March 21, 2013

Statistical Analysis on logarithmic trend, annual rate of increase, estimate imports






It appears that the imports of carbon black have been increasing by about 10 percent annually.

Amount of Carbon Block imported in different years

Year
Imports of Carbon Block (thousands of tons)
Year
Imports of Carbon Block (thousands of tons)
1990
124
1997
2463
1991
175
1998
3358
1992
306
1999
4181
1993
524
2000
5388
1994
714
2001
8027
1995
1052
2002
10587
1996
1638
2003
13537

Note: Add last three digits of your ID with imports of Carbon Block

i)                    Determine the logarithmic trend.

ii)                  Find the annual rate of increase.
iii)                Estimate imports for the year 2006.













Year
Import of carbon block
Import of carbon block + ID (047) (Y)
Time (t)
LogY
1990
124
171
1
2.23299611
1991
175
222
2
2.346352974
1992
306
353
3
2.547774705
1993
524
571
4
2.756636108
1994
714
761
5
2.881384657
1995
1052
1099
6
3.040997692
1996
1638
1685
7
3.226599905
1997
2463
2510
8
3.399673721
1998
3358
3405
9
3.532117116
1999
4181
4228
10
3.626134979
2000
5388
5435
11
3.735199548
2001
8027
8074
12
3.907088745
2002
10587
10634
13
4.026696656
2003
13537
13584
14
4.133027673





The logarithmic trend equation is; y’ =0 .772log (t) + 1.853

 

 


Here, intercept, a = 1.853 and slope, b=0.772
So the anti-log of 0 .772 is 5.9156
Subtracting 1 yield 4.9156
So we may conclude that imports of carbon block increased at a rate of 4.9156 percent annually during the Period (1990-2003). The annual rate of increase is 49.156% i.e.; the import of the next year will 49.156% more than the previous year.

 

iii) The estimated sales for the year 2006 will be y’ = .772(t) + 1.853 =.772*17 +1.853= 14.977
The anti log of 14.977 is 948418463300897.144 (Thousand tons)
Thus the estimated sales for the year 2006 will be about 948418463300897.144 thousands of tons.
 

 







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