The accompanying data represent the price (in $) in a certain city for a pound o

Question

The accompanying data represent the price (in $) in a certain city for a pound of a certain metal at the end of each quarter from 2004 through 2011.

b. Develop an exponential trend forecasting equation with quarterly components. In this equation caret Yi is the ith value of price, Xi is the ith coded quarter, and Q1, Q2, and Q3 are the quarter 1, 2, and 3 dummy variables, respectively.

* Can someone please help explain how to do this on MiniTab or Excel? I tried multiple times on both software but couldn't get the right answer(s); my number(s) is/are just a bit off. Can anyone help? A step by step explanation would be great!

The exponential equation below is the answer to the problem which I couldn't get correct.

Quarter Coded_Quarter Price Q1 Q2 Q3 2004-1 0 7.9 1 0 0 2004-2 1 5.9 0 1 0 2004-3 2 6.7 0 0 1 2004-4 3 6.9 0 0 0 2005-1 4 7.1 1 0 0 2005-2 5 7.1 0 1 0 2005-3 6 7.5 0 0 1 2005-4 7 8.9 0 0 0 2006-1 8 11.5 1 0 0 2006-2 9 10.6 0 1 0 2006-3 10 11.7 0 0 1 2006-4 11 12.7 0 0 0 2007-1 12 13.6 1 0 0 2007-2 13 12.4 0 1 0 2007-3 14 14.4 0 0 1 2007-4 15 14.8 0 0 0 2008-1 16 17.8 1 0 0 2008-2 17 18 0 1 0 2008-3 18 13.1 0 0 1 2008-4 19 10.8 0 0 0 2009-1 20 13.1 1 0 0 2009-2 21 13.8 0 1 0 2009-3 22 16.3 0 0 1 2009-4 23 16.8 0 0 0 2010-1 24 17.6 1 0 0 2010-2 25 18.5 0 1 0 2010-3 26 21.7 0 0 1 2010-4 27 31 0 0 0 2011-1 28 38.5 1 0 0 2011-2 29 34.9 0 1 0 2011-3 30 30 0 0 1 2011-4 31 27.8 0 0 0 log i 0.7840 0.0219 Xi 0.0516 Q1 0.0050 0.0006 )Q3

Explanation / Answer

I don't think what's the problem you are facing but if you know basic regression in excel, you will get it easily. I am noting down possible mistake you can commit.

(i) You may have forget to take logarithm of price value. That may give you diffeent regression result.

(ii) You may have taken ln(p) value with the exponential base. You must take it on logaithm of base 10. Please check it.

(iii) You may have forget one of the four variables.

I am atttaching here excel results . please check.

This is the total table having all required values including log1 0 p

Now I am atttaching regression outpur summary

SO

Here log (Y) = 0.7840 + 0.0219 Xi + 0.0516 Q1 + 0.0050 Q2 - 0.0012 Q3

Yes, There is difference in Q3 's coefficient. It may be wrong in the answer or may be due to some human error. But the above equation is correct at 4 places.

Quarter Price log (p) Q1 Q2 Q3 Coded_Quarter 2004-1 7.9 0.89762709 1 0 0 0 2004-2 5.9 0.77085201 0 1 0 1 2004-3 6.7 0.8260748 0 0 1 2 2004-4 6.9 0.83884909 0 0 0 3 2005-1 7.1 0.85125835 1 0 0 4 2005-2 7.1 0.85125835 0 1 0 5 2005-3 7.5 0.87506126 0 0 1 6 2005-4 8.9 0.94939001 0 0 0 7 2006-1 11.5 1.06069784 1 0 0 8 2006-2 10.6 1.02530587 0 1 0 9 2006-3 11.7 1.06818586 0 0 1 10 2006-4 12.7 1.10380372 0 0 0 11 2007-1 13.6 1.13353891 1 0 0 12 2007-2 12.4 1.09342169 0 1 0 13 2007-3 14.4 1.15836249 0 0 1 14 2007-4 14.8 1.17026172 0 0 0 15 2008-1 17.8 1.25042 1 0 0 16 2008-2 18 1.25527251 0 1 0 17 2008-3 13.1 1.1172713 0 0 1 18 2008-4 10.8 1.03342376 0 0 0 19 2009-1 13.1 1.1172713 1 0 0 20 2009-2 13.8 1.13987909 0 1 0 21 2009-3 16.3 1.2121876 0 0 1 22 2009-4 16.8 1.22530928 0 0 0 23 2010-1 17.6 1.24551267 1 0 0 24 2010-2 18.5 1.26717173 0 1 0 25 2010-3 21.7 1.33645973 0 0 1 26 2010-4 31 1.49136169 0 0 0 27 2011-1 38.5 1.58546073 1 0 0 28 2011-2 34.9 1.54282543 0 1 0 29 2011-3 30 1.47712125 0 0 1 30 2011-4 27.8 1.4440448 0 0 0 31

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