The dataset "US macro data".xls contains quarterly time series data for the US for the period Q1 2002 to Q4 2018. Here Q1 20xx stands for the first quarter of the year 20xx, and so on. The variables are:

Year: 20xx

Quarter: 1 to 4

lgdp: logarithm of US Real Gross Domestic Product, Billions of Chained 2012 Dollars, Quarterly, Not Seasonally Adjusted

lcons: logarithm of US Real Personal Consumption Expenditures, Billions of Chained 2012 Dollars, Quarterly, Not Seasonally Adjusted

Conduct regression analysis . Discuss the dummy variable bias in this context. ? Fully discuss. Based on the estimated model, what are the average log real consumptions in Q1 and Q4?

Year Quarter Igdp Icons 2002 1 8.090727405 7.693344439 2002 8.12074481 7.72093452 2002 3 8.132059982 7.729213877 2002 4 8.150086309 7.769002535 2003 1 8.114433022 7.717169235 2003 N 8.14116416 7.750348662 2003 3 8.160887893 7.764183474 2003 4 8.18940026 7.805388232 2004 1 8.156672577 7.761059352 2004 2 8.182812167 7.784881808 2004 3 8.193427879 7.794406261 2004 4 8.222503422 7.844228958 2005 1 8.190303099 7.792566489 2005 2 8.216992014 7.823049915 2005 3 8.234528909 7.834903257 2005 4 8.251790155 7.874189545 2006 1 8.226165529 7.827541096 2006 8.253569775 7.856307178 WN 2006 8.252284232 7.859554843 2006 4 8.274634633 7.902287343 2007 1 8.240737203 7.855593126 2007 2 8.268126008 7.878880348 2007 w 8.274430946 7.880646358 2007 4 8.297485481 7.918891719 2008 8.26891079 7.87469882 2008 2 8.274636417 7.88642871 2008 AWN 8.26790354 7.87350833 2008 8.26465224 7.891799608 2009 8.215542004 7.842955691 2009 8.236355377 7.865876393 WN 2009 8.24677615 7.870092223 2009 4 8.273794125 7.896420252 2010 1 8.234644322 7.852717041 2010 8.265770014 7.883548874 2010 3 8.276412771 7.887272797 2010 4 8.296775172 7.920745407 2011 1 8.258488263 7.876671098 2011 N 8.28025062 7.904861835 2011 3 8.286445048 7.903693071 2011 4 8.310299641 7.93417494 2012 1 8.28807206 7.896673974 2012 2 8.302246702 7.919464185 2012 3 8.310429505 7.914470457 2012 4 8.32406101 7.948595436 2013 1 8.295481864 7.901073716 2013 2 8.316074062 7.930162321 2013 3 8.331764171 7.9315535 2013 4 8.353926453 7.97351891 2014 1 8.313740987 7.920852162 2014 2 8.340411382 7.957549803 2014 3 8.360010119 7.963636462014 4 8.379707706 8.009244426 2015 1 8.346591093 7.960388898 2015 2 8.377084329 7.997674559 2015 3 8.386560907 8.000297515 2015 4 8.397710086 8.039418324 2016 1 8.36214651 7.989860404 2016 2 8.389897176 8.023711292 2016 3 8.400298861 8.026028355 2016 8.417715339 8.06629893 2017 1 8.375307455 8.011115611 2017 2 8.411973999 8.050637372 2017 3 8.425534596 8.050759821 2017 4 8.444487436 8.093293608 2018 8.40805399 8.03838322 2018 8.44206784 8.077521347 2018 3 8.452242212 8.079670073 2018 4 8.473009929 8.12039928