4. (Fox 6.9) Suppose that the \"true\" model generating a set of data is Y = 0: + {3X1 + e. A researcher ts the model Y = a + ,8le + {3ng + e, which includes the explanatory variable X2, that is the true value of ,82 is 0. Had the researcher t the (correct) simple regression model, the variance of 81 would have been (using hte simple regression formula) V(Bl) = 02/ XXXH X1)2. a) Is the model Y = a + 51X 1 + [3ng + 5 wrong? In other words, is 31 for this model a biased estimator of 31? b) What is the variance of 31 in this model? 0) Considering (a) and (b), what is the cost of including the irrelevant explanatory variable X2? How does this compare to the cost of failing to include a relevant explanatory variable