Post on 24-Apr-2023
CHAPTER ONE
1.1 INTRODUCTION
Why do people get married? Love, Sex, Children, money. Why
do people get divorced? Probably for the same reasons,
while most people would, at most want to hear economist
have to say about the financial aspects of marriage,
economist have to say about the financial aspects of
marriage, everyone else) have taken it on economics is one
of many academic disciplines to weigh in particularly once
important change in marriage and divorce over the last
several decades began to grab national attention.-
In this chapter, we will illustrate the insights
offered by the economic approach to analysing marriage and
divorce. For Example, economists have studied whether
divorce. For example, economist have studied whether
divorce law affect the divorce rate. Before 1970, many U.S
states required both spouses to agree before a divorce
could take place; now, most states allows one spouse to
initiate a divorce unilaterally, under certain assumptions
that economist have spelled out the type of divorce law
would not actually affect the number of divorces, even
while it does affect the way that divorced couples share
resources.
Economist has tested this hypothesis and, to the
extent possible, the assumptions it rest on. Furthermore,
economist have shown that the type of divorce law affects
how married couples share resources, even if they do not
divorce, and extending the ideas further, it might even
influence how often they have sex.
In order to understand these ideas, we have to
develop a model of both marriage and divorce (or, in other
words, a model of that allows for changes over time in the
utility from marriage). In this chapter, we will set the
stage for this analysis with a brief discussion in section
1 of trends in marriage and divorce in the U.S. then, to
keep things simple we will discuss separately the gains
from marriage versus living together (in section 2) the
reasons why people marry (in section 3) the nature of
decision making within marriages (in section 4), and the
nature of the decisions to marry and to divorce (in
section 5).
Marriage versus cohabiting
What is the difference between shacking up and getting
hitched? Marriage is a contractual arrangement, with rules
determined by church or state. For examples, Jewish
weddings are not complete until the bride and groom sign
the ketubah, a marriage contract which spells out the
husband’s obligations to the wife during marriage,
conditions of inheritance upon his death, and obligations
regarding, the support in the event of divorce.
Brides in many cultures brought (or still brings)
dowries to their husbands, with religious or secular law
determining the disposition of the dowry in the event of
death or divorce. In other cultures, husbands must provide
a pride price to the bride or her father. With some
exception, non-marital relationships do not entail the
same contractual obligations, several aspects of marriage
as a contract are important.
First, marriage as a transaction may be costly in
terms of time, effort, and/or money to enter into and to
leave it implies that the utility from marriage must
exceeded the utility from being apart as well as the
cost involved in getting married, and possibly divorced as
well as the costs involved in getting married, and
possibly divorced (although we do not emphasize this in
the model of getting married which we develops later).
Second, divorce as the dissolutions of a contract
entails financial obligations between the spouses. For
example, one spouse may be required to pay income support
to the other and property acquired during the marriage (or
even before) must be split according to some rule, perhaps
depending on behaviour during the marriage.
There are a few motives for these financial
obligations associated with divorce. One is to provide
support for children issuing from the marriage, although
these rules affect childless couples as well. Another
motive is to punish certain types of behaviour which are
viewed as violating the contractual obligations of
marriage. An additional motive is to compensate spouses
for some types of investments in the marriage which are
undertaken with the belief that the marriage will last. We
will elaborate on the motives for these. Sharing rules, as
we outline the reasons why people marry and subsequently
divorce.
Third, the nature of the marriage contract has varied
greatly across religions, countries and time periods. The
Old Testament, for example, established a right of
husbands to unilaterally divorce their wives, for any
reason or no reason, although not without absolving all
financial.Jesus, in various gospels, recognized (though
disapproved of) divorce while the Roman Catholic Church
forbids it. Occasionally legal and/or religious divorce
law has changed in response to demands of influential
society members (e.g, Henry VII). We will discuss some
reasons why the legal regime governing marriage and
divorce has varied as the circumstances surrounding
marriage have shifted?
What are the gains from marriage?
At the outset, we listed several reasons: love, sex,
children and money why people might have married. Let’s
consider in turn how each of them affects and individuals
utility and moreover why the impact may depend on whether
the couple marries instead of just living together.
Love and sex
While love may be one of many splendored things, we will
model it as a simple gain in utility from your life with
another love may matter because you enjoy being the one
you love, and it may matter because it causes you to care
about the well being of the one you love. In other words,
love may be an argument of your utility function and it
may change your utility function by placing weight on the
utility of another person. Next, there is sex.
But sex any different from love from a modeling point
of view? They both require another, and the both offer
utility, given the right partner. Sex may complement love;
if emotional intimacy enhances sexual satisfaction.
However, there are other important characteristics of sex.
One which we will ignore in this chapter is that there is
a relatively well functioning market for sex (via
partition), but not one for love, since sex is an act but
love is an emotion which is difficult to transact. Another
characteristic of sex is that it involves certain risks.
it may be for the latter reason that sex is often
associated with marriage.
One risk of sex is diseases. Monogamy reduces the risk of
disease, but how does one insure monogamy?
First, both marriage and co habilitation increase
physical proximity and hence the ability to monitor the
partner.
Secondly marriage as a legal contract often specifies
penalties which raise the cost of adultery. For instance,
it may provide grounds for the other partner to end the
marriage or affect the distribution of income and property
after divorce. Another risk of sex is pregnancy. the risk
of pregnancy explains why sex within marriage may be
preferred to sex outside of marriage, Because the welfare
children, and so the welfare of parents who care about
their children, is enhanced by making marriage difficult
to end and by the financial obligation may be imposed for
children born out of wedlock as well) seen in this light
once can understand why the advert of effective
contraction in recent decades. By reducing the risk of
pregnancy resulting from sex has reduced the frequency of
marriage and increase the frequency of living together.
While condoms have been around for over millennia, the
introduction of the birth control pill has had a drastic
effect, especially after decisions in the late 1960s
allowed it to be distributed widely among unmarried women.
That is because it allows women to control their fertility
and women bear more of the costs of child bearing than men
do.
CHILDREN
Sex naturally brings us to talk about children. There are
a few reasons why people have kids besides the possibility
that they are an accidental by product of sex. One that
they feel a biological imperative, another is that the
enjoy kids. Those two reasons look the same in a simple
economic model. They are things that raise an individual's
utility. What makes kids interesting for our purposes is
that one kid are public, not private goods. In other
words, one kid provides utility to two parents, and the
utility one parent gets from spending time with the kid is
not diminished by the utility the other gets from spending
time with the kid as long as the parents live together. If
not, then kids are more like other private goods, for
example, spaghetti. If one person eats the spaghetti, the
other cannot.
Since kids cost about the same whether they live with
one parent or both, it is efficient, from this
perspective, for parents to live together. we will not
have a chance to say anything about the decision of
whether to have kids, although it may have some of the
same features as other types of marital decision, which we
will not discuss about, how many kids to have, and the
tradeoff between investing in child quantity (by having
more kids).
Whether they are assessing options for reforming
social security, contemplating changes to the tax code, or
trying to improve the well being of children, policy
makers require an accurate assessment of trends in
marriage, divorce and other living arrangements.
Historically, vital statistics data collected at the state
and local levels and consolidated by the national center
for health statistics (NCHS) provided the most complete
information on marriage and divorce rates.
These data were based on administrative record of
actual marriage and divorces that occurred in the
reporting jurisdictions. Prior 1996, the federal
government provided more financial support to state to
collect marriage and divorce data. In 1996, NCHS
discontinued funding for the collection of detailed
marriage and divorce data for a number of reasons. First,
there were resource constraints. By easing funding to
state for the collection of detailed marriage, divorce the
agency was able to redirect & 1.25million per year to
maintain birth and death data system. Second, there were
coverage and quality concerns. NCHS was not consistently
receiving data from all states. Similarly the quantity of
the data never rose to the level expected by NCHS or
researchers. Data reporting was often incomplete or of
uncertain reliability. States were facing staffing
shortages and internal funding issues, resulting in many
relegating the reporting and collection of marriage and
divorce data to a lower priority than birth and death
data.
Finally, the collection of marriage and divorce
information was an uneasy fit for an agency that focuses
on health statistics, few NCHS staff worked with marriage
and divorce data, thus, when the budget needed to be cut,
there were few advocates for the continuation of its
collection. In addition, staff argued that the data could
be captured in surveys, such as the national survey of
family growth, and in census data. As a result, the
quantity and quality of national, state and local
information on marriage and divorce deteriorated while
policy makers need for this information increased.
The administration for children and families and the
effect of the assistant secretary for planning and
evaluation, within the us department of health and human
services (DHHS) contracted with the Levin group and the
Urban institute to explore options for collecting marriage
and divorce information. This report examines the
feasibility and potential benefits of using existing
survey data sets to provide reliable, tike tamely
information. This report examines the feasibility and
potentials benefits of using existing survey data sets to
provide reliable, timely information on marriage and
divorce.
It assesses the ability of a variety of data sets to
produce marriage and divorce statistics of the national,
state and local levels. The main criterion is whether the
existing survey data sets provide or can be modified to
provide information on marriage and divorce rates, as was
possible using data collected under the vital statistics
system. Beyond their potential to provide information on
marriage and divorce rates, survey data sets can also
provide information on current marital status, alternative
living arrangements such as co habilitation and the
correlates of marriage, divorce and other living
arrangements.
To his report first describes criteria for evaluating
survey data sets on their ability to provide information
on marriage and divorce.
HISTORY OF ILE-OLUJI/OKEIGBO LOCAL GOVERNMENT
Ile-oluji/Okeigbo Local government council was created on
27th August 1991, with Ile-Oluji as the headquarters,
according to the federal government gazette No 34 Vol 78
of 21st October 1991.
Ile-Oluji/Okeigbo Local government by the administration
was carved out of the Old Ifesowopo local government by
the administration of General Ibrahim Babangida, it is
made up of Ile-Oluji/ Okeigbo and other villages,
farmsteads and hamlets. It is instructive to note that the
creation of Ile-Oluji/Okeigbo local government was made
possible largely by the persistent agitations of the
people of the Ile-Oluji, especially the Jegun – in-
council and influential community leaders. The local
Government is situated in the western part of Ondo state,
sharing boundries in the east with ondo and Ifedore Local
governments, and in the west by Osun state. The
provisional result of the 1991 national head count put the
population of the local government at 123, 397 with the
Yoruba being the predominant ethnic group.
There are also sprinkling of mainly farmers, while
subsistence crops include Yam, Cassava, Maize, Plantain,
Banana, fruits. Two third of the population are Christians
while Muslims and traditionalists are also to be found in
the hook and grannies of local government.
Apart from the major towns of Ile-Oluji and okeigbo there
are about 306 other villages and farmlands.
INDUSTRY/COMMERCE
Ile Oluji cocoa processing company limited is the most
prominent industrial outfit in the local government are
first Bank, Co-operative Bank, Owena Bank, UBA and
community Banks, Major hotels are Gboluji guest house,
Jossy international Hotel, Quiet Hotel, New Era, Valentine
Hotel.
VEGETATION
The local government lies within the tropical rainforest
belt. There is luxuriant vegetation because of high
humidity structures in the face of urbanization. Tropical,
the local government has a relatively high plain
punctuated by the rolling tableland of rocks structures.
The area has the loamy soil type, well drained and
fertile.
1.2 STATEMENT OF PROBLEM
This study was to determine the number of marriage and
divorce in Ile-Oluji/Okeigbo local government area.
1.3 AIMS AND OBJECTIVES
This project work have it aims and objective for
conducting the research which are as follows:
1. To study and determine the trend of marriage against
time in Ile-Oluji/Oke-Igbo local government for the
year under study using regression analysis.
2. To study and determine the trend of the divorce against
time in Ile-Oluji/ Okeigbo Local Government of the year
under study using regression analysis.
3. To study and determine the degree of relationship
between marriage divorce against time in
Ile-Oluji/Okeigbo local government using correlation
analysis.
1.4 SIGNIFICANCE OF THE STUDY
The finding of the study would provide understanding
of the factors that influence people for engaging in
marriage and divorce. The result is expected to help
the society as well as government to project the plan
for necessary future improvement.
1.5 SCOPE AND COVERAGE
This project work focus mainly on marriage and divorce for
the year 2005- 2014 in Ile Oluji/ Okeigbo local
government.
1.6 DEFINITION OF TERMS
Marriage: Can be defined as a socially acknowledge
and approved sexual union between two adults of
opposite sex.
Divorce; can be defined as the legal dissolution of a
marriage by a court or other competent body.
Sororate marriage: these occurs when a man marries
two sisters
Leviratic Marriage: It occurs when a man marries a
woman to raise children to the memory of his brother.
Ghost marriage: Occurs when a man provides the bride
price and the consort for another woman in other that
the children born will be hers.
Absolute divorce: The final ending of a marriage.
Both parties legally free to remarry
Alimony: it is a payment of support provided by one
spouse to the other\
Annulment: A marriage can be dissolved in a legal
proceeding in which the marriage is declared void, as
though it never took place. In the eye of the law,
the parties were never married.
Group marriage: this is where a group men will share
marital relations with a group of women
Condo nation: is the act of forgiving one’s spouse
who has committed an act of wrong doing that would
constitute a ground for divorce.
Polygamy: this is where a man can/may marry more than
one woman
Polyandry: This appears when a woman simultaneously
marries two or more men.
CHAPTER TWO
LITERATURE REVIEW
For better or for worse, an analysis of marriage and divorce
changes in Japan (BY BRYAN NICOL) Under the supervision of
professor Leslie Winston. “For better or for Worse?” analyzes
the changes in Japanese marriage and divorce culture in the
100 years surrounding the turn of the 20th century. In a
relatively short period of time, Japanese society underwent
fascinating transformation from having the world’s highest
recorded divorce rate in 1885, to one of the lowest in the
world only sixty years later.
First, I will analyze the pre – industrial and industrial era
culture in order to illustrate fully the social implications
of marriage and divorce and how they have change over time. I
follow this with an analysis of the theories that attempt to
explain divorce rate changes across these specific time
periods both of the theories that attempt to explain divorce
rate changes across these specific time periods, both of which
lasted for roughly 50 years since 1860 and saw distinct
changes in divorce rate trends.
Finally, comparisons will be made between the periods with
analysis regarding the changes in women’s well being with
respect to the marriage institution to show that the
implementation of a marriage and divorce system based on
cultural values foreign to the Japanese society inevitable led
to a decrease in Japanese women’s socio – economic well being.
The meiji period (1868-1912) of Japan, up until the passage of
the meiji Civil code in 1898, was characterized by a unique
feature. It was at this point in time that Japan had the
world’s highest divorce rate. Harald Fuess, in his book
divorce in Japan, offers statistical data that claims that the
divorce rate of Japan was not only the highest in the world
during the 1800s, but that the only country to see an
equivalent divorce trend was the united states almost a
country later (2004). Yet the reason for the drastic
difference is simply because the Japanese society as a whole
differed from its western counterparts on various cultural
aspects. A community based on the ideas of the i.e. a trial
marriage system, and a complete lack of codification of the
marriage institution all facilitated divorce during the meiji.
Period, which inevitably left Japanese brides with a greater
sense of socio – economic well being than the western form of
the institution did.
In order to understand how the institution impacted brides
during the meiji Era, it is important to analyze the marriage
and divorce decisions during the 1800s were made through the
i.e. defined as the societal, communal and familial based
relationships that even today is regarded with great
importance throughout Japan. There is a small, lineage based
community comprised of family within the same dwelling with
one another (Long 1990). Both Susan orpett long, in her book
family change and the life course in Japan, and Joy Hendry, in
marriage in changing Japan, agree that marriage was, during
this time, a cultural institution driven to perpetuate the
i.e. (Hendry 1981, Long 1990). For Pre- Industrial Japan, this
was achieved by means of the arranged marriage rather than a
love marriage primarily because a love marriage implies an
individual affair – rather than a community based decision –
whereas with an arranged marriage the entire family was
typically involved (Hendry 1981).
Furthermore, the marriage was not simply the union of two
individuals, but rather was considered to be the marriage
between two entire families (Long 1990). In the Meiji period
and in previous era, this inevitable gave rise to a trial
marriage system, wherein spouses were tested with one another
for a certain amount of time to ensure that a well suited
match was made.
The trial marriage system seems match to be Japan’s equivalent
to the dating system in America and Europe. Western style
courtship has only recently begun developing as a social norm
in Japan (Ritsuko 1990), so it can be said that dating as a
catalyst for marriage was completely non – existing in Pre –
industrial Japan. Trial marriage, however, may almost be
analogous. According to fuess, during the end of the 1800s,
nearly 50 percent of all marriage, ended in divorce, while
half of all divorce were realized within the first two years
marriage themselves were, in a sense, a form of dating,
coupled with cohabitation with a spouse and his on her family.
Interestingly, since there was a definitive lack of marriage
codification in the government, trial marriages, as well as
their subsequent divorces, became an easy and common affair.
The absence of a legalized form of marriage in the Japanese
culture during the 1800s, undoubtedly had a drastic impact on
the relative ease of divorce in comparison to America and
Europe. Fuess argues that cultural signals that a couple had
consumed its marriage were more dominant than actual legal
registration of the union itself, and, in fact, registration
of marriages was not even required by the government until
shortly before the beginning of the 20th century (Cornell 1990;
Fuess 2004). Rather, a young Japanese woman with blackened
teeth or a certain hair style could indicate that a marriage
had recently taken place, while in other instances it was the
birth of the first child that indicated the commencement of a
marriage (Cornell 1990; fuess 2014). There was some record of
marriage ceremonies taking place, but Fuess states that on a
whole, scholars at the time regarded these ceremonies as small
affairs, devoid of much religious, social, or legal meaning
(Fuess 2004)
Divorce proceedings seemed to be an equally simple matter in
pre – industrial Japan, as well. Joy, Hendry, for example,
refers to the ease with which a husband could divorce his
wife. Fuess concurs with Hendry stating that not only was the
mikudarihan the only required notice to complete a divorce,
but on a social scale. It was seen as mainly the husband’s
prerogative (Fuess 2004). Fuess also adds that in Japan’s
entire history, state institutions were involved in only a
very minute’s portion of total divorces (Fuess 2004). With
very little government interaction taking place within the
institution of marriage during the end of the 20th century,
marriage and divorce from a legal stand point could occur with
relative ease. These three factors – the lack of a legal
codification of marriage, the importance of the i.e. and the
trial marriage system – helped develop a society in which
divorce was both typical and frequent during the 1800s. Yet it
was not a system that was free from heavy criticism by both
not system that was free from heavy criticism by both scholars
of the time and today. Various European scholars at the time
claimed that Japan’s high divorce rate was highly indicative
of the inequality between the sexes and a lack of concern for
the overall institution of marriage itself, while some even
claimed that the high divorce rate was such a problem that it
prevented Japan from becoming a “modern society” (Fuess 2004,
141). Hendry claims, for example, that the ease with which a
husband could obtain a divorce from his wife reflects her
lowly social status as she had very limited options when
initiating divorce (Hendry 1981). While Fuess agrees that
there was indeed sexual inequality in terms of obtaining a
divorce, he points out that women were not as entirely
helpless as Hendry may indicate. Fuess sites evidence
indicating that a woman’s parents could coerce a husband into
providing a mikudarihan, or in extreme cases she had the
option of using a divorce temple as a mediator to settle
disputes (Fuess 2014). Fuess also quotes the scholar J.E de
becker who states that “the Japanese wife was not regarded so
seriously as at present by the house, when she was unfortunate
enough to incur the displeasure of her lord and his relative.
Seeming to imply that it was not entirely uncommon for a wife
to be divorced on whim (Fuess 2004:124). On the other hand,
Laurel Cornell in her essay “peas Becker and ant women and
divorce in pre-industrial Japan”. Argues that a wife was
actually an invaluable aspect to the i.e. while both de becker
and Hendry strongly argue that the high divorce rate is
clearly indicative of women’s powerlessness in Japan in the
1800s was a society culturally constructed in such a way that
divorce was not uncommon practice. As previously stated, 25%
of all marriages was expected to end within the first two
years of marriage (Fuess 2004), and it is entirely plausible
that with the trial marriage system in plausible that with the
trial marriage system in place it was more likely a mismatch
of spouses that led to a divorce rather than the malevolence
of the husband or his parents. This, however, should not
consider a universal truth. Inevitable there will be
individual cases in which a spouse of either sex desires to
procure a divorce and is unable to do so. Yet the Japanese
woman during the Meiji period seemed to be at a clear
disadvantage over her make cohort, which clearly indicates a
difference in social status.
During the meiji period, the frequency of divorce created a
social stigma towards divorces much different from that of
modern Japan. According to Fuess, the divorce was left with
two options remarriage or returning to her natal home.
Fuess states that there was no legal prohibition against
immediate remarriage for either sex (Fuess 2004). In fact,
recent divorces were expected to remarry quickly after
divorce, and according to Cornell most did she states that a
third of divorced women in one particular case study had
remarried within the first year of being divorced, implying
that even after divorce women in no way removed from the
marriage market (Cornell 1990). Although the Japanese woman’s
options after divorce were limited, the ability to return to
her family or to remarry implies that some level of her
economic well being remained stable, as either her family or
her new husband would presumably provide for their needs.
Thus, the argument that the high rate of divorce among
Japanese couples during this time period reflected a lack of
regard for the institution itself may not be entirely true.
Rather, the trial marriage system helped to ensure that an
agreeable match could be made between families and allowed for
a simple dissolution of mismatched marriages. This facilitated
a generally positive well-being for Japanese women
specifically in terms of this institution, since simple
divorce should not then, be so simply associated with a
relatively low state of well-being for Japanese women in the
pre – industrial era as many critics are willing to argue.
Surely the unequal access to initiating divorce represent
differences in the social status of women versus men, yet in
spite of this there does not seem to be any substantial or
valid argument that can attest to the fact that women’s socio-
economic well being in terms of marriage and divorce was not,
in fact, equal to that of men’s. Women who were divorced were
not subject to any social stigma, were not placed in economic
danger as they had the opportunity to return to their natal
home or to remarry immediately after divorce, and were not
removed from the marriage market since most divorces took
place within the first few years of marriage. Yet the heavy
criticism from foreign scholars on the various aspects
marriage and divorce in Japan did not go unheeded and
beginning in 1898 with the passage of the Meiji civil code,
the Japanese began to enter into a cultural transformation
that would span the next fifty years. Yet this was based on
arguments from foreign scholars regarding the status of women
and the marriage institution in Japan that may not have ever
been accurate. Traditionally the Japanese society based its
marriage and divorce values on a Confucianism doctrine, while
many of the foreign scholars were attempting to analyze and
critique the Japanese system of marriage and divorce from a
Judeo- Christians point of view. Despite the social inequality
between men and women in their ability to procure a divorce,
Japanese women of the 19th century maintained a theoretically
positive socio- economic well – being, and thus any changes in
the system in place had the potential to change this.
Regardless, by the end of the 20th century a variety of factors
were influencing Japan in such a way that an extraordinary
transformation would be seen almost immediately.
The Meiji civil code actually expanded the right to divorce to
the wife in addition to the husband. Various scholars claimed
that the passage of the code brought modernity and security to
the Japanese family and rejoiced in the immediate decline in
recorded divorce rate by nearly 50% (Fuess 2004). De becker
argued that the decline represented society’s rejection of
divorce which was caused, he believed, by the equality of men
and women in their ability to obtain a divorce (Fuess 2004).
Fuess, on the other hand, argues that there are actually two
periods of declination worthy of review. First is the extreme
decline that took place from 1898 to 1899 immediately
following the passage of the code, followed by a second and
more gradual decline from 1900 to 1940, both of which are
represented by figure I from Fuess’s Divorce in Japan found at
the end of this essay.
The first decline, fuess argues, is due in part to four
different possibilities from changes in marriage and divorce
practices, the adoption of a new registration for families,
statistical errors, or a combination of all three (Fuess
2004). One of the major problems with the statistics,
collected at the time is that they no longer recognized common
– law marriages as full marriages and thus their data
disappeared from the official records (Fuess 2004). The new
registration required by families would have much the same
effect, as the number of marriages recognized by legal
standards clearly would differ from those recognized purely by
social standards.
This first possibility listed above is perhaps more likely, to
explain the general downward trend in divorce rate that took
place over the following fifty years. The scholars in Meiji
Japan who had heavily critiqued society for its high divorce
rates had also been calling for a reformation of the marriage
ceremony, saying that the ease with which one could marry and
divorce detracted from the significance of the institution
itself (Fuess 2004). A complete renovation in the marriage
ceremony began to take place. Scholars and even the government
now wanted the ceremony to reflect religious principles and
the resulting ceremony became a grandiose affair that would
incorporate heavy influences from its Christian counterparts.
(Fuess 2004). Fuess quotes various scholars who comment on the
elaborateness of the affair, saying that previously one could
marry for a mere five yen, while after the transformation
marriages saw nearly unbelievable cost increases (Fuess 2004).
In either case, women who desired to procure a divorce during
Japan’s Industrial era inevitability saw an increase in the
social and economical opportunity costs for doing so, which
further restricted opportunities for the dissolution of
mismatched marriages. Thus while foreign scholars were
focusing so heavily on their fight to create “equality” for
Japanese women in terms of the law, they did not consider that
the ramifications of the implementation of a foreign value
system of marriage and divorce into Japan’s highly active
divorce culture. Women who found themselves in unhappy
marriages were now faced with two options to suffer through
the relationship or as Trucco writes, to be worse than “dead
to society”. Thus, the Meiji code, the foreign scholars and
the government had failed Japanese women.
Completely, creating a zero – sum game for those who, before
1898, could have divorced and entered into a new relationship.
CHAPTER THREE
3.0 RESEARCH METHODOLOGY AND STATISTICAL TOOLS
3.1 REASEARCH METHODOLOGY
It comprises definition of data, source of data, types of data,
method of data collection and limitation of data.
STATISTICAL TOOLS
It comprises definition of statistical tools to be used to
analyze this project. They are:
1. REGRESSION ANALYSIS
2. CORRELATION ANALYSIS
3. CO-EFFICIENT OF DETERMINATION
4. ANALYSIS OF VARIANCE (ANOVAs)
5. CHARTS AND DIAGRAMS
Data is information collected; collection is the act of
gathering things together. Therefore, data collection is the
act of gathering information together in order to draw
references from it.
More so, it’s refers to as the numerical description or
representation of things either in quantitative or qualitative
or both.
QUANTITATIVE DATA: Are those that can be described in numerical
form.
QUALITATIVE DATA: Are characteristics which cannot be described
in numerical form.
3.1 TYPES OF DATA
There are two types of data namely:
PRIMARY DATA: Are data that is collected for a specific purpose
and used for that specific purpose that is collected for. These
types of data are collected and published by the organization
that collected them.
3.1.1 MERIT OF PRIMARY DATA
It is completed because theory supply exact information needed.
Interpretations are give and more details. Errors which are
sometimes introduced in secondary data are omitted and such as
reliable.
3.1.2 DEMERITS OF PRIMARY DATA
It may be costly to collect.
It is very expensive.
There is usually large non-response.
3.1.3 SOURCES OF PRIMARY DATA
Census for instance, population census.
Scientific experiment
Sample survey e.g. an enquire on the health.
Administrative purpose e.g. records of births and deaths.
3.2 SECONDARY DATA: Are data which have been collected for
some other purpose by someone else and used for another
purpose. Most published statistical data are secondary data to
the user.
3.2.1 MERIT OF SECONDARY DATA
It allows for timely result
It is less expensive to collect
The information is quickly gathered.
3.2.2 DEMERIT OF SECONDARY DATA
It may be outdated.
It is less detail.
The sample size required might not be met.
The sources of data may not be known.
3.2.3 SOURCES OF SECONDARY DATA
Research organization.
Publication and annual abstract of statistics.
Administrative records e.g. school records, office
records.
Tertiary institutions e.g. Federal school of statistics,
Ibadan, primary schools, polytechnics, universities.
Media organization e.g. print and electronic.
3.3 INTERNAL AND EXTERNAL DATA
INTERNAL DATA: This is data collected within an organization
and used by the same organization.
EXTERNAL DATA: This is data collected by the organization
outside the organization outside the organization.
The day-to-day record of attendance in an organization is
internal data while data collected outside the organization say
on welfare package for workers is external data.
3.4 METHOD OF DATA COLLECTION
a) Personal interview or direct method
b) Postal questionnaire method
c) Observation method
d) Telephone interview
e) Electronic (internet) method of data collection
f) Documentary method
g) Reports
h) Result experiment
3.5 PROBLEM OF DATA COLLECTION
Since the data used in this project work is secondary some of
the problems encountered are those peculiar to data collection
through secondary sources.
However, some of the problems are:
1. Language barrier
2. Religion belief
3. Culture
4. Non-response
That I encountered are:
1. CALL BACK: There was the need for call backs. Before it was
possible to get the required document to extract the data
needed for this work.
2. BUREAUCRACY: The exercise was seen as a kind of probing
into the activities of the local government. This
necessitates the writing of letter to the zonal officer who
later rendered his assistance.
1.6 LIMITATION OF DATA COLLECTION
The quality of a statistical result depends on the quality
of the raw material for example the level of accuracy and good
result depend on the raw material which the measurable aspect
of things it does not usually give a complete solution to a
problem rather it only provides a basis for good judgment.
Hence, the scope of the data used for analysis is limited.
Also, as stated earlier, one of the demerits of secondary
data is that it is less accurate and secondary data is used in
this project, it therefore becomes necessary to advise all
those that like to use the work to employ some degree of
caution in analysis and interpretation there in.
1.7 CHARTS AND DIAGRAMS
Statistical data can be used or represented in chart,
diagram or graphs. This may be in form of component of bar
chart, simple bar chart, multiple bar chart and pie chart.
Chart and diagrams serves as a way of simplifying data for
easy and fast reading. It gives information at a glance. A
simple well constructed diagram that will be used in this work
for visual impression of the data.
SIMPLE BAR CHART
This is a diagrammatic presentation of series of
rectangular block erected at regular equidistance internal
along the axis (either horizontal or vertical) it can be used
to compare aggregate that is the whole magnitude, only one
variable can be shown with this diagram.
COMPONENT BAR CHART
It is a special bar chart in which each bar is sub divided into
component. On the other hand the bar of the component bar chart
could be referred to as block diagrams.
MULTIPLE BAR CHARTS
This is a chart where two or more bars are drawn together; it
is used to compare two or more variable. The bars are drawn
either horizontal or vertical.
1.8 REGRESSION ANALYSIS
This is a statistical process for estimating the
relationship among two variables.
Linear regression is an approach to model the relationship
between a scalar dependent variable “Y” and one or more
explanatory variables denoted “X”.
The case of one explanatory variable, it is called SIMPLE
LINEAR REGRESSION. For more than on explanatory variable, it is
called MULTIPLE LINEAR REGRESSIONS.
Also simple linear regression is the least squares
estimator of a linear regression model with a single
explanatory variable. In the words, simple linear regression
fits a straight line through the set of N points in such a way
that makes the sum of squared residual of the model (that is,
vertical distance between the points of the data set and the
fitted line) as small as possible.
The relationship could be shown in a scatter diagram on
which a line of best fit (trend & regression) can be drawn.
The line of best fit can be drawn using an equation known
as regression equation, that shown the nature of the
relationship between the two variable. This will be used to
show the relationship between ADMISSION & GRADUATION.
1.8.1 REGRESSION EQUATION
This is the equation of the regression line. It gives the
linear regression between two variables. If the values of one
variable using this equation:
Y=a + b(x)
Where: Y is dependent variable
X is independent variable
A is the point slope of the line
B is the slope of the line
1.8.2 HOW TO OBTAIN “a” & “b” FROM GENERAL EQUATION
The parameter “a” and “b” could be obtained by using the
general equation Y= a + bί + eί
Where “a” and “b” are constant and “e” is the error margin
and the equation is regression equation of “Y” on “X” in the
least square method approach we week for “a” and “b” that
minimize the sum of square error of prediction.
Y= a + b(xί) + eί
Make eί the subject of the formula
eί = ( yί - a - b(xί))
Sum of the square error
e∑ ί 2 = ( yί - a - b(xί))2
Differentiate by function with respect to “a” and hold “b” has
constant
δ e∑ ί 2 = 2 ( y∑ ί - a - b(xί)) x-1= 0
δa
= -2 ( y∑ ί – a – b(xί)) = 0
Divide both sides by -2
= ( y∑ ί – a – b(xί)) = 0
= y∑ ί - na - b x∑ ί = 0
= y∑ ί = na + b x∑ ί …………………………….. (i)
Similarly e∑ ί = ( y∑ ί - a - b(xί)) sum of the square error
differentiate by function of function with respect to “b” and
hold “a” has constant.
δ e∑ ί 2 = 2 ( y∑ ί – a – b(xί)) x-1= 0
δa
= -2 x∑ ί ( yί – a – b(xί)) = 0
Divided both sides by -2
x∑ ί ( yί - a - b(xί)) = 0
x∑ ί yί - a x∑ ί – b x∑ ί2 = 0
x∑ ί yί = a x∑ ί – b x∑ ί2 …………………….(ii)
Multiply equation (i) by x∑ ί and equation (ii) by n
x∑ ί yί = na x∑ ί – b( x∑ ί2) …………………….(iii)
n x∑ ί yί = na x∑ ί – nb( x∑ ί2) …………………….(iv)
Then subtract equation (ii) from (iv)
i.e. n x∑ ί yί – x∑ ί y∑ ί = na x∑ ί – na x + nb x∑ ∑ ί2 – b( x∑ ί)2
nb x∑ ί2 – b( x∑ ί)2 = n x∑ ί yί – x∑ ί y∑ ί
b(n x∑ ί2 – b( x∑ ί)2) = n x∑ ί yί – x∑ ί y∑ ί
Divide both side by (n x∑ ί2 – b( x∑ ί)2)
b = n xy – x y∑ ∑ ∑
n x∑ 2 – ( x)∑ 2
To obtain “a” from equation (i)
i.e. nb y∑ ί ≤ na + b x∑ ί
Make na the subject of the formula
i.e. na = y∑ ί – b x∑ ί
Divide both sides by n
na = y∑ ί – b x∑ ί
n n
where i.e.
Y = y∑ X = x∑
n n
Therefore a= y – b(x)
1.9 CORRELATION
Correlation is the study of the degree to the strength of
the relationship between two variables. When two variables are
involved, the correlation is said to be simple.
1.9.1 INTERPRETATION OF CORRELATION
1. POSITIVE CORRELATION: As X increase and the regression line
slope upward from the left right.
2. NEGATIVE CORRELATION: As X increase Y decrease or vice-versa
and the regression line slopes downward from the left to
right.
3. NO CORRELATION: If there is no definite pattern in the
direction of the variable.
1.9.2 CORRELATION CO-EFFICIENT OR PRODUCT MOMENT
CORRELATION “r”
The formula for computing the correlation Co-efficient is given
by:
r = n xy – ( x)( y)∑ ∑ ∑
√ (n∑x2−∑ (x )2 )¿¿
1.9.3 INTERPRETATION OF CORRELATION CO-EFFICIENT
“r” must always lie between –1 and +1 (–1 ≤ r ≤ +1)
1. When r = 1 there is a perfect positive linear
relationship.
2. When r = –1 there is a perfect negative linear
relationship.
3. When 0.5 < r < 1 there is a strong positive linear
relationship.
4. When –1 < r < –0.5 there is a strong negative linear
relationship.
5. When 0 < r < 0.5 there is a weak positive linear
relationship.
6. When 0.5 < r < 0 there is a weak negative linear
relationship
7. When r = 0 there is no linear correlation.
1.9.4 CO-EFFICIENT OF DETERMINATION (R²)
It shows how much of the dependent variable can be
explained by the independent variable. It is an increasing and
usually denoted by R². It values ranges between 0 and 1 i.e. 0
≤ R² ≤ 1.
R² can be computed directly from the result obtained for
the product moment correlation of (y) on (x) with that of
regression Co-efficient of (x) on (y).
R² = (n∑xy−∑x∑yn∑x²−(∑x)²) (n∑xy−(∑x)(∑y)
n∑y2−(∑y)² )1.10 TEST OF HYPOTHESIS ABOUT SIMPLE REGRESSION AND CORRELATION
The regression co-efficient “b” is an estimate of
population regression co-efficient “b”. it has become customary
to use the sample estimate “b” to test the hypothesis about the
population or to estimate for population regression co-
efficient “b”.
The commonest significant test is the one that test whether “b”
is significant different from zero or not. The normal analysis
of variance table (ANOVAs TABLE) for simple linear regression
is below.
ANOVA TABLE
Source of
variation
Sum of
square
(SS)
Degree of
freedom(D.F
)
Mean
square
(MSS)
Fcal or
Fratio
Between
treatment
S.S.R K – 1 MSR =
SSR
1
F =
MSR
MSE
Within
treatment
S.S.E N – K MSE =
SSE
2
Total
variation
S.S.T N–1
Procedure: we assume that the terms are normally distributed so
that the above hypothesis can be tested by using the Fratio test,
when the test for linearity between X and Y is true, the ratio;
The hypothesis is given by
H0: a = b = 0 [there is no linearity between admission (x) and
graduation (y)]
H1: a ≠ b ≠ 0 [there is linearity between admission (x) and
graduation (y)]
Has an F-distribution with I, and n – 1 degree of freedom.
The sum of square are given by sum of square total (S.S.T)
SST = y² - ( y)²∑ ∑
n
Sum of square regression that is between the treatment (S.S.R)
S.S.R = b [∑xy− (∑x ) (∑y )n ]
Sum of square error that is within the treatments (S.S.E)
S.S.E = S.S.T – S.S.R
3.11 STEPS FOR TESTING HYPOTHESIS
1. State the hypothesis
H0: The null hypothesis
H1: The alternative hypothesis
2. State your critical region
e.g. [Fα, Fv1, Fv2]
3. DECISION RULE: The decisions to accept or reject (H0) null
hypothesis based on the test statistics. Hence, we reject H0:
if the test statistics calculated value is greater than test
statistics tabulated and vice versa.
4. State your test statistics
e.g. F = MSR
MSE
5. CONCLUSION: compare your computed statistics with your
tabulated statistics write your conclusion based on your
decision.
1.10.1 TEST OF HYPOTHESIS: This is referred to as the
statistical procedure to determine, whether or not a hypothesis
is acceptable.
a) HYPOTHESIS: This is known as a statistical claim about a
population, which has not been claimed to be true.
b) NULL HYPOTHESIS: Any hypothesis which states that there is
no difference between hypothesis value and sample result, it is
donated by H0.
c) ALTERNATIVE HYPOTHESIS: Any hypothesis which differs from
the null hypothesis, in order word, it is the hypothesis that
claims the null hypothesis untrue and it is the donated by H1.
d) LEVEL OF HYPOTHESIS: This is the minimum probability with
which the risk of type 1 error can be taken. It is denoted α.
It is implies the confidence level for example 5% level of
significance to 95% confidence interval.
e) TYPE 1 ERROR: This is the error of rejecting the null
hypothesis (H0) when it ought to be accepted.
f) TYPE 2 ERROR: This is the error of accepting the null
hypothesis (H0) when it ought to be rejected.
g) DEGREE OF FREEDOM: The degree of freedom of a statistics
is given by the sample size minus the number (K) of a
population parameter. Which must be estimated from sample
observation i.e. D.F = n – k when n is sample size.
h) TEST OF STATISTICS: This is the statistics computed from
the sample data to which a decision whether or not the null
hypothesis is should be rejected is made. The statistics has
distribution that depends on the nature of the data.
i) CRITICAL REGION: All possible value that tests statistics
can assume are divided into two group or region by a certain
pre-determine value number called the critical value. The set
of all possible value of the test statistics that lie to one
side of the critical value that are to other side of the
critical value constitute the acceptance region.
j) DECISION RULE: The decisions to accept or reject (H0) null
hypothesis based on the test statistics. Hence, we reject H0:
if the test statistics calculated value is greater than test
statistics tabulated and vice versa.
FORECAST
In any statistical investigation prediction is very important
to be made by possess. Present situation to project for future
event, in the light of this prediction will be made on the
admission and discharged of student in Ojoo High school,
Akinyele Ibadan from (2004-2013).
1.11 TEST OF HYPOTHESIS ABOUT SIMPLE CORRELATION CO-EFFICIENT
In this project we also wish to test the correlation co-
efficient and the procedure for testing this hypothesis is
given as, it follows:
I. State the null hypothesis H0 and an appropriate
alternative hypothesis H1.
II. Using the sampling distribution of an appropriate test
statistics, determine a critical region of size X, where Y is
specified.
III. Computed the value of the test statistics from sample data
IV. Data whether to reject the null hypothesis or to accept
and whether to reserve the judgment.
V. The test statistics to use is t- statistics and is given
as:
T = r √ n−21−r²
CHAPTER FOUR
ANALYSIS OF DATA
Presentation of data on marriage and divorce in
Ile-Oluji/Okeigbo Local Government
YEAR MARRIAGE DIVORCE
2005 36 4
2006 66 7
2007 42 5
2008 26 8
2009 79 13
2010 40 8
2011 34 6
2012 58 5
2013 62 10
2014 82 15
SOURCE: ILE – OLUJI/ OKEIGBO LOCAL GOVERNMENT
REGRESSION ANALYSIS OF MARRIAGE ON TIME
X Y XY X2 Y2
1. 36 36 1 1296
2. 66 132 4 4356
3. 42 126 9 1764
4. 26 104 16 676
5. 79 395 25 6241
6. 40 240 36 1600
7. 34 238 49 1156
8. 58 464 64 3364
9. 62 558 81 3844
10. 82 820 100 6724
55 525 3113 385 31021
X = Time passage
Y= Number of marriage
Regression analysis of marriage and time:
Where regression line = Y = a + bx
b=nεxy−εxεynεx2−¿¿
b=10 (3113)−(55)(525)
10(385 )−¿¿
= 31130−288753850−3025
=2255825
= 2.733
b = 2.733
a = y⃛−bx⃛
a = 525−(2.733 )10
5510
= 52.5 – (2.733) 5.5
= 52.5 – 15.0315
= 37.4685
Recall that Y = a + bx
Therefore Y = 37.4685 + 2.733x
Interpretation; The regression equation shows that for every
increase in time there will be an increase of 3 in the number
of marriage while in the absence of time there will be 37
marriage.
TEST FOR LINEARITY OF REGRESSION OF MARRIAGE ON TIME
HO : There is no linearity
H1: There is linearity
Critical Region F0.05 (V1V2)
Where V1 = K- 1 = 2-1 -1
V2 = N –K = 10-2 = 8
COMPUTATION
SST = εy2−¿¿
= 31021 - ¿¿
= 31021−27562510
= 31021 – 27562.5
= 3,458.5
SST = 3, 458.5
SSA = b(εxy−εxεyn )
= 2.733(3113−(55) (525 )
10 )= 2.733 (3113−
2887510
)
= 2.733 (3113 – 2887.5)
= 2.733 (225.5)
= 616.2915 ≈616.3
SSA = 616.3
SSE = SST – SSA
= 3,458.5 – 616.3
= 2842.2
SSE = 2842.2
SOURCE DEGREE OF
FREEDOM
SUM OF
SQUARE
MEAN OF SUM
OF SQUARE
FRATION
REGRESSION
ERROR
1
8
616.3
2842.2
616.3
355.3
1.73
TOTAL 3458.5
Fcal = 1.73
Critical region
F0.05 (1,8) = 5.32
Ftab= 5.32
Decision Rule: Accept Ho if Fcal < Ftab otherwise reject.
Conclusion: Since Fcal (1.73) < Ftab (5.32) we accept Ho and
conclude that there is no linearity between marriage and time
in Ile-Oluji/Okeigbo Local government.
CORRELATION ANALYSIS OF MARRIAGE AND TIME
X= Passage of time
Y= Marriage
r = nεxy−εxεy√¿¿¿
r = 10(3113)−(55)(525)√¿¿¿
= r = 31130−28875√(3850−3025 )(310210−275625)
= 2255
√(825) (34585 )
= 2255√28532625
= 22555341.6
= 0.42
r = 0.42
There is week positive correlation between marriage and time
in Ile – Oluji/Okeigbo local government.
COEFFICIENT OF DETERMINATION
= R2 × 100%
= (0.42)2 × 100%
= 0.1764 × 100%
= 17.64% ≈18 %
= 18%
18% of variation in marriage can be explained by time while
82% can be explained by other factors.
TEST FOR THE SIGNIFICANCE OF CORRELATION
Ho : P = 0 (correlation is not significant)
H1 : P ≠ 0 (correlation is significant)
Critical Region
Ttab= T α/2 V, Where V = n-2 = 10-8 =8
= T0.05/2, 8
= T0.025, 8 = ± 2.306
Ttab = ± 2.306
COMPUTATION
t = r√n−2√1−r2
= 0.42√10−2√1−(0.42)2
= 0.42√8√1−0.1764
= 0.42(2.83)
√0.8236
= 1.18860.9075
= 1.3098 ≈1.31
Tcal = 1.31
Decision Rule: Accept Ho if Tcal < Ttab otherwise reject.
Conclusion: Since Tcal (1.31) < Ttab (±2.306) we therefore accept
Ho and conclude that the correlation between marriage and time
is not significant.
REGRESSION ANALYSIS OF DIVORCE ON TIME
X Y XY X2 Y2
1. 4 4 1 16
2. 7 14 4 49
3. 5 15 9 25
4. 8 32 16 64
5. 13 65 25 169
6. 8 48 36 64
7. 6 42 49 36
8. 5 40 64 25
9. 10 90 81 100
10. 15 150 100 225
55 81 500 385 773
X = Time passage
Y= Number of divorce
Regression analysis of divorce and time:
Where regression line = Y = a + bx
b=nεxy−εxεynεx2−¿¿
b=10(500)−(55)(81)
10 (385 )−¿¿
= 5000−44553850−3025
=545825
= 0.661
b = 0.661
a = y⃛−bx⃛
a = 81−(0.661 )10
5510
= 8.1 – (0.661) 5.5
= 8.1 – 3.6355
= 4.4645
Recall that Y = a + bx
Therefore Y = 4.4645 + 0.661x
Interpretation; The regression equation shows that for every
increase in time there will be an increase of 1 in the number
of divorce while in the absence of time there will be 4
divorce.
TEST FOR LINEARITY OF REGRESSION OF MARRIAGE ON TIME
HO : There is no linearity
H1: There is linearity
Critical Region F0.05 (V1V2)
Where V1 = K- 1 = 2-1 -1
V2 = N –K = 10-2 = 8
COMPUTATION
SST = εy2−¿¿
= 773 - ¿¿
= 773−656110
= 773-656.11
= 116.9
SST = 116.9
SSA = b(εxy−εxεyn )
= 0.661(500−(55) (81)10 )
= 0.661 (500−445510
)
= 0.661 (500 – 445.5)
= 0.661 (54.5)
= 36.0245
SSA = 36.0245
SSE = SST – SSA
= 116.9– 36.0245
= 80.8755
SSE = 80.8755
SOURCE DEGREE OF
FREEDOM
SUM OF
SQUARE
MEAN OF SUM
OF SQUARE
FRATION
REGRESSION
ERROR
1
8
36.0245
80.8755
36.0245
10.1094
3.5635
TOTAL 116.9
Fcal = 3.5635
Critical region
F0.05 (1,8) = 5.32
Ftab= 5.32
Decision Rule: Accept Ho if Fcal < Ftab otherwise reject.
Conclusion: Since Fcal (3.5635) < Ftab (5.32) we accept Ho and
conclude that there is no linearity between divorce and time
in Ile-Oluji/Okeigbo Local government.
CORRELATION ANALYSIS OF DIVORCE AND TIME
X= Passage of time
Y= Divorce
r = nεxy−εxεy√¿¿¿
r = 10(500)−(55 )(8)√¿¿¿
= r = 5000−4455√(3850−3025 )(7730−6561 )
= 545
√(825) (1169)
= 545√964425
= 545982.05
= 0.55
r = 0.55
There is weak positive correlation between divorce and time in
Ile – Oluji/Okeigbo local government.
COEFFICIENT OF DETERMINATION
= R2 × 100%
= (0.55)2 × 100%
= 0.3025 × 100%
= 30.25%
= 30%
30% of variation in divorce can be explained by time while 70%
can be explained by other factors.
TEST FOR THE SIGNIFICANCE OF CORRELATION
Ho : P = 0 (correlation is not significant)
H1 : P ≠ 0 (correlation is significant)
Critical Region
Ttab= T α/2 V, Where V = n-2 = 10-8 =8
= T0.05/2, 8
= T0.025, 8 = ± 2.306
Ttab = ± 2.306
COMPUTATION
t = r√n−2√1−r2
= 0.55√10−2√1−(0.55)2
= 0.55√8√1−0.3025
= 0.55(2.828)
√0.6975
= 1.55540.8352
= 1.8623 ≈1.86
Tcal = 1.86
Decision Rule: Accept Ho if Tcal < Ttab otherwise reject.
Conclusion: Since Tcal (1.86) < Ttab (±2.306) we therefore accept
Ho and conclude that the correlation between divorce and time
is not significant.
REGRESSION ANALYSIS OF DIVORCE ON TIME
X Y XY X2 Y2
36 4 144 1296 16
66 7 462 4356 49
42 5 210 1764 25
26 8 208 676 64
79 13 1027 6241 169
40 8 320 1600 64
34 6 204 1156 36
58 5 290 8364 25
62 10 620 3844 100
82 15 1230 6724 225
525 81 4,715 31,021 773
X = Marriage
Y= Divorce
Where regression line = Y = a + bx
b=nεxy−εxεynεx2−¿¿
b=10(4715)−(525 )(81)
10 (31021 )−¿¿
= 47150−42525310210−275625
= 462534585
= 0.1337
b = 0.1337
a = y⃛−bx⃛
a = 81−(0.1337 )10
52510
= 8.1 – (0.1337) 52.5
= 8.1 – 7.02
= 1.08
Recall that Y = a + bx
Therefore Y = 1.08 + 0.1337x
Interpretation; The regression equation shows that for every
increase in marriage there will be no increase of in the
number of divorce while in the absence of marriage there will
be 1 divorce.
TEST FOR LINEARITY OF REGRESSION OF MARRIAGE ON TIME
HO : There is no linearity
H1: There is linearity
Critical Region F0.05 (V1V2)
Where V1 = K- 1 = 2-1 -1
V2 = N –K = 10-2 = 8
COMPUTATION
SST = εy2−¿¿
= 773 - ¿¿
= 773−656110
= 773-656.11
= 116.9
SST = 116.9
SSA = b(εxy−εxεyn )
= 0.1337(4715−(525 ) (81)
10 )= 0.1337 (4715−
4252510
)
= 0.1337 (4715 – 4252.5)
= 0.1337 (462.5)
= 61.836 - 61.84
SSA = 61.836
SSE = SST – SSA
= 116.9– 61.836
= 55.064
SSE = 55.064
SOURCE DEGREE OF
FREEDOM
SUM OF
SQUARE
MEAN OF SUM
OF SQUARE
FRATION
REGRESSION
ERROR
1
8
61.836
55.064
61.836
6.883
8.984
TOTAL 116.9
Fcal = 8.984
Critical region
F0.05 (1,8) = 5.32
Ftab= 5.32
Decision Rule: Accept Ho if Fcal < Ftab otherwise reject.
Conclusion: Since Fcal (8.984) < Ftab (5.32) we reject Ho and
conclude that there is no linearity between marriage and
divorce Ile-Oluji/Okeigbo Local government.
CORRELATION ANALYSIS OF MARRIAGE AND DIVORE
X= MARRIAGE
Y= DIVORCE
r = nεxy−εxεy√¿¿¿
r = 10(4715)−(55)(81)√¿¿¿
= r = 47150−42525√(310210−275625 ) (7730−6561)
= 4625
√(34585 )(1169)
= 4625√40429865
= 465256358.4483
= 0.7474
r = 0.73
There is weak positive correlation between marriage and
divorce in Ile – Oluji/Okeigbo local government.
COEFFICIENT OF DETERMINATION
= R2 × 100%
= (0.73)2 × 100%
= 0.5329 × 100%
= 53.29%
= 53%
53% of variation in divorce can be explained by marriage while
47% can be explained by other factors.
TEST FOR THE SIGNIFICANCE OF CORRELATION
Ho : P = 0 (correlation is not significant)
H1 : P ≠ 0 (correlation is significant)
Critical Region
Ttab= T α/2 V, Where V = n-2 = 10-8 =8
= T0.05/2, 8
= T0.025, 8 = ± 2.306
Ttab = ± 2.306
COMPUTATION
t = r√n−2√1−r2
= 0.73√10−2√1−(0.73)2
= 0.73√8√1−0.5329
= 0.73(2.828)
√0.4671
= 2.06440.6834
= 3.0208 ≈3.02
Tcal = 3.02
Decision Rule: Accept Ho if Tcal < Ttab otherwise reject.
Conclusion: Since Tcal (3.02) < Ttab (±2.306) we therefore reject
Ho and conclude that the correlation between marriage and
divorce is significant.