In: Statistics and Probability
Suppose the sale of a particular product Y and the
advertisement expenditure X assumes a two variable linear relation
model given by Yj=α+βXj+ej, j=1, 2, ..., n
(a)Suppose that Xj are random variables and ej is the error term.
State the necessary assumptions that enable the estimation and
investigation of the estimators α ̂ and β ̂. [6 marks]
(b)Define a least square estimator of α and β which minimize the
squared error
(c)Derive the least squares estimator of β. [6 marks] (d)Show that
α ̂=Y ̅-β(X̄) [3 marks