My id number – 00006885 Question 1

My ID number – 00006885

Question 1.

a)

= - -

= - - ) ^2

By doing this,

= ( - - ) ^2=0, : (-2)

= ( - - ) ^2=0, :(-2)

- - ) =0

-n - =0

Since =n n -n - n =0 |: n

- - =0

=

Then ( - - ) =0

- - ) =0

- - = 0

By inserting

- ( ) - = 0

-n +n - = 0

- n = - n

- n = ( -n )

= =

b)

= = = we define as

Thus = = = ( +u) = + +

= + +

Since = = - n = n - n = 0, inserting this

= = = - n = - 2n + n = -

2 + =

= =

This one is created = 0 = 1

= + + = +

- =

= = = =

By using this assumption and = 0

=( => =

= = - = - = - ( ) (

c)

OLS Assumptions

1. 
   This regression is Linearity in parameters:
   

and . Coefficients are and linear when and factors are not important.

2. in repeated sampling, X value is fixed 3. Zero mean value of disturbance E( )= 0. Error term must be 0

4. Homoscedasticity or constant variance of u E(u, x)= 0. Variance of error term and independent of observation is the same

5. Error term is independent of X cov( , )= 0

6. Zero covariance between X and it. X and o numbers need to be compared with each other because otherwise it will be difficult to determine which one will be affected by Y. Also, it cannot be covariated with X because it cannot be an explanatory variable.

7. Number of observations should be greater than X variables.

8. X values must not not all be the same all the time that is cov(X)>0 variance of x is finite number

9. The regression model is shown correctly. There should be no inaccuracies or errors in the collection of empirical data and in the structured model.

10. There are no perfect multicollinearity among independent variables.

d)

=1

= = = (α+β

+β + =β+ where

E( =E(β)+E( E( =β