Question

A government researcher is analyzing the relationship between retail sales (in $ millions) and the gross national product (GNP in $ billions). He also wonders whether there are significant differences in retail sales related to the quarters of the year. He collects 10 years of quarterly data. A portion is shown in the accompanying table. Retail sales (in millions) GNP (in billions) d1 d2 d3 2000 1 696048 9740.5 1 0 0 2 753211 9983.5 0 1 0 3 746875 10048.0 0 0 1 4 792622 10184.9 0 0 0 2001 1 704757 10206.2 1 0 0 2 779011 10350.9 0 1 0 3 756128 10332.2 0 0 1 4 827829 10463.1 0 0 0 2002 1 717302 10549.7 1 0 0 2 790486 10634.7 0 1 0 3 792657 10749.1 0 0 1 4 833877 10832.2 0 0 0 2003 1 741233 10940.2 1 0 0 2 819940 11073.6 0 1 0 3 831222 11321.2 0 0 1 4 875437 11508.3 0 0 0 2004 1 795916 11707.8 1 0 0 2 871970 11864.2 0 1 0 3 873695 12047.3 0 0 1 4 938213 12216.6 0 0 0 2005 1 836952 12486.3 1 0 0 2 932713 12613.0 0 1 0 3 940880 12848.7 0 0 1 4 987085 12994.1 0 0 0 2006 1 897180 13264.0 1 0 0 2 987406 13423.3 0 1 0 3 978211 13514.8 0 0 1 4 1018775 13683.2 0 0 0 2007 1 923997 13859.8 1 0 0 2 1016136 14087.6 0 1 0 3 1002312 14302.9 0 0 1 4 1062803 14489.9 0 0 0 2008 1 953358 14520.7 1 0 0 2 1032919 14647.3 0 1 0 3 1006551 14689.2 0 0 1 4 966329 14317.2 0 0 0 2009 1 839625 14172.2 1 0 0 2 919646 14164.2 0 1 0 3 926265 14281.9 0 0 1 4 985649 14442.8 0 0 0

a. Estimate y = β0 + β1x + β2d1 + β3d2 + β4d3 where y is retail sales, x is GNP, d1 is a dummy variable that equals 1 if quarter 1 and 0 otherwise, d2 is a dummy variable that equals 1 if quarter 2 and 0 otherwise, and d3 is a dummy variable that equals 1 if quarter 3 and 0 otherwise. Here the reference category is quarter 4. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

d-1. Reformulate the model to determine, at the 5% significance level, if sales differ between quarter 2 and quarter 3. Your model must account for all quarters. Use quarter 3 as the reference category. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

Answer 1

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