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.