International Journal of Scientific & Engineering Research, Volume 4, Issue 12, December-2013 288
ISSN 2229-5518
The search period thirty-one year since 1980 to 2010, a period filled with lots of economic changes. This research is based on the standard statistical
method and quantitative economic analysis.
—————————— ——————————
Search stretched over thirty-one year since 1980 to 2010, a period filled with many of the economic changes, Such as the appearance of the actual impact of economic openness, which began in 1974, and the period of economic reform in the beginning of the nineties and the
beginning of a privatization since 1996, As well as the occurrence of
The type of mathematical formula to offset what is suggested by economic theory, or that which is inspired by the shape of the spread of points dependent variable with the independent variables one at a
time, or as evidenced Applied Studies earlier., And you must know the theoretical predictions of the relations between the variables under study, as there are some assumptions basic to build econometric
models, and that the consequent drop one of them or all of them some
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some economic variables such as domestic and foreign second Gulf
W ar in 1991. The decline in global economic activity and local levels and the emergence of a recession in the Egyptian economy.
In this study was to identify a number of factors or variables of importance to the national economy and directly affect the banking sector and specifically on the size of deposits.
Those variables are Gross Domestic Product (GDP), Money Supply, and the volume of Foreign Trade and population, which can be defined as follows:
- GDP is the sum of the values for each of the cash commodity
production and service of the economy during a certain period of time.
of the problems which may affect the ability of the predictive model and
interpret estimates.
1) the dependent variable linear function in the coefficients of independent variables plus term of error. The model takes the following form:
Yi = B0 + B1 X1i +……. + Bk Xki + ei (1) Where: i = 1, 2, n
(Variable has a positive impact on the volume of deposits).
- Money Supply is the amount and effective means or domestic
liquidity include all of the cash in circulation outside the banking system
YRiR
BR0R
X , .. .. , X
refers to the dependent variable, refers to the constant term.
refers to the independent variables,
and deposits, current and non-current local currency and foreign
R1iR
B ,……, B
R kiR
refers to Partial regression coefficients of linear
currency deposits.( Variable has a negative impact on the volume of deposits).
R1R
eRiR
R kR
regression model.
refers to the extent of the error,
- Foreign trade volume of exports and imports require open letters of
credit banks. (Variable has a positive effect on the size of deposits).
- Population are based on the generation of GNP and all aspects of economic activity (Variable has a positive effect on the size of deposits).
The economic theory test means verification of compatibility with the practical reality, and then be accepted, amended or rejected or to reach a new theory.
And the drop that hypothesis occur an error the identification and formulation of the relationship of economic, as a result ignored or eliminated some of the important independent variables in determining the form, or the inclusion of some unimportant independent variables in the model, or that the true relationship between the dependent variable and the independent variables relationship is non linear or change of coefficient regression during the time period in which data were collected through them.
2) The expected value for error be equal to zero
The econometric methodology is determined as follows:
Ε(ei ) = 0
(2)
this is known as the expression of economic theory in the form of an equation or set of equations, the equation is a relationship between the dependent variable and the independent variable and one or several independent variables.
And the consequent drop that hypothesis of a problem the constant
Bias.
The bias is the difference between the mathematical expectation parameter estimates and estimated its real value,
( Bias = 𝐸�𝜃�� − 𝜃1T)
Dependent Variable = f (Independent Variables)
3 ) Homo-Scedasticity
2 ) σ e 2
var(ei ) = E(ei =
(3)
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International Journal of Scientific & Engineering Research, Volume 4, Issue 12, December-2013 289
ISSN 2229-5518
This means that the variance error limit for not dependent on the values of the independent variables in the case of multiple regression,
n
∑ (yˆ i
− y) 2
and the consequent drop that hypothesis a Hetero-scedasticity
R 2 = SS regression = i =1
(7)
problem that limits the errors do not have the same variance.
SS total
∑ (yi i =1
− y) 2
In the sense that the estimated value reduce error in a certain period of time independent of the appraised value reduce error in an unprecedented period of time
The structure of the test of the relationship linear regression as follows: Null hypothesis: all regression coefficients equal to zero.
H 0 : all of B i = 0 i=1,2,….,k
Against the alternative hypothesis:. No regression coefficient at least
Cov (eie j ) = Ε(eie j ) = 0
i ≠ j
(4)
one not equal to zero
And the consequent drop the hypothesis that the problem of
Autocorrelation
H1 : at least one of B i ≠ 0 i=1,2,….,k
the statistics used to test the Null hypothesis is the F statistic
F = R
2 /k
(8)
Based on these assumptions (2-4) past can be incorporated as
(1 − R
)/n − k − 1
follows
ei ~ i.i.d .N (0, σ 2 )
(5)
And the decision is made according to the following rule: accepted that
the regression coefficients are not all equal to zero if the p-value (sig.)
of the statistic is less than the used level of significant (α ).This
indicates that the estimated regression equation as a whole statistically
6) Independent variables non-random variables and the consequent drop the hypothesis of a record problems such as There are errors in the measurement of the independent variables.
significant in explaining the behavior of the dependent variable of the economic relationship.
Parameters are evaluated regression models estimated separately,
Multicollinearity.
IJSEafter ascertainingRthe extent of acceptance in accordance with the
8) Error limit independence from the independent variable for each
watch.
criteria of economic and make sure the model as a whole is significant
and the structure of the test as follows
cov(Xiui ) = E(Xiui ) = 0
(6)
H0 : B i = 0 i=0,1,2,......,k
To reach accurate estimates of the values of the coefficients of the
H1 : B i ≠ 0 i=0,1,2,......,k
the statistics used to test the hypothesis is the t statistic
proposed models, and considers the ordinary least squares (OLS)
method of the most used methods to obtain these estimates with the
t = Bˆ i
S.E(Bˆ i )
(9)
need for the availability of the previous assumptions. Since the method of least squares capabilities Best Linear Unbiased Estimators ( BLUE)
Estimates are evaluated based on three basic criteria:
economic theory. W here they are sure of the extent of agreement signals the estimated regression coefficients with the expected signs according to economic theory .Also be sure of the extent of agreement estimated values for the regression coefficients with counterparts contained in economic theory.
According to this criterion is the evaluation process in accordance with the following stages:
Using the coefficient of determination R2 to express the explanatory
power of the models (the responsibility of the explanatory variables in explaining the changes in the dependent variable of the economic
This test follows the probability distribution of student T. The decision is in accordance with the following rule: the alternative hypothesis is accepted the if the p-value (sig.) of the statistic is less than the used level of significant (α )
It reflects the ability of the model to predict the estimated values of past or present during the time period of the estimate. This test is done according to one of the following methods
That whenever the value of the high coefficient of determination whenever explained on the quality of the estimated model to predict the current values during the time period of the estimate.
The structure of the test as follows
relationship). The coefficient of determination represents the ratio
H 0 : yˆ i
− y i = 0
between the sum of the squares regression to the total sum of squares
can be formulated as follows
H 1 : yˆ i − y i ≠ 0
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International Journal of Scientific & Engineering Research, Volume 4, Issue 12, December-2013 290
ISSN 2229-5518
Where: yi is the watch for value of the variable, 𝑦�Ri is the predicted
value.
The statistics used is the t-test and be worded as follows:
Data were obtained from the Egyptian Central Agency for Public Mobilization and Statistics (CAMPS) and Egyptian Cabinet Information and Decision Support Center (IDSC).Data covers the period from 1980
t = yi − yˆ i
(10)
to 2010. Computer Program SPSS17, Minitab 16 and E-VEIW S7 are
σˆ 1 + 1 +
(X i − X)
used in analysis and the same results had.
u n
∑ (X i
i =1
− X) 2
According to the concept of economic theory, the volume of deposits is
estimated as a function of the independent variables affecting it, as shown next model
This test follows the distribution of T. the decision is made according
to the following rule:, the null hypothesis is accepted ( no significant difference between the predicted value and the actual value ),if the p- value (sig) is exceed the level of significance used. This decision which indicates the quality of the predictive ability of the model estimated with respect to No. i
and knows Theil coefficient of inequality (U) as follows
𝑦𝑖 = 𝑢 + 𝑏1 𝑋1 + 𝑏2 𝑋2 + 𝑏3 𝑋3 + 𝑏4 𝑋4 + 𝑒𝑖
X1 Gross Domestic Product (GDP),
1 n (Yˆ
− Y ) 2
X2 Money Supply ,
X3 the volume of Foreign Trade
X4 population.
U = n i =1
(11)
1 n Y 2 +
n i =1
1 n ˆ 2
n i =1 i
𝒊 ~ 𝑰𝑵(𝟎,𝝈𝒆 )
Applying the method of ordinary least squares (OLS) on the data
The value of the parameter U lies between zero and one
0≤ U ≤1
available. Obtaining the following results
- If the parameter value is equal to zero U = 0, this indicates that fully reconcile the estimated
model to predict during the time period of the estimate.
- If the parameter value is equal to the one true U = 1, it indicates poor ability Predictive models
to predict estimated during the time period of the estimate.
- If the parameter value ranged between zero and one 0 < U <1, In this case must describes the
various sources of error in forecasting.
This criterion measures the extent Reliability criterion in assessing the statistical model Proposal. Among these tests DW (Durbin W atson ) test for autocorrelation, and test Multicollinearity, and test of Herteroscedasticity
The main objective of the standard models is to predict future values of the variable values on the basis of the known or anticipated future of the independent variables .
It can predict the values of the dependent variable in two ways:
It is intended to predict the future value of one variable 's , under the assumption of a certain value Independent variables separately. Second : prediction for the Interval Prediction
It is intended to predict the period which can be the future of the true value of the significant value equal to (1- α )% W here the limits of
confidence , which takes the following form:
Table (1)
Table (1) shows the values of means and standard deviations and numbers of the dependent variable and the independent variables.
Pr{Yˆ t − tα
و(n − k ) se(Yˆ t ) ≤ Yt ≤ Yˆ t + tα
2
,(n − k ) se(Yˆ t )} = (1 − α )
2
(12)
se (Yˆ ) =
σ 2 ( 1 +
( X t − x )
n
(13)
n ∑ ( X i
i =1
− x ) 2
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International Journal of Scientific & Engineering Research, Volume 4, Issue 12, December-2013 291
ISSN 2229-5518
Sig. (2-
tailed)
.000 .000 .000 .000
N 31 31 31 31 31
G.D.P Pearson
.985** 1 .993** .830** .950**
Correlation
Sig. (2-
.000 .000 .000 .000 tailed)
N 31 31 31 31 31
Table(3)
According to the Table ( 3 )W e note that the independent variables remaining 1.1% as a result of random variations and this is illustrated
by the value of the coefficient of determination R2.also find that the value of test D.W refers to the absence of the problem of autocorrelation.
Money
Supply
Pearson
Correlation
Sig. (2- tailed)
.978** .993** 1 .863** .963**
.000 .000 .000 .000
N 31 31 31 31 31
Foreign
Trade
Pearson
Correlation
Sig. (2- tailed)
.865** .830** .863** 1 .884**
.000 I.000 J.000 S.000 ER
N 31 31 31 31 31
Population Pearson
.965** .950** .963** .884** 1
Correlation
Table (4)
According to Table ( 4 ) reports the ANOVA result for the model, we
find that the significance of the model is less than 0.001 Therefore we can say that the statistically significant regression.
Sig. (2-
tailed)
.000 .000 .000 .000
N 31 31 31 31 31
**. Correlation is significant at the 0.01
level (2-tailed).
Table (2)
Table (2) Shows the correlation coefficients matrix and the level of significance between all the independent variables and the dependent variable. Through the matrix, we find that GDP has the greatest impact on the dependent variable, followed by the money supply and population.
W e also find that there are internal correlations between the independent variables, suggesting that we are in the process of Multicollinearity problem.
To test the hypothesis H 0: ρ = 0 VS H1 : ρ ≠ 0
The p value is less than 0.0001 indicating that the correlation is significant. W hich describes the strength of the linear relationship between variables.
Model Summaryb | |||||
Model | R | R Square | Adjusted R Square | Std. Error of the Estimate | Durbin- W atson |
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International Journal of Scientific & Engineering Research, Volume 4, Issue 12, December-2013 292
ISSN 2229-5518
Populatio n
4296.737
1082.10
6
0.333
3.97
1
0.00
1
0.061
16.27
8
[1] Doane, D. & L. Seward. 2007, Applied Statistics, Mc
Graw..Hill Irwin,2nd Edition.
a. Dependent
Variable: Deposits
Table (5)
[2] Greene, W .H. 2000. Econometric Analysis ,4th
Jersey: Prentice
Hall
Edition. New
Table (5) shows the results of the regression analysis and estimating constant and regression coefficients where they are statistically significant.
The model is
From standardized coefficient column, we find that GDP and money supply are more variables with the largest impact on the volume of deposits.
To detect the presence of Multicollinearity problem between the independent variables
1
W e find that the value of the variance inflation factor ( 𝑉𝐼𝐹𝑖 = )
𝑖𝑖
if it is greater than 100 was evidence of a high linear-correlation
between the independent variable associated with this parameter with the rest of the other independent variables.
[3] Maddala ,G.S. 1977, Econometrics. McGRAW HILL USA.
[4] Mirer, T. 1990, Economic Statistics and Econometrics: 2nd
Edition Maxwell
Macmillan International Editions.
[5] Stock, J. & M. W atson. 2005. Introduction to Econometrics.
Pearson Education Inc.
Details about Author: Maie M. Kamel
statistic Department
Faculty of commerce, Tanta University
Egypt maie.m.kamel@gmail.com
W e found that money supply has a higher VIF then G.D.P then
Population.
To find out any independent variables requires entry into the model is the use of so-called Tolerance scale which is the inverted to VIF
.Tolerance scale must be less than or equal to 0.01
According to this scale the variables must be in equation are money supply and G.D.P.
Theil coefficient of inequality U = 0.0003, and that value refers to the quality of the estimated model to predict during the time period of the estimate.
In this search we cannot compare the actual values and the predicted values due to the political and economic conditions and the absence of stability experienced by the country since 2011 and so far.
Statistical analysis showed a strong relationship between the total volume of deposits in the Egypt banking system and independent factors affecting it, such as GDP ,Remittances from Egyptians working abroad , Money Supply, Foreign Trade and Population.
From the study, we find a structural relationship between variables (the dependent variable and the independent variables), which corresponds to the economic theory.
One of the challenges that directs the Egyptian banking system is working to increase the volume of deposits because of their key role in financing economic development programs.
It should be noted that the presence of Multicollinearity is not considered a problem in itself, but the problem is in the degree of Multicollinearity. If the degree of Multicollinearity low can accept such couplings, where it is expected to continue the case of Multicollinearity between the variables in the future to the same degree as they were in appreciation of the period. If, however, a high degree of coupling will lead to the difficulty of determining the estimated values for the
regression coefficients.
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