1. Let M-B+ BXY- ISM: P- 15F Show the following results: EM ( X, - X)Y. _EM ( X - X) ( Y - Y) ELIX, (Y - Y) EMI (X, - X) EMI (X, - X)' EM, (X, - X)' 2. A researcher suggested instead of computing 8 from the usual OLS estimation procedure that minimizes the sum of squared residuals, one can compute it as follows. First compute X" and Y- and then compute Yix = Yi - Y and Xix = Xi - X. Now, choose B * that minimizes The researcher claims that B * = , where B , is the OLS estimator in the simple regression model we have discussed in class. Would that be necessarily true? Explain. 3. Assume that you are in charge of the central monetary authority in amythical country. You are given the following historical data on the quantity of money and national income (both in million of dollars ) : Year Quantity of Money National Income 1997 4.0 7.7 1998 4.2 8.4 1999 4.6 9.0 2000 4.8 9.7 2001 5.0 10.0 2002 5.1 10.5 2003 5.5 11.7 2004 5.8 12.5 2005 6.4 13.5 2006 6.8 14.5 2007 6.2 12.1 2008 5.8 12.2 2009 6.3 13.5 2010 6.7 14.7 2011 7.1 15.8 2012 7.3 16.8 2013 7.7 17.1