Chapter 5: SLR Assumptions

Question 1

SLR Assumptions:

Answer 1

1. Linear in parameters
2. Random sampling
3. There is sample variation in x
4. Zero conditional mean
5. • 4. -> Unbiasedness of Beta0hat and Beta1hat
6. Homoskedasticity

Question 2

SLR1 - Linear in parameters:

Answer 2

y=Beta0^1+Beta1^1*x+u

Violation:
y=Beta0^2+Beta1^2*x=u

Question 3

SLR2 - Random sampling:

Answer 3

((xi;yi):i=1,2,…,n), so yi=Beta0+Beta1*xi=ui

Violation:
Cov(ui;uj) is unequal 0 for all i unequal j

Question 4

SRL3 - There is sample variation in x:

Answer 4

Summation of (xi-xbar)^2 >0

Violation:
Summation of (xi-xbar)^2=0

Question 5

SRL4 - Zero conditional mean:

Answer 5

E(ui|xi)=0

Violation:
E(ui|xi) unequal 0.

Question 6

SRL5 - Homoskedasticity:

Answer 6

The conditional variance of u is a constant.
Var(ui|xi)=Sigma^2 (=const.)
-> Var(ui)=Sigma^2 (=const.)
-> Var(yi|xi)=Sigma^2 (=const.)

Violation:
Var(ui|xi)=Sigmai^2