The accompanying data represent the price in a certain city for a pound of a cer

Question

The accompanying data represent the price in a certain city for a pound of a certain precious element at the end of each quarter from 1999 through 2009. Complete parts? (a) through? (g).

Year   Quarter_1   Quarter_2   Quarter_3   Quarter_4

1999   36,261   37,881   33,812   39,001

2000   36,202   40,265   36,096   39,952

2001   36,584   37,289   32,640   37,903

2002   37,885   42,282   37,973   44,418

2003   42,894   44,519   40,064   42,587

2004   42,361   42,314   36,552   41,150

2005   39,857   42,332   39,547   41,684

2006   40,815   40,582   36,791   46,008

2007   44,723   42,873   39,121   44,935

2008   45,135   44,548   40,856   46,550

2009   41,100   42,000   36,700   40,300

B.) Develop an exponential trend forecasting equation with quarterly compounds. logYi=_ + (_)xi + (_)Q1 + (_)Q2+(_)Q3

e.) What are the forecasts for all four quarters in 2009?

f.) What are the forecasts for all four quarters in 2010?

Explanation / Answer

Solution:

All the steps were performed in Excel Software :

output of Regression Equation :

B.) Develop an exponential trend forecasting equation with quarterly compounds. logYi= 4.5900 + (0.0015)xi + (-0.0156)Q1 + (-0.0038)Q2+(-0.052)Q3

e.) What are the forecasts for all four quarters in 2009?

Q1 : 4.634

Q2: 4.647

Q3: 4.600

Q4:4.654

f.) What are the forecasts for all four quarters in 2010?

Q1:4.640

Q2:4.653

Q3: 4.606

Q4: 4.660

Note : The Forecasted Values are in Logbase10

Revenue Log Revenue Coded Qtr Q1 Q2 Q3 36,261 4.55944 1 0 1 0 0 37,881 4.578421 2 1 0 1 0 33,812 4.529071 3 2 0 0 1 39,001 4.591076 4 3 0 0 0 36,202 4.558733 1 4 1 0 0 40,265 4.604928 2 5 0 1 0 36,096 4.557459 3 6 0 0 1 39,952 4.601539 4 7 0 0 0 36,584 4.563291 1 8 1 0 0 37,289 4.571581 2 9 0 1 0 32,640 4.51375 3 10 0 0 1 37,903 4.578674 4 11 0 0 0 37,885 4.578467 1 12 1 0 0 42,282 4.626156 2 13 0 1 0 37,973 4.579475 3 14 0 0 1 44,418 4.647559 4 15 0 0 0 42,894 4.632397 1 16 1 0 0 44,519 4.648545 2 17 0 1 0 40,064 4.602754 3 18 0 0 1 42,587 4.629277 4 19 0 0 0 42,361 4.626966 1 20 1 0 0 42,314 4.626484 2 21 0 1 0 36,552 4.562911 3 22 0 0 1 41,150 4.61437 4 23 0 0 0 39,857 4.600505 1 24 1 0 0 42,332 4.626669 2 25 0 1 0 39,547 4.597114 3 26 0 0 1 41,684 4.619969 4 27 0 0 0 40,815 4.61082 1 28 1 0 0 40,582 4.608333 2 29 0 1 0 36,791 4.565742 3 30 0 0 1 46,008 4.662833 4 31 0 0 0 44,723 4.650531 1 32 1 0 0 42,873 4.632184 2 33 0 1 0 39,121 4.59241 3 34 0 0 1 44,935 4.652585 4 35 0 0 0 45,135 4.654513 1 36 1 0 0 44,548 4.648828 2 37 0 1 0 40,856 4.611256 3 38 0 0 1 46,550 4.66792 4 39 0 0 0 41,100 4.613842 1 40 1 0 0 42,000 4.623249 2 41 0 1 0 36,700 4.564666 3 42 0 0 1 40,300 4.605305 4 43 0 0 0

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