Wk2

Question 1

Clar 1

Answer 1

Bivariate linear b1 and b2 are constant and there’s an error term - not effected by external shocks

Question 2

Clra2

Answer 2

X is fixed non stochastic we chose the level of x variable to see effects on Y

Question 3

Clra3

Answer 3

There is variation in the x variable not constant

Question 4

CLRA 4

Answer 4

Error has expected value of 0 - zero mean errors on average no systematic error

Question 5

CLRA5

Answer 5

No 2 errors are correlated no autocorrelation only applicable to time series model

Question 6

CLRA6

Answer 6

Homesdastic variance of the error term are constant for all observations - vio happens in cross sectional models

Question 7

CLRA7

Answer 7

Population error is normally distributed with the same mean and variance

Question 8

Theoretical results 1

Answer 8

Under 1-4 hold OLS will hold

Question 9

TR2

Answer 9

CLRA1- 6 hold the gauss marker theorm the OLS is thr best linear unbiased estimator and if efficient - lowest variance.

Question 10

TR3

Answer 10

CLAR1 -7 minimum variance unbiased estimator in the class of all linear and non linear estimators

Question 11

Clar2 2.0

Answer 11

There is variation in the X variable it is not a constant term - x is random

Question 12

Clra3 2.0

Answer 12

The error has an expected value of 0 given for any value of X E(e|Xi) =0 for all i - zero conditional mapean assumption
- for time series data e at time t is uncorrelated with X at time t OLS is consistent but unbiased

Question 13

CLAR 4 2.0

Answer 13

The disturbances are conditionally uncorrelated, 𝑐𝑜𝑣(𝜀𝑖, 𝜀𝑗|𝑋) = 0 for all 𝑖 ≠ 𝑗
where 𝑖 and 𝑗 are time periods, because this only affects time-series models. The errors are
said to be not autocorrelated.

Question 14

CLRA5

Answer 14

Homoscedasticity is now stated such that each disturbance has the same finite
conditional variance, 𝑣𝑎𝑟(𝜀𝑖|𝑋) = 𝜎2 for all i.

Question 15

CLRA6

Answer 15

The population error, conditional on 𝑋, is normally distributed, 𝜀𝑖|𝑋~𝑁(0, 𝜎2).

Question 16

CLRA 1 - multi

Answer 16

𝑌 𝑖 = 𝛽0 + 𝛽1𝑋1𝑖 + 𝛽2𝑋2𝑖 + … + 𝛽𝑘𝑋𝑘𝑖 + 𝜀𝑖
where 𝛽0, … , 𝛽𝑘 are unknown parameters (constants) and 𝜀𝑖 is an unobservable random error
term.

Question 17

CLRA2 - multi

Answer 17

The error has an expected value of 0 given any values for the independent variables,
i.e. 𝐸(𝜀|𝑋1, … , 𝑋𝑘) = 0

Question 18

CLRA 3 - multi

Answer 18

None of the regressors are constant and there are no exact linear relationships among
the regressors (this means we have no exact collinearity or no perfect collinearity

Question 19

ClRA4 - multi

Answer 19

The disturbances are conditionally uncorrelated, 𝑐𝑜𝑣(𝜀𝑖, 𝜀𝑗|𝑋1, … , 𝑋𝑘) = 0 for all
𝑖 ≠ 𝑗 where 𝑖 and 𝑗 are time periods, i.e. they are not autocorrelated.

Question 20

CLRA5

Answer 20

The disturbances are conditionally homoscedasticity, 𝑣𝑎𝑟(𝜀|𝑋1, … , 𝑋𝑘) = 𝜎2
.

Question 21

CLRA6

Answer 21

The population error, conditional on the regressors, is normally distributed,
𝜀𝑖|𝑋1, … , 𝑋𝑘~𝑁(0, 𝜎2)