CORRELATION AND REGRESSION ANALYSIS ON SAVINGS AND LOANS

CHAPTER ONE

1.0   INTRODUCTION

The term regression was originally used by FRANCIS GALTON (1822 - 1911) in a statistical examination of human inheritance to denote certain hereditary relationship very often in practice, a relationship is found to exist between these variables and often this make it possible to predict one or more variables in terms of others. For instance, studies are made to predict the future sales of a new product with respect to its price, family expenditure on feeding in terms of the family income, the consumption of certain food items in relation to the amount spend on its advertisement, quality of a product depending on the temperature of the product at production etc.

In this study, the focus is to examine the relationship between savings and loans with reference to EDE COMMUNITY MICRO FINANCE BANK NIGERIA LIMITED (ECB).

The group of data to be used involved only two variables; savings and loans, hence the simple linear regression and correlation analysis shall be used. The saving is taken to be independent variable (X) on which the loans (Y) depend.

The statistical model for sample linear regression assumes that for each value of X, the observed value of the response variable Y are normally distributed about a mean that depends on X. we use my to represent these means. Rather than just two m1 and m2, we are interested in how many means mychanges as X changes. In general the my changes according to any sort pattern as X changes. In linear regression, we assume that they all line on a line when plotted against X. the equation of the line is given by

Y = a + bx

Where,

y = dependent variable

a = constant parameter which is autonomous (intercept)

b = parameter which shows the rate of change y with respect to x (slope).

With intercept a and slope b; this is the regression line. It describes how the mean response change with x. actually observed y’s will vary the mean. The model assumes this variation measures by the standard deviation r is the same for all the value of x. the response y to a given x is a random variable that will take different value if we have several observations with the x – value.

The strength of this relationship is determined by the amount of effect that any change in one variable may cause on the other hand.

1.1   Historical Background of Regression and Correlation Analysis

The fundamental philosophy of Regression and Correlation were first proved and applied by SIR FRANCIS GALTON (1822 - 1911).

Galton was engaged in the study of heredity one of his observation was that the children of tall parents tends to be taller than average but not do tall as their parents. Whereas children of unusually short person tends to be shorter than their parents. This regression toward mediocrity gave these statistical method their name.

In a sense, the successive generation of offspring from tall person “regress” downward toward the mean height of population and reverse is true of the offspring from short families. Since Galton used one variable (i.e. height of the parent) to predict another (i.e. height of the child) the original term regression was eventually applied to general analysis by which the unknown variables are predicted through the known variables.

Correlation analysis also tell us the degree to which two variables are related. It is useful in expressing how efficiently one variable has estimated the value of the other variable. The word that is used to describe relationship between two categorical variables is association.

 If two variables are found to be either associated or correlated, that doesn’t necessarily mean that a cause and effect relationship exist between the two variables whether two variables are found to be casually associated depends on how the study was conducted.

1.2   AIMS AND OBJECTIVES OF THE PROJECT

One of the aims of writing this project is to best the ability of the writers to apply theoretical knowledge acquired in the study of statistics at OND level with a particular application of Regression and correlation to real life practical and condition.

The objectives of the project are stated below:

i.      To study the relationship between two variables savings and loans

Ii.     To estimate the dependence of loans on savings

iii.     To estimate the trend of the savings and loans over five years (20003-2007)

iv.     To predict the future behaviour of these two variables and lay the attitude of the banks towards loans in future

v.     To apply all necessary statistical tools in order  to explain the variables on how savings affect loans and loans affecting savings

vi.     To design an hypothesis to test the significance or reliability of the regression and correlation coefficient

1.3   SCOPE AND COVERAGE OF THE PROJECT

Regression and correlation analysis are common methods of analysis data to provide useful decision and information. We are to examine the relationship that exists between savings and loans made and recorded by Ede Community Micro Finance Bank Nigeria Limited (ECB).

The project covers a period of five years (2003-2007). The prediction shall be made. It will cover the behaviour of these variables within the period given. The total savings every month in Naira as independent variable shall show the minimum accuracy of loan given out as dependent variable. To estimate the expected value Y(loan recorded) and its behaviour towards independent variable X (savings).

Finally correlation will also be used to measure the degree of association between the two variables and all essential test will be employed to establish these facts.       

1.4   HISTORICAL BACKGROUND OF EDE COMMUNITY MICRO FINANCE BANK NIGERIA LIMITED (ECB) EDE

  The  federal government of Nigeria in the 1991 budget proposals further reiterated their commitment to the even development of Nigeria by concentrating on developing the rural areas a long side the urban centres.

Many attempts had in the past been made to force the big financial houses to establish the rural braches. The government realising that the banks and others, compelled by their own economic considerations are not willing to take up the challenges of rural development, introduced the idea of communities coming together to form their own bank. This effort is believed to have a dual advantage of bringing the banking culture to all and sundry.

To this end some interested and enthusiastic members of the Ede Community initiated the idea that culminated into what we know as Ede Community Bank Nigeria Limited.

1.5   TARGET OF THE BANK

  The bank operates on target savings scheme such as Ileya saving fund, Christmas savings fund, educational funds and housing and house equipping funds.

The bank has several sections such as savings and current department, loan recording department, marketing department, administration department and entry department.

The savings and current department are called the operational system i.e. they deal with clearing of cheques and keeping of the summary of the daily activities.

1.6   RANGES OF SERVICES PROVIDED

        The following are the services that the bank has planned for the benefit of people.

I.         Saving account

II.         Current account

III.         Private banking

IV.         Fixed deposit account

V.         Short term finances

VI.         Community project financing

VII.         Equipment leasing

VIII.         Cooperative development financing

IX.         Special loans and other credits

X.         Bank guarantees

XI.         Financial Advisory services

XII.         Safe deposit services

XIII.         Investment banking

Other services include:

1)     Overseas customer: People can send draft in foreign currencies the naira value of which would be paid to credited into the account of the owner with the bank.

2)     Foreign Remittance: The bank through their chain of correspondence bank abroad could abroad could easily purchases from abroad or remittance of funds.

1.7   DEFINITION OF TERMS

Below are the definitions of some term used in this project for easy comprehension.

Correlation co-efficient: This is referring to the degree of association between a bivariate distribution

Correlation: This is the measure of degree of association that exist between two variables considering one as independent (x) and another dependent (Y)

Regression: This is also referred to as the slope of a regression equation. It is the measure of the rate of changes between two or more variables.

Analysis of Variance (ANOVA): This is a common method of analysis experimental data. It attempts to analysis the total variation of a response by decor-posing it into independent and meaningful portion attributed to each of the variable (independent) sop as to chance variable.