Question 1
Consider the following model:
? = ?? + ?,
known as the Classical Linear Regression Model (CLRM), where y is the dependent variable, X is the set of independent variables, ? is the vector of parameters to be estimated and ? is the error term.
a) List and discuss the assumptions you need for the Ordinary Least Squares (OLS) to be a Best Linear Unbiased Estimator (BLUE). Derive the OLS estimator, discussing where the assumptions are needed for the derivation.
b) Discuss the properties of linearity, unbiasedness and efficiency, discussing what assumption you need for each of these properties to hold, and where assumptions are needed.
c) In what sense can decisions based upon the OLS framework be regarded as rational? What are the warnings of using the OLS approach for hypothesis testing? Discuss.
d) Present and discuss the R square and the adjusted R square. Why should the adjusted R square be regarded as a “soft rule”? Discuss.