Factors influencing the Import Expenditure

Running Header: Factors influencing the import expenditure 1
Factors influencing the import expenditure
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Factors influencing the import expenditure 2
Introduction
The study examines the relationship between import expenditure (IMPORTS), Consumer
Price Index (CPI) and GDP in the UK from 1985 to 2015. The study examines the import
function while evaluating the significance of the variables (CPI and GDP) which influences
the import expenditure. Simple linear regression models were used in investigating the
relationship between import expenditure and CPI and GDP separately while a multiple
regression analysis was used in investigating the relationship between import expenditure and
CPI and GDP together.
Part (A): Simple Linear Regression Model
Assumptions of Classical Linear Regression Model (CLRM)
According to Hose & Hans (2019), there are seven assumptions of CLRM.
First Assumption: The parameters of a regression model are. Violating this assumption
produces errors during extrapolation of the assumed model.
Second Assumption: The regressors are not stochastic or fixed. Violating this assumption
produces unreasonable predictions especially beyond the range of sample data.
Third Assumption: The mean value of the error term is 0 given the values of the independent
variables. Violation of this assumption biases the regression coefficient produced by the OLS.
Forth Assumption: Each error term variance given the independent variables values is
homoscedastic. Violating this assumption leads to the regression coefficient produced to be
less reliable since the data point across each independent variable does not influence equally.
Fifth Assumption: The error terms belonging to two different observations have no
correlation.
Sixth Assumption: The independent variables have no perfect linear relationship. Hence there
is no multicollinearity. Violating assumptions 5 and 6 causes the regression coefficient
variance to increase.

Factors influencing the import expenditure 3
Assumption 7: Correct specification of the regression model in use. Hence, there is no bias or
specific error. Violating this assumption makes the regression coefficient to be less reliable.
Properties of OLS Estimators
The linear property of the OLS estimators suggest than the OLS belongs in an estimator class
which is linear to the dependent variable (Rahman et al,, 2018). The estimator needs to be an
unbiased estimator of the true population or parameter values making it the most desirable
property of any estimator. The best minimum variance property places an estimator as being
efficient. Thus, the estimator will have the variance that is the least when taking all unbiased
estimators of the unknown population parameter. The asymptotic unbiasedness means when
the sample size of an OLS estimator increases, the unbiasedness disappears. Finally, an
estimator is pointed out to be coherent if its value approached the true parameter population
value when there is an increase in the sample size.
Scatterplots
Figure 1: Scatterplot for Imports Expenditure against GDP
0 2000 4000 6000 8000 10000 12000 14000
0
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Scatterplot for Imports Expenditure against GDP
GDP
Impors Expenditure
Figure 2: Scatterplot for Imports Expenditure against CPI

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40 60 80 100 120 140 160 180 200 220
0
200000
400000
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1000000
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Scatterplot for Imports Expenditure against CPI
CPI
Imports Expenditure
There exists a linear relationship between imports expenditure and CPI and imports
expenditure and GDP since the estimated regression lines are linear. Conversely, the
correlation coefficients of the two can be deduced to be between 0 and 1.
Relationship between imports expenditure and GDP
The estimated regression equation is:
IMPORTS=133.36*GDP–195,427.9
The import expenditure when all other factors are kept constant is -195,427.9 units. Notably,
a unit increase in GDP leads to a 133.36 unit increase in the import expenditure.
The developed hypothesis of the slope coefficient is as shown below:
H0: There is no association between Imports expenditure and GDP
H1: There is an association between Imports expenditure and GDP
From the output, it is seen that the p-value of the slope coefficient is less than the significance
level (p<0.05).