production, do not hesitate to go for high productive breed as this will produce more compare to the less productive once.
Hen age at egg laying period as a factors affecting eggs production in layers
Age of laying birds determine the sizes of eggs produced, early starter lay more eggs of small sizes. The sizes keep increasing as they are getting to more maturity in life, so this early eggs are
Called scattered plot
The reason behind this is that they are not fully matured laying birds, with time they will more and bigger eggs.
Diseases as a factors affecting eggs production in layers
Diseases and parasites can cause losses in egg production. Some breeds of birds are resistance to certain diseases which make them superior to those that are easily infected by many diseases. More over if you want your laying birds for maximum production, do all you could to prevent them against any kind of diseases. In case of any outbreak of diseases treat them immediately so that their production will not be tampered with. In addition, you would never want to breed an ill chicken they could pass the illnesses down to future generations and you would have a constant battle in your hands . Always raised the healthiest chickens together the more generations and that have healthy chickens the more resistance they build up to diseases.


Molting flock as a factors affecting eggs production in layers
Molting or less feather is natural phenomenon common to all poultry laying birds regardless of their species and breeds. Molting is a sign of good health in the poultry farm, so you discover this in your farm, no problem. As the birds are aging this process occur and the production begin to reduced, this is natural, if this happen to your flock when aging, no need to be worried.
Housing is another factors affecting eggs production in layers
This is another important factor that affects eggs production in laying birds. If your hens are comfortable and not stressed they will lay better. If you free range all day, they are likely going to lay in tall grass and you will be losing those eggs. You can still free range just later in the day after most have laid.In addition to this, if you allow your bird on the floor, there is high tendency of outbreak of diseases always and this is bad for them. To me, battery cage is the best if you want to have maximum production from them.
Egg collection as a factors affecting eggs production in layers
Collecting eggs several times a day is important especially if you have birds that tend to go broody. The more eggs that are in the nesting boxes and the longer they stay in there the more birds may want to sit on them. Collecting eggs many times a day also helps keep eggs clean, if there are too many eggs in one nest box they could get broken and soil the other eggs.
Laying bird behaviors
Laying birds behaviors is also an important role in eggs production, as matter of fact is one of the factors affecting eggs production in layers.    As mentioned earlier some birds love being broody. There are also ways to break a broody that include isolation in a wire cage for several day or ice packs under her in the nest.   Another hen behavior that will put a dent in the eggs you are able to gather is egg eating. Egg Eating is a very bad behavior that is hard sometimes impossible to break. Sometimes eggs get broken accidentally and the chicken will eat it, that does not make them an egg eater, but if they (layers) break the eggs purposely and eat them they are egg eaters. One more behavior that can affect production is birds guarding the nesting boxes, some birds might guard a nest and chase other birds off and make those birds lay elsewhere.
Laying birds (hens) body weight as a factors affecting eggs production in layers
Generally, optimum body weight during the laying period should be around 1.5 kg, although this varies according to breed and species . Underweight as well as overweight birds lay eggs at a lower rate. Proper management and the correct amount of feed are necessary in order to achieve optimum body weight.
2.5 GUIDELINES FOR IMPROVING HOUSEHOLD POULTRY PRODUCTION
Potential and Constraints
Constraints. The main limitation to improved household poultry production is the extremely high loss of birds before they reach maturity caused by inadequate nutrition and disease. This loss means that a high proportion of all the eggs laid have to be kept for replacement stock leaving little, if any, surplus for sale or consumption.
The main causes of loss are:
 Poor nutrition is the major cause of loss and predisposes birds to disease, poor immune response to vaccines and predation.
Disease, especially the highly infectious viral Newcastle Disease (ND) which is believed to be endemic in most rural flocks. Clinically the disease is cyclic and occurs at times of climatic and nutritional stress. The virulent (velogenic) strain common in Africa and Asia can, but not always, cause up to 80% mortality in unvaccinated chickens. Fowl Cholera (pasteurellosis), Coccidiosis, Gumboro disease (infectious bursal disease) and Fowl Pox can also, to a lesser extent, cause problems in rural flocks.
 Poor, or nonexistent housing, is also a major predisposing cause of the high losses. Without being able to confine birds at night it is almost impossible to catch and vaccinate them, although new types of ND vaccine can be administered in the feed (see section on heat stable vaccines). Shelter can also provide protection for young birds against predators and can ensure that all the eggs are laid in the proper place and not lost.
 The majority of indigenous breeds or strains of chicken/fowl have evolved to survive under harsh conditions where they largely have to fend for themselves. Such hardiness, however, is at the expense of higher levels of productivity and they are less able to exploit the advantages of improved management, nutrition, etc. than breeds with a greater genetic potential for egg production and feed conversion (growth).
Potential Improved management and disease control can have a substantial impact on household economies. Under traditional management the majority of eggs are hatched to ensure sufficient replacements with only the male birds being sold or consumed. Reduced losses will ensure that more birds could be successfully reared and, assuming the extra birds can be properly fed, this will allow more eggs to be collected and consumed or sold as a regular source of income.
Design Considerations. · Constraint Analysis: An initial review of poultry production in the pilot area, and any external factors that affect it, needs to be undertaken in order to assess what interventions would be appropriate. In addition, an assessment of the likely demand for additional poultry products will be required. Most information can be obtained from PRAs either undertaken specifically for poultry or, more likely, as an element in a more general PRA covering the pilot area(s). Guidelines to the type of information required are given in the final section “Type and Sources of Information”. It is important that constraints beyond the scope of the SP, but that could be addressed by other parties, are identified - for instance: supply of drugs and vaccines, hatchery facilities, quality control of commercial feeds etc. ·
Level of intervention: The choice of intervention: simple improved husbandry, improved husbandry combined with the introduction of improved (dual purpose) breeds, or more specialized small-scale layer or broiler production, will depend largely on local circumstances. Factors to take into consideration include: access to markets, access to inputs and services (extension, vaccines, hatcheries etc), available feed resources, existence of functioning producer/women or credit groups, capacity of the target producers to accept the increased risk associated with higher inputs. ·
Approach: In the context of the Special Programme (SP) a phased approach is considered most appropriate. Starting with ND control on a communal basis, closely followed by the introduction of improved husbandry packages for interested participants and leading, eventually, to the selection of a few more specialized farmers producing meat, eggs or 5 breeding stock. Farmers are naturally not interested in making investments in feed, improved breeds or housing were losses from ND remain high. It is, however, important to understand the relationship between disease and poor nutrition and they should not be seen, or tackled, in isolation.
The SPFS should not assist in the development of capital intensive, large-scale, commercial egg or broiler production which is best left to the private sector to support. At an early stage it is necessary to identify a master farmer(s) within the community who will be capable of putting into practice, with inputs and assistance from the SP, improved husbandry practices. These farmers’ units will act as local demonstrations as well as providing a focal point for vaccination programmes and training, a local source of advice and, possibly, for the supply of inputs. The use of schools and school clubs (Young Farmers Clubs or 4H Clubs) may also provide a valuable focal point for the programme.
 Organization and Management: In the initial stages it will be difficult to establish a programme without the involvement of government-run services. The longer-term aim should be to make the programmes as independent as possible and this will entail the eventual commercialization of input supply. This would entail encouraging entrepreneurs and the private sectors to be involved in the supply of inputs (feeds, chicks, fertile eggs, vaccines etc) and services (vaccination, marketing, extension). The development of producer groups can provide the necessary critical mass and purchasing power to access, or provide for themselves, goods and services including informal credit.
For an interim approach, it might be possible to contract some of the input supply and management activities of the programme to either an international or local NGO. The contract could specify the timing and extent to which the responsibility of programmer’s activities are transferred to the producers.


Potential Interventions
 The basis for any improvement programme will be improved husbandry, notably housing, nutrition and disease control, primarily Newcastle Disease. Subsequent interventions would concentrate on further improving nutrition and the introduction of improved breeds/strains. · Improved Feeding: Most household flocks rely on scavenging and household scraps and, depending on conditions, this is usually adequate for survival and a low level of production. Although inadequate nutrition, exacerbated by marked seasonal fluctuations, remains a major predisposing factor to disease and high mortality. As investments are made in improved animal health, housing and, especially if improved birds are to be introduced, then attention must to be given to diet supplementation or feeding a complete diet in the case of totally confined birds.
Conventional feed materials such as maize, wheat, barley, oil cakes, fish meal etc. are rarely available to the back-yard producer. In many developing countries these are in short supply and even compounded feeds may be of dubious quality. For household production systems, however, there are usually a wide range of locally available feedstuffs that can be used in addition to household scraps and include: surplus/broken or second grade grains (cereals, maize, sorghums and millet); roots and tubers (sweet potatoes, cassava etc.), green material (legumes and leaf meals, sweet potato vines etc), residues and agro-industrial by-products 6 (brans, rice polishing, oil-seed cakes, etc.). Unless a complete balanced ration is available, then the ability to free range is important to allow the birds to feed on insects and worms, green material, etc. so that they can balance their essential amino acids, mineral, vitamin, as well as energy requirements. Where appropriate, improved feeding systems (troughs etc.) should be supplied to reduce wastage. Access to clean water is always essential and a source of calcium (ideally ground oyster shell) is highly recommended. ·
 Control of Newcastle Disease (ND) and other health constraints. Effective vaccines have been available against most strains of ND for a long time. However, the vaccination of rural chicken has always been a logistical problem, because: -
 Until recently, the potency of vaccines were highly sensitive to temperature which meant that the provision of an effective vaccine at village level required a ‘cold chain’ of refrigerators, cool boxes etc. from the manufacturing laboratory through to the farm. The majority of vaccines are still highly sensitive to temperature and fall within this class;
Conventional vaccines are sold in large dose vials, usually 1000 doses, aimed at the commercial producer but unsuitable for use at the village or household level;
Village flocks are usually small, scattered and multi-aged which makes them difficult to target by mass vaccination campaigns. Catching free range, often semi-feral chickens to vaccinate them individually has always proved difficult, and
Vaccination of a multi-age flock has be undertaken on a continuous basis (monthly) to be effective.
 A new ‘heat stable’ oral vaccine has been developed and widely tested in Asia and Africa. The primary advantage is that it no longer requires a complete cold chain to maintain its potency. It is also possible to administer the vaccine orally by applying the vaccine to the surface of certain feeds (commercial pellets, cooked rice, barley and wheat), but not all, foodstuffs are suitable as carriers. In many countries it will be necessary to test their own vaccine/feed/water interactions to find the most suitable carrier. The cost of a controlled, replicated trial examining three different grains would be in the region of $5-7,000. If birds can be easily caught then the vaccine can still be given via the more traditional conjunctiva sac or nasal cavity routes.
Oral vaccination is not, however, the most efficient route and birds really need to be vaccinated two to three times. Trials in Ethiopia have shown that the Haemagglutination Inhibition (HI) levels in birds were not high enough to resist a full ND attack until after the third feed-mixed vaccination
Queensland University in Australia have made available free to laboratories in developing countries a seed virus, designated I2, to those who wish to explore the possibilities of vaccine production. This opens the door for producing with intermediate levels of technology, the fresh (not freeze dried) vaccine at regional laboratories for use within a few weeks of production. In addition, a commercial V4 vaccine is also available, but not in large quantities and it remains expensive. 7 Potentially these vaccines offer the possibility of overcoming the problems of transport, storage and the difficulty of catching individual chickens. They are not, however, available everywhere, and applying the vaccine to feeds is not without problems. The question of who produces the vaccine remains an issue and experience has shown that projects may be able to introduce the technology but often production ceases once external inputs are removed.
 Conventional vaccines remain a viable option if there is a reliable ‘cold chain’ and if housing is provided that allows the birds to be caught easily and that sufficient numbers of owner’s participate making the use of large vials economic, although their is often little difference in cost between 200 and 1,000 dose vials. A major problem with the larger vials is to find and catch 1,000 village chickens within the two hours or so that these ‘old’ heat sensitive vaccines remain viable. Almost all birds in rural flocks are infected with a variety of internal parasites which cause reduced growth rate, weight loss and lower egg production. Strategically timed treatment(s) with inexpensive anthelmintics (eg. fenbendazole and other benzimidazoles) given in the feed can easily eliminate the majority of these parasites.
Improved Housing: The basic aim should be to provide simple (using local materials wherever possible), yet secure housing for the birds at night. Approximately 0.1m2 (1ft2 ) should be adequate per bird. Housing should provide: perches for birds to roost on; access to clean water, a creep feed for chicks, and nest boxes for laying and brooding. Location should be close to the house to deter theft and preferably raised off the ground to provide protection from predators and to reduce dampness. The shelter should have easy access to allow for catching the birds with the minimum of disturbance. Such housing can usually be provided cheaply using local materials (timber, mud, thatch etc.), but more complex designs may require more expensive sawn timber and wire netting.
Improved Breeds: Once standard levels of husbandry (housing, feeding and disease control) have been achieved, then improving the genetic potential of the birds offers the next step in increasing productivity. One strategy is to use local birds to incubate and rear higher egg producing breeds.
Two choices are available. The introduction of pure-bred, dual purpose breeds (eg. the Rhode Island Red or Australorp) or the commercial hybrids which are usually selected either for meat (broiler) or egg production. Traditionally, the dual-purpose breeds have been the exotic breed of choice; the exception has been the White Leghorn, a laying breed that has proved unsatisfactory in adapting to village conditions. Obtaining grandparent stock of these breeds is becoming increasingly difficult and expensive. Some commercial companies now offer a more hardy, dual purpose type of hybrid bird that could be used in certain situations.
Securing a regular source of healthy birds from well managed hatcheries can be problematic. Traditionally, government services have maintained poultry farms with imported parent stock and have supplied day-old-chicks (DOCs) or point-of-lay (POLs) birds to farmers. However, as with so many state run operations, there are real problems in managing such enterprises efficiently. Lack of working capital and staff incentives have resulted in most operating at a very low level of productivity and at a financial loss. The alternative of placing such activities in the private sector as soon as possible is to be encouraged. Initially this may involve a phased approach through increasing cost-recovery to full privatization of 8 government services. NGO’s can have a role in providing skills, start-up loans etc. to assist private entrepreneurs establish themselves. Wherever possible the incubation, brooding, rearing and production of hatching eggs can be undertaken by separate specialized producers within the village.
In the majority of LIFDCs improved birds have to be imported. There are a number of options that can be considered: -
Importing grand-parent stock to produce parent stock in the country. This requires high levels of management, a regular supply of quality inputs, and a sufficient demand for parent stock.
Importing parent stock as either fertile eggs or day-old chicks to supply commercial birds for distribution. This is usually the most economic option if acceptable levels of production can be maintained.
Importing commercial fertile eggs or day-old chicks for direct supply to farmers. This option might be feasible to establishing a programme but it is costly. Although the full costs involved in producing DOCs locally from parent stock may exceed the cost of importing commercial DOCs if managment and performance is low. With full cost recovery, these costs will have implications for the financial viability of the enterprise that must be understood.
There are other issues that also need to be considered. The indiscriminate distribution of imported breeds could have long-term adverse effects in diluting the advantageous traits in the indigenous breeds, especially broodiness in local hens.
There is potential for improving locally adapted breeds by selection. Virtually all the indigenous breeds have not been subjected to any selection process, other than natural selection. The consequence is that there is a large variation in production traits (ie. number of eggs laid etc.) between individuals in the overall population. By identifying and selecting the top performers for a given trait, and given the chicken’s short generation interval, it would be possible to make substantial gains in genetic potential within the existing production environment. Care must be taken, however, since some traits are genetically negatively correlated ie. roodiness and egg production.
 The logistical constraints in successfully implementing such a programme are formidable, however, and would be beyond the scope of the Special Programme. ·
Training. The transfer of knowledge and skills must be an important component in every programme. Training is required at different levels:
Awareness: Senior officials, politicians and decision makers and community leaders need to be aware of the potential for improving household poultry production if they are to support such programmes.
Technical: Ideally there should be a Subject Matter Specialist(s) available to the programme that have undertaken specific training in rural poultry production and, ideally, epidemiology. There are relevant 3-12 months post-graduate courses available at agricultural colleges and universities in both developing and developed countries.
Advisory level: Extension and advisory staff need the necessary background theory to understand why certain interventions are necessary and how they work. More importantly they need the practical skills to be able to demonstrate interventions to farmers. This level of training can be provided through short in-service courses
Awareness of Farmers: Many farmers may not be aware of the consequences of disease, poor feeding and housing. Master farmers, school teachers or demonstrators need to be given the necessary knowledge, skills and confidence to set-up successful units and to assist other individuals or groups to develop similar packages. Ordinary poultry keepers, preferably in common interest groups or associations, also need access to the same skills and information. This type of training should be undertaken at village level wherever possible and should include the active participation of master farmers as resource persons. ·
Institution Support. The promotion and development of producer groups, as the basis for self-sufficiency, should be supported through: training (technical and business management) and start-up capital in the form of goods or services. Involvement and support for the private sector in the provision of goods and services should be encouraged and, initially, this would involve the introduction of cost recovery for government goods and services that provide a ‘private’ than a ‘public’ benefit.




CHAPTER THREE
RESEARCH METHODOLOGY
3.0 INTRODUCTION
In statistics regression analysis includes any techniques for modelling and analyzing several variables when the focus is on the relationship between a dependent variable and one or more independent variables. Regression analysis is a statistical tool used to investigate the nature of relationship between two or more variables, where one of the variables depends on the other variable(s). The variable that depends on the other is called the dependent or response variable on the variable on which it depends on is called independent, regression or predictor variables.
3.1 SOFTWARE USED
In this research work, SPSS (20) and Minitab (16) statistical package was used.
3.2 SOURCES OF DATA
The data for this project is a secondary Data Collected from Chick Tech. Farms limited.
3.3 METHODOLOGY
This section presents the technical details of least squares regression analysis according to Rawlings (1973) using a mixture of summation and matrix notation. Because this module also calculates weighted linear regression, the formula will include the weights when weights are not used, they are set to one. wjwj
The purpose of undertaking regression analysis among others are:
To obtain a mathematical summary of the relationship between variables.
To explain the variation in the dependent variable using the independent variables
To predict the values of the dependent variable given values of the independent variables.
Define the following vectors and matrices.
(3.1)

3.3.1 Least squares
Using this notation, the least squares estimates are found using the equation

Note that when the weights are not used, this reduces to

The predicted values of the dependent variable are given by

The residuals are calculated using
(3.2)
3.3.2 Estimated Variances
An estimate of the variance of the residuals is computed using
(3.3)
An estimate of the variance of the regression coefficients is calculated using

(3.4)
An estimate of the variance of the predicted mean of Y at a specific value of X, say X0, is given by
(3.5)
An estimate of the variance of the predicted value of Y for an individual for a specific value of X, say X0, is given by
(3.6)


i. Hypothesis Tests of the Intercept and Slope
Using these variance estimates and assuming the residuals are normally distributed, hypothesis tests may be constructed using the Student’s t distribution with N - 2 degrees of freedom using

And
(3.7)
Usually, the hypothesized values of B0 and B1 are zero, but this does not have to be the case.
Confidence Intervals of the Intercept and Slope
A 100(1 - α)% confidence interval for the intercept, B0, is given by
   (3.9)
A 100(1- α)% confidence interval for the intercept, B1, is given by

Confidence Interval of Y Given X
A 100(1 - α)% confidence interval for the mean of Y at a specific value of X, say X0, is given by
(3.10)
Note that this confidence interval assumes that the sample size at X is N.
A 100(1 - α)% prediction interval for the value of Y for an individual at a specific value of X, say X0, is given by

3.3.6 Confidence interval of X for Given Y
This type of analysis is called inverse prediction or calibration A 100(1 - α)% confidence interval for the mea  n value of X for a given value of Y is calculated as follows. First, calculate X from  Y using
(3.11)
Then, calculate the interval using

(3.13)
(3.14)
A 100(1 - α)% confidence interval for an individual value of X for a given value of Y is


R – Squared (Percent of Variation Explained)
Several measures of the goodness-of-fit of the regression model to the data have been proposed, but by far the most popular as R2. R2 is the square of the correlation coefficient. It is the proportion of the variation in Y that is accounted by the variation in X. R2 varies between zero (no linear relationship) and one (perfect linear relationship).
R2 officially known as the coefficient of determination, is defined as the sum of squares due to the regression divided by the adjusted total sum of squares of Y. The formula for R2 is
(3.16)
(3.17)
R2 is probably the most popular measure of how well a regression model fits the data. R2 may be defined either as a ratio or a percentage. Since we use the ratio form, its values range from zero to one. A value of R2 near zero indicates no linear relationship, while a value near one indicates a perfect linear fit. Although popular, R2 should not be used indiscriminately or interpreted without scatter plot support. Following are some qualifications on its interpretation.
Additional independent variables. It is possible to increase R2 by adding more independent variables, but the additional independent variables may actually cause an increase in the mean square error, an unfavourable situation. This usually happens when the sample size is small
Range of the independent variable. R2 is influenced by the range of the independent variable. R2 increases as the range of X increases and decreases as the range of the X decreases.
Slope magnitudes. R2 does not measure the magnitude of the slopes.
Linearity. R2 does not measure the appropriateness of a linear model. It measures the strength of the linear component of the model. Suppose the relationship between X and Y was a perfect circle. Although there is a perfect relationship between the variables, the R2 value would be zero.
Predictability. A large R2 does not necessarily mean high predictability, nor does a low R2 necessarily mean poor predictability.
No-intercept model. The definition of R2 assumes that there is an intercept in the regression model. When the intercept is left out of the model, the definition of R2 changes dramatically. The fact that your R2 value increases when you remove the intercept from the regression model does not reflect an increase in the goodness of fit. Rather, it reflects a change in the underlying definition of R2.
Sample size. R2 is highly sensitive to the number of observations. The smaller the sample size, the larger its value.
Correlation is the interdependence between variables. It enables us study the strength of relationship between variables and test for significance of the relationship without calculating a regression equation.
Rbar-Squared (Adjusted R-Squared)
R2 varies directly with N, the sample size. In fact, when N = 2, R2 = 1. Because R2 is so closely tied to the sample size, an adjusted R2 value, called Ř2, has been developed. Ř2 was developed to minimize the impact of sample size. The formula for Ř2 is
(3.18)
Where p is 2 if the intercept is included in the model and 1 if not.
THE CORRELATION COEFFICIENT
The correlation coefficient can be interpreted in several ways. Here are some of the interpretations. (Montgomery et al 1992)
If both Y and X are standardized by subtracting their means and dividing by their standard deviations, the correlation is the slope of the regression of the standardized Y on the standardized X.
The correlation is the standardized covariance between Y and X
The correlation is the geometric average of the slopes of the regressions of Y on X and of X on Y.
The correlation is the square root of R-squared, using the sign from the slope of the regression of Y on X.
The corresponding formulas for the calculation of the correlation coefficient are
     (3.19)

  (3.20)

(3.21)
    (3.22)

Where SXY is the covariance between X and Y, bXY is the slope from the regression of X on Y, and bYX  is the slope from the regression of Y on X, is calculated using the formula

The population correlation coefficient, p, is defined for two random variables, U and W, as follows
(3.24)
   (3.25)

Note that this definition does not refer to one variable as dependent and the other as independent. Rather, it simply refers to two random variables.
Facts about the Correlation Coefficient
The correlation coefficient has the following characteristics.
The range of r is between -1 and +1 inclusive.
If r = 1, the observations fall on a straight line with positive slope.
If r = -1, the observations fall on a straight line with negative slope.
If r = 0, there is no linear relationship between the two variables
r is a measure of the linear (straight-line) as
sociation between two variables
The value of r is unchanged if either X or Y is multiplied by a constant or if a constant is added.
The physical meaning of r is mathematically abstract and may not be very help. However, we provide it for completeness. The correlation is the cosine of the angle formed by the intersection of two vectors in N-dimensional space. The components of the second vector are the corresponding values of Y. these components are arranged so that the first dimension corresponds to the first observation; the second dimension corresponds to the second observation, and so on.
Hypothesis Tests for the Correlation
You may be interested in testing hypothesis about the population correlation coefficient, such as p = p0. When p0 = 0, the test is identical to the t-test used to test the hypothesis that the slope is zero. The test statistic is calculated using
(3.26)
Confidence Intervals for the Correlation
A 100(1 - α)% confidence interval for p may be constructed using either of the two hypothesis methods described above. The confidence interval is calculated by finding either directly using method 2 or by a search using method 1, all those values of p0 for which the hypothesis test is not rejected. This set of values becomes the confidence interval. Be careful not to make the common mistake in assuming that this confidence interval is related to a transformation of the confidence interval on the slope β1. The two confidence intervals are not simple transformations of each other.

INDEPENDENT ERRORS
The Y’s, and thus the errors, are assumed to be independent. This assumptions is usually ignored unless there is a reason to think that it has been violated, such as when the observations were taken across time. An easy way to evaluate this assumption is a scatter plot of the residuals versus their sequence number (assuming that the data are arranged in time sequence order). This plot should show a relative random pattern.
The Durbin-Watson statistic is used as a formal test for the presence of first-order serial correlation. A more comprehensive method of evaluation is to look at the autocorrelations of the residuals at various lags. Large autocorrelations are found by testing each sung Fisher’s z transformation. Although Fisher’s z transformation is only approximate in the case of autocorrelations, it does provide a reasonable measuring stick with which to judge the size of the autocorrelations.
If independence is violated, confidence intervals and hypothesis tests are erroneous. Some remedial method that accounts for the lack of independence must be adopted, such as using first differences or the Cochrane-Orcutt procedure.
DURBIN – WATSON TES
The Durbin-Watson test is often used to test for positive or negative, first-order, serial correlation. It is calculated as follows.
(3.27)

The distribution of this test is difficult because it involves the X values.  Originally, Durbin-Watson (1950, 1951) gave a pair of bounds to be used. However, there is a large range of ‘inclusion’ found when using these bounds. Instead of using these bounds, we calculate the exact probability using the beta distribution approximation suggested by Durbin-Watson (1951). This approximation has been shown to be accurate to three decimal places in most cases which is all that are needed for practical work (Montgomery et al 1992).
DEFINITIONS USED IN RESIDUAL DIAGNOSTICS
Residual
The residual is the difference between the actual Y value and the Y value predicted by the estimated regression model. It is also called error, the deviate, or the discrepancy.
(3.28)
Although the true errors, £j, are assumed to be independent, the computed residuals ej, are not. Although the lack of independence among the residuals is a concern in developing theoretical tests, it is not a concern on the plots and graphs.
The variance of the £j is sigma. However, the variance of the ej is not sigma. In vector notation, the covariance matrix of e is given by
(3.29)




CHAPTER FOUR
DATA ANALYSIS, RESULT AND DISCUSSION
4.0 INTRODUCTION
This chapter deals with the presentation of data collection, analysis and interpretation  of data for total number of egg produced in chick-tech farm considering Total hen, Age, Feed and Average weight for the period of 70days using multiple regression and correlation, the statistical package used is SPSS


Figure 4.1 Histogram of Number of Eggs
A histogram of the residuals will help in checking the assumption of normality of the error term. The shape of the figure should approximately follow the shape of normal curve. This histogram is acceptably close to the normal curve from the figure above.

Figure 4.2Probability Plot
Figure 4.2: shows the normal P-p plot of regression standardized residual, this P-p plotted residuals should follows the 45 degree line on the quadrant, the histogram nor the normal P-p plot is used to know the  normality, and since it is in 45 degree is assumed not  violated.


4.1 SCATTER PLOT SECTION
Show the plot of dependent variable (total eggs) and the respective independent variables (feed, age, average weight, total hen) in a regression line. The regression shows the relationship between the response variable and the predictor, the straight line passed through a desirable number of observations indicating the linear regression model fit the data.

Figure 4.3 Age of Hen Vs Total Number of Eggs
Figure 4.3 show that there is a strong positive relationship between the (Age and total eggs) and this means that both of them are changing at the same rate. The total number of egg (dependent variable) produced tend to increase relatively with an increase in the independent variables.



Figure 4.4 average weight of hen vs total number of eggs
Figure 4.4 shows that there is a strong positive relationship between the (average weight and total number of egg) and this means that both of them are changing at the same rate. The total number of eggs (dependent variable) produced tends to increase relatively with increase in the average weight (independent variable).






Figure 4.5 Feed Vs Total Number of Eggs
Figure 4.5 shows that there is a strong positive relationship between the (feed and total number of eggs) and this means that both of them are changing at the same rate. The total number of eggs (dependent variable) produced trends to increase relatively with increase in the feed (independent variable).





TABLE 4.1 DESCRIPTIVE STATISTICS

Mean
Std. Deviation
N

Egg
Age
Feed
Weight
4963.5484
55.0000
113.8387
18.7077
596.07912
9.09212
2.14626
0.16045
31
31
31
31

Table 4.1 shows the mean and standard deviation of the five variables involved in the analysis. It is particularly useful for checking missing values and also the correct variables are selected.
TABLE 4.2: CORRELATION


Egg
Age
Feed
Weight

Pearson Correlation
Egg
Age
Feed
Weight
1.000
0.838
0.765
0.911
0.838
1.000
0.864
0.961
0.765
0.864
1.000
0.845
0.911
0.961
0.845
1.000























Table 4.2 shows the Pearson correlations of all the variables were given. Using the method of row-wise deletion, these correlation coefficients show which independent variable are highly correlated with the dependent variable to each other. The result show high positive correlation between the total egg & age, total egg &feed, total egg & average weight, age & average weight, Age & feed with (0.838), (0.765), (0.911), (0.864), (0.961) and (0.845) respectively and also , there is a prefect positive correlation between the same variable with 1.000 each.
TABLE 4.3: VARIABLES ENTERED/REMOVED
Model
Variables Entered
Variables Removed
Models

1
Weight, Feed, Age

Enter

Dependent Variable: Egg
All requested Variables entered.
Table 4.3 shows the dependent and independent variable. The average weight, feed and age are the independent variables while the total egg produced is the dependent variables.
TABLE 4.4 MODEL SUMMARY
Model
R
R Square
Adjusted R Squares
Std Error of the Estimate
Durbin-Watson

1
0.922
0.850
0.833
243.50774
0.825

Predictors: (Constant), Weight, Feed and Age
Dependent Variable: Egg
Table 4.4 shows the model summary report, the strength of the relationship between the model and the dependent variable.  R (0.922) is the multiple correlation coefficient which indicates the linear correlation between the observed and the model predicted values of the dependent variable. It shows a strong relationship R-square of 85% (0.850), considering the standard deviation error of the estimate (243.50774) compared to the standard deviation of the total egg (000.00000) reported in the descriptive statistic table (table 4.1) to measure the strength of the model fit for linear regression model. The Durbin-Watson test is used to test for first order serial correlation in regression data taken over time. Since the Durbin-Watson estimate (0.825) is less than 1, we therefore conclude that the data is not serially correlated.
TABLE 4.5 ANOVA
Model
Sum of Squares
Degree of freedom
Mean of Squares
F
Significant

Regression
Residual
Total
9058317.213
1600992.465
10659309.677
3
27
30
3019439.071
59296.017
50.921

0.000


Dependent Variable: Egg
Predictors: (Constant), Weight, Feed and Age
Table 4.5 shows the analysis of variance (ANOVA) test, the acceptability of the model from a statistical point of view is obvious. The regression and residual sums of squares are 9058317.213 and 1600992.465 respectively. The significance value (0.000) of the F statistic is less than the alpha value (0.05), which means that the variation explained by the model is accepted statistically. The ANOVA is useful test of model ability to explain any variation in the dependent variable, it does not directly address the strength of that relationship







TABLE 4.6 COEFFICIENTS
Model
Unstandardized Coefficients
Standardized Coefficients
T
Significant


Beta
Std Error
Beta



Constant
Age
Feed
Weight
-90330.021
-35.571
23.526
5055.224
17929.456
18.862
41.410
1004.888

-0.543
0.085
1.361
-5.038
-1.886
0.568
5.031
0.000
0.070
0.575
0.000

Table 4.6 summarizes the multiple regression result. The equation of the straight line relating Total Egg verses Age, Feed & Average Weight is estimated as:
Total Egg = (-90330.021) + (-35.51) Age + (23.526) Feed + (5055.224) Average Weight.
As seen from the table above, the value of Age and Feed are not significance but the value of Weight is significant, hence we reject the null hypothesis that none of the independent variables (age, feed, weight) have effect on the dependent variable (number of eggs)
TABLE 4.7: RESIDUAL STATISTICS

Minimum
Maximum
Mean
Std Deviation
N

Predicted Value
Residual
Std Predicted Value
Std Residual
3851.1011
-394.36447
-2.024
-1.620
5555.6855
388.68228
1.078
1.596
4963.5484
0.000
0.000
0.000
549.49423
231.01172
1.000
0.949
31
31
31
31

 Table 4.7 shows the values of the prediction and residual. This is however calculated by substituting the individual independent variables into the model to get predicted number of Total Egg while the residual is the difference between the actual and predicted values of the dependent variable. However the minimum predicted and residual value were given as (3851.1011) and (-394.36447) while the standard deviation were given as (549.49423) and (231.01172) respectively.

CHAPTER FIVE
SUMMARY, CONCLUSION AND RECOMMENDATION
5.0 INTRODUCTION
This chapter provides the summary of the multiple regression analysis conducted on egg production in Chick-Tech Farms Limited. The data has been analyzed using SPSS package which signifies goodness of fit of the regression model.
5.1 SUMMARY
The methodology employed follows the technical details of least squares regression analysis according to Rawlings (1973) which was used to fit the model, analyze the variation, obtain the co-efficient of determination and the correlation between the dependent variable (total eggs) and the  independent variables (age, feed and average weight).
The final analysis has revealed that there is a desirable correlation between the independents and the dependent variables, there is also a strong relationship between the model and the dependent variable. The  strength of the relationship between the model and the dependent variable R (0.922) is the multiple correlation coefficient which indicate the linear correlation between the observed and model- predicted value of the dependent variable, it shows a strong relationship R-square of 85% (0.850), considering the standard deviation error of the estimate (243.50774) compared to the standard deviation of the total egg reported in the descriptive statistic table (596.07912) to measure the strength of the model fit for linear regression model.
The Durbin –Watson test is used to test for first order serial correlation in regression data taken over time, since Durbin-Watson estimate (0.825) is less than 1, we conclude that the data is not serially correlated. The equation of the straight line relating Total Egg and Age, Feed & Average Weight is estimated as: Total Egg = (-90330.021) + (-35.51)Age + (23.526)Feed + (5055.224)Average Weight.
5.2 CONCLUSION
It could be seen from the above research work, that there is statistical relationship between the dependent variable (total eggs) and the independent variables (total hen, age, feed, and average weight) thereby constituting the factors responsible for a reasonable production of the total eggs by the poultry farm.
Again, the range of a possible prediction (forecast) for total numbers of egg production was obtained from the analysis. Notwithstanding, proper management improved feeding practice and atmospheric conditions were identified as the factors that will yield high total number of egg production in the farm.
5.3 RECOMMENDATIONS
Based on the conclusion, it was observed that hen produce more eggs when fed much grams of feed. I hereby recommend that;
The Chick-Tech farm limited should increase the grams of feed given to the hen and provide facilities such as crates, filter trays and air condition in the storage room in order to avoid breakage and spoilage before marketing.
Finally, the farm should sell the old hen in time so that there will be enough space for rearing the young hen which produce more eggs than the old hens.

REFERENCES
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APPENDIX

S/N
TOTAL NUMBER OF HEN
AGE
FEED(G) /BIRD
TOTAL EGGS
AVERAGE WEIGHT

1
9,937
40
110
4200
18.40

2
9,722
41
110
4290
18.43

3
9,414
42
113
4230
18.43

4
9,699
43
113
4050
18.47

5
9,654
44
113
3840
18.49

6
9,637
45
112
4320
18.49

7
9,627
46
110
4440
18.53

8
9,906
47
110
4290
18.61

9
9,596
48
110
4290
18.61

10
9,586
49
113
4380
18.61

11
9,582
50
113
4560
18.67

12
9,569
51
114
4710
18.67

13
9,557
52
114
4860
18.67

14
9,547
53
114
5040
18.71

15
9,533
54
114
4710
18.71

16
9,507
55
113
5280
18.74

17
9,499
56
113
5460
18.74

18
9,480
57
114
5700
18.81

19
9,469
58
114
5700
18.83

20
9,452
59
116
5700
18.83

21
9,431
60
116
5730
18.85

22
9,398
61
116
5730
18.85

23
9,367
62
116
5550
18.85

24
9,344
63
116
5460
18.86

25
9,298
64
116
5490
18.86

26
9,295
65
116
5280
18.87

27
9,278
66
116
5310
18.87

28
9,264
67
116
5340
18.87

29
9,263
68
116
5370
18.87

30
9,251
69
116
5280
18.87

31
9,248
70
116
5280
18.87

Source :CHICK TECH LIMITED Sokoto