From the linear model we find expected u
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; from here we derive β_{1}: ; from here we derive β_{2}:
as Assumptions depicts that ; and ; and The variance of can be found using the same way:
Assumption 1: Linear regression model (in parameters) means that the model’s coefficient must be in the degree of one. Assumption 2: X values are fixed in repeated sampling, which means that regressor must be nonstochastic. Assumption 3: Zero mean value of : , the value of the random disturbance term (error term) is zero. Assumption 4: Homoscedasticity or equal variance of : Theoretically, the equation characterizes the assumption of homoscedasticity, or equal variance. In other words, it means that the Y populations corresponding to various X values have the same variance. Assumption 5: No autocorrelation between the disturbances: With The disturbances u_{i} and u_{j} are uncorrelated, i.e., no serial correlation. This means that, given x_{i}, the deviations of any two Y values from their mean value do not exhibit patterns. Assumption 6: Zero covariance between u_{i} and X_{i} The error term u and righthand side variable X are uncorrelated. Assumption 7: The number of observations n must be greater than the number of parameters to be estimated. Assumption 8: Variability in X values. They must not all be the same. If all values of X is the same, then , which makes the denominator 0 and calculation of β_{1} and β_{2} will be impossible. Assumption 9: The regression model is correctly specified.in other words, the model that is used in empirical analysis must not have specification errors. Assumption 10: There is no perfect multicollinearity between Xs. That is to say, the relationship between independent variables must not be perfect.
; ; ; ; ; from this equation we found out βhat: ; ; ; ; ; ; By using assumption we prove that the coefficient of OLS is unbiased Download 0.84 Mb. Do'stlaringiz bilan baham: 
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