Question

Q: Answer yes or no to each of the items from a to c. If yes, briefly justify the statement, if no, provide a counter-example or disprove the statement.

a) We have a sample of an individuals, indexed by i = 1, · · · , n. For the i-th individual, we can observe X_i andY_i. If we assume our sample is i.i.d. cross-sectionally, it implies Xi and Yi are independent with each other.

b) In multivariate OLS, we have three regressors X1, X2, X3. If (X1, X2), (X1, X3), and (X3, X2) are not perfectly correlated, then we do not have the perfect multicollinearity.

c) T-test is still valid when OLS assumption 1 correct specification is violated.

Answer 1

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Answer:

a)

False

Let us consider Xi and Yi as variables for heights and weights of a certain population. There may be some dependency between the two variables. To be precise it can be said that, (Xi,Yi) is independent to (Xj,Yj) given that i j but it canot be said that Xi can be dependent on Yi

b)

True

Suppose consuder that in mutivariate OLS, we have here 3 regressors, X1, X2 and X3. The OLS assumption of multicollinearity signifies that there should not be no linear relationship between the independent variables. So considering that pairs of (X1,X2) , (X2,X3) and (X3,X1) are not perfectly correlated, then we do not have the perfect multicollinearity.

c)

True

T test is used for conducting hypothesis test on regression coefficients. Violations of normality in OLS can be mitigated by t tests