This chapter focuses on the
research method that will be adopted. Regression analysis based on the
classical linear regression model, otherwise known as Ordinary Least Square
(OLS) technique is chosen by the researcher. The researcher’s choice of
technique is based not only by its computational simplicity but also as a
result of its optimal properties such as linearity, unbiasedness, minimum
variance, zero mean value of the random terms, etc (koutsoyiannis 2001,
Gujarati 2004).
MODEL
SPECIFICATION
In this study, hypothesis has been
stated with the view of evaluating the impact of foreign aid on poverty
reduction in Nigeria.
In capturing the study, these
variables were used as proxy. Thus, the model is
represented in a functional form. It is shown as below:
P = f(ODA,
GR,PGR,CAP,GRGDP)……….…………. 3.1
Where
P =
Population in Poverty (dependent
variable)
ODA = Net
official development assistance
GR = Grants
received, excluding technical co-operation
PGR = Population
growth rate
CAP = Capital
expenditure
GRGDP=
Growth rate of GDP
In a linear function, it is
represented as follows,
P = b0
+ b1ODA + b2GR + b3PGR + b4CAP
+ b5GRGDP+Ut ……3.2
Where
b0
= Constant term
b1 = Regression coefficient of ODA
b2
= Regression coefficient of GR
b3
= Regression coefficient of PGR
b4
= Regression coefficient of CAP
b5
= Regression coefficient of GRGDP
Ut
= Error Term
MODEL
EVALUATION
At this level of research, using a
time series data, the researcher estimates the model with ordinary least square
method. This method is preferred to others as it is best linear unbiased
estimator, minimum variance, zero mean value of the random terms, etc
(Koutsoyiannis 2001, Gujarati 2004, Baltagi, 1999, and Nwobi 2001).
However, due to conventional
reasons, the researcher will make use of E-view software statistical package in
running the regression. This as believed by the researcher will help in
determining the result of the various tests that is to be carried out. The
tests that will be considered in this study include:
Coefficient
of multiple determination (R2 )
Standard
Error test (S.E)
T-test
F-test
Durbin
Watson Statistics
Coefficient of Multiple Determination
(R2 ): It is used to
measure the proportion of variations in the dependent variable which is
explained by the explanatory variables. The higher the (R2) the
greater the proportion of the variation in the independent variables.
Standard Error test
(S.E): It is used to test for the
reliability of the coefficient estimates.
Decision Rule
If
S.E < ½ b1, reject the null hypothesis and conclude that the
coefficient estimate of parameter is statistically significant. Otherwise
accept the null hypothesis.
T-test:
It is used to test for the statistical significance of individual estimated
parameter. In this research, T-test is chosen because the population variance
is unknown and the sample size is less than 30.
Decision Rule
If
T-cal > T-tab, reject the null hypothesis and conclude that the regression
coefficient is statistically significant. Otherwise accept the null hypothesis.
F-test:
It is used to test for the joint influence of the explanatory variables on the
dependent variable.
Decision Rule
If
F-cal > F-tab, reject the null hypothesis and conclude that the regression
plane is statistically significant. Otherwise accept the null hypothesis.
Durbin
Watson (DW): It is used to test for the presence of
autocorrelation (serial correlation).
Decision Rule
If
the computed Durbin Watson statistics is less than the tabulated value of the
lower limit, there is evidence of positive first order serial correlation. If
it is greater than the upper limit there is no evidence of positive first order
serial correlation. However, if it lies between the lower and upper limit,
there is inconclusive evidence regarding the presence or absence of positive
first order serial correlation.
SOURCES OF DATA
The data for this research project
is obtained from the following sources: Central Bank of Nigeria Statistical
Bulletin for various years; National Statistical Bulletin, National Bureau of
Statistics, World Bank Statistical Bulletin. United States common database and
the internet.
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