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As noted earlier, given the assumptions of the classical linear regression model, the least-squares estimates possess some ideal or optimum properties. These
properties are contained in the well-known Gauss –Markov theorem. To
understand this theorem, we need to consider the best linear unbiasedness property
of an estimator. The OLS estimator is said to be a best linear unbiased estimator BLUE if the following hold Brooks, 2002:
1. It is linear, that is, a linear function of a random variable, such as the
dependent variable Y in the regression model.
2. It is unbiased, that is, its average or expected value, E
β
2
, is equal to the true value,
β
2
. 3. It has minimum variance in the class of all such linear unbiased estimators;
an unbiased estimator with the least variance is known as an efficient
estimator.
The classical assumption test needed to ensure that the regression model is the best estimator or BLUE. The classical assumption test also used to detect any
mislead of the classical linear model. The test used are Heteroscedastic Test, Auto-Correlation Test, and Multi-Colinearity Test.
a. Heteroscedastic Test
One of the important assumptions of the classical linear regression model is that the variance of each disturbance term u
i
, conditional on the chosen values of the explanatory variables, is some constant number equal to
σ
2
. This is the
assumption of homoscedasticity, or equal homo spread scedasticity. When the
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variance of each disturbance u
i
is not constant however, there is heteroscedasticity on that variance. Still according to Gujarati in his book Basic Econometric, the
consequences of heteroscedasticity in the regression model is as follows:
1. The estimator produced will still be consistent, but that estimator will be
no longer efficient. Meaning that, there are variance that has little error than the estimator produced in the regression model that contains
heteroscedasticity.
2. Estimator produced from the regression linear model is no longer have an
accurate heteroscedastic. This will cause the hypothesis testing become not accurate.
In short, if we persist in using the usual testing procedures despite heteroscedasticity, whatever conclusion we draw or influences we make may be
very misleading. To detect whether heteroscedasticity is present in the data, researcher will conduct
a formal test using White Test method. Th e reason why researcher use White‟s
General Heteroscedasticity Test is because it does not rely on the normality assumption and easy to implement. The White test proceeds as follows:
Step 1. Given the data, we estimate regression model and obtain the residuals
,u
i
�
3.13 Step 2.
We then run the following auxiliary regression:
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3.14 Step 3.
Formulate the Hypothesis Test H
= There is no heteroscedastic H
a
= There is heteroscedastic Under the null hypothesis that there is no heteroscedasticity, it can be shown that
sample size n times the R
2
obtained from the auxiliary regression asymptotically follows the chi-square distribution with df equal to the number of regressors
excluding the constant term in the auxiliary regression. That is,
�
3.15 Step 4.
If the chi-square value obtained in 3.15 exceeds the critical chi-square value at the chosen level of significance, the conclusion is that there is
heteroscedasticity. If it does not exceed the critical chi-square value, there is no heteroscedasticity, which is to say that in the auxiliary regression 3.14.
If heteroscedasticity truly exist, one can use the Generelized Square Method or White Test method. White Test method developed heteroscedasticity-
corrected standard error. Software Eviews 5 has already provided White method to overcome heteroscedastic.
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b. Autocorrelation Test
The term autocorrelation may be defined as correlation between members
of series of observations ordered in time [as in time series data] or space [as in cross-sectional data] Gujarati, 2004, p.442. In the fifth assumption of the
classical linear regression model, it assumes that such autocorrelation does not exist in the disturbance u
j,.
The classical model assumes that the disturbance term relating to any observation is not influenced by the disturbance term relating to
any other observation. As in the case of heteroscedasticity, in the presence of autocorrelation the OLS
estimators are still linear unbiased as well as consistent and asymptotically normally distributed, but they are no longer efficient i.e., minimum variance.
Therefore, the usual t and F tests of significance are no longer valid, and if applied, are likely to give seriously misleading conclusions about the statistical
significance of the estimated regression coefficients.
To detect autocorrelation, the writer use The Breusch-Godfrey BG Test in the
application software EViews 5. BG Test, which is also known as Lagrange- Multiplier LM Test involves the following hypothesis:
Ho: There is auto-correlation H1: There is no auto-correlation
After we run the test, we can analyze the result by comparing the value of ObsR- squared
, which comes from the coefficient determination R squared multiple
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with the number of observation, and the value of the probability with the significant value
α, as follows: If the Probability
α = 5, there is no auto-correlation, thus we reject H
o
. If the Probability
α = 5, there is auto-correlation, thus we failed to reject H
c. Multi-Collinearity Test
Estimator that has BLUE characteristic supposed to be not contains multicollinearity. Since multicollinearity is essentially a sample phenomenon,
arising out of the largely nonexperimental data collected in most social sciences, there is no one unique method of detecting it or measuring its strength. In this
research, the writer will detect the existence of multi-collinearity by using
software Eviews 5. The method that will be used is through the examination of partial correlation
. This method is developed by Farrar and Glauber. They suggested that in examining the existence of multicollinearity one should look at
the partial correlation coefficient Gujarati, 2004. Thus, in the regression of Y on X
2
, X
3
, and X
4
, a finding that R
2 1.234
is very high but r
2 12.34
, r
2 13.24
, and r
2 14.23
are comparatively low may suggest that the variables X
1
, X
2
, and X
3
are highly intercorrelated and that at least one of these variables is superfluous.
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3. Hypothesis Test
