1. Answer to the question no: 1
Net sales of different years (1997-2010 in $ million)
Year Code Net Sales ($)
1997 1 50,600
1998 2 67,300
1999 3 80,800
2000 4 98,100
2001 5 124,400
2002 6 156,700
2003 7 201,400
2004 8 227,300
2005 9 256,300
2006 10 280,900
1.The least square equation:
Y= bx+a
From scatter diagram Here, b=27093
a=5366
Y= 27093x + 5366
Estimated sale for 2010:
For 2010, X=14
Y= (27093*14) + 5366

2. =384668 $ million
2.Plot:
Net Sales ($)
300,000
y = 27093x + 5366.
250,000
200,000
150,000 Net Sales ($)
100,000 Linear (Net Sales ($))
50,000
0
0 5 10 15
Fig: Sales are increasing year after year. There is an upward trend of sales. X represents year in
X-axis and sales amounts are in Y-axis. There is a straight line represents trend line.

3. Answer to the question no: 2
Amount of Carbon Block imported in different years (1990-2006)
Imports of Carbon Block
Year Code Log Y (thousands of tons)
1990 1 2.093422 124
1991 2 2.243038 175
1992 3 2.485721 306
1993 4 2.719331 524
1994 5 2.853698 714
1995 6 3.022016 1052
1996 7 3.214314 1638
1997 8 3.391464 2463
1998 9 3.526081 3358
1999 10 3.62128 4181
2000 11 3.731428 5388
2001 12 3.904553 8027
2002 13 4.024773 10587
2003 14 4.131522 13537
1.Logarithmic Trend:
Logarithmic trend
y = 0.157x + 2.033
4.5
4
3.5
3
2.5
log Y
2
Linear (log Y)
1.5
1
0.5
0
0 2 4 6 8 10 12 14 16

4. Fig: Number of imported books are increasing at a increasing rate. This is an upward logarithmic trend.
X-axis represents years and Y-axis represents the value of logarithm. The straight line connecting points
is logarithm trend line.
2.Annual rate of increase:
we have to find out anual rate of increase by using geomatric mean (G.M)
Log b=0.157
b= Antilog (0.157)
=1.435489433
G.M = 1.435489433-1
= 0.435489
So the annual rate of increase is 44%
3. Estimated import for 2006:
We know,
For 2006, X=17
Log Y = log b * x + Log a
Log Y = 0.157*17+ 2.033
Log Y= 4.702
Y= antilog (4.702)
Y= 50350.06
So the estimated import of 2006 is 50350.06 thousands of tons.

5. Answer to the question no: 3
Year Production 4 Quarter 4 Quarter Specific
Quarter total Average Centered moving average Seasonal
1998 Winter 90
Spring 85
333 83.25
Summer 56 86.375 0.648335745
358 89.5
Fall 102 90 1.133333333
362 90.5
1999 Winter 115 91.125 1.262002743
367 91.75
Spring 89 92.75 0.959568733
375 93.75
Summer 61 100 0.61
425 106.25
Fall 110 108.875 1.010332951
446 111.5
2000 Winter 165 116.125 1.42088267
483 120.75
Spring 110 138 0.797101449
621 155.25
Summer 98 159.75 0.613458529
657 164.25
Fall 248 168.25 1.473997028
689 172.25
2001 Winter 201 173.75 1.156834532
701 175.25
Spring 142 178.5 0.795518207
727 181.75
Summer 110 188 0.585106383
777 194.25
Fall 274 197.125 1.389980977
800 200
2002 Winter 251 201.875 1.243343653

6. 815 203.75
Spring 165 207.625 0.794701987
846 211.5
Summer 125 210.25 0.594530321
836 209
Fall 305 208.125 1.465465465
829 207.25
2003 Winter 241 208.125 1.157957958
836 209
Spring 158 208.25 0.758703481
830 207.5
Summer 132 210.5 0.627078385
854 213.5
Fall 299 216.875 1.378674352
881 220.25
2004 Winter 265 221.5 1.196388262
891 222.75
Spring 185 227 0.814977974
925 231.25
Summer 142 233.375 0.608462775
942 235.5
Fall 333 234.25 1.421558164
932 233
2005 Winter 282 234.875 1.200638638
947 236.75
Spring 175 238.875 0.732600733
964 241
Summer 157 242 0.648760331
972 243
Fall 350 246.25 1.421319797
998 249.5
2006 Winter 290 253.25 1.145113524
1028 257
Spring 201 263.25 0.763532764
1078 269.5
Summer 187
Fall 400

7. 1. Develop a seasonal index for each quarter and
interpret.
Quarter
year winter spring summer fall
1998 0.648335745 1.133333333
1999 1.262002743 0.959568733 0.61 1.010332951
2000 1.42088267 0.797101449 0.613458529 1.473997028
2001 1.156834532 0.795518207 0.585106383 1.389980977
2002 1.243343653 0.794701987 0.594530321 1.465465465
2003 1.157957958 0.758703481 0.627078385 1.378674352
2004 1.196388262 0.814977974 0.608462775 1.421558164
2005 1.200638638 0.732600733 0.648760331 1.421319797
2006 1.145113524 0.763532764
Total 9.78316198 6.416705328 4.935732468 10.69466207
Average 1.222895248 0.802088166 0.616966559 1.336832758
Adjusted 1.23213627 0.808149286 0.621628774 1.346934769
Seasonal Index
(%) 123.213627 80.81492856 62.16287743 134.6934769
Correlation factor = (4/3.97) = 1.007557
Interpretation:
Annual average sales=100%
Interpretation for winter: 123.21% (positive seasonal effect)
The production of pine lumber during winter quarter was 123.21% higher than the winter quarter
annual average sales and it is 23.21%.

8. Interpretation for spring: 80.81% (negative seasonal effect)
The production of pine lumber during Spring quarter was 80.81% lower than the spring quarter
annual average sales and it is 19.19%
Interpretation for summer: 62.16% (negative seasonal effect)
The production of pine lumber during Summer quarter was 62.16% lower than the summer
quarter annual average sales and it is 37.84%
Interpretation for fall: 134.70% (positive seasonal effect)
The production of pine lumber during Fall quarter was 134.70% higher than the fall quarter
annual average sales and it is 34.70%
year Seasonal
Quarter Code Production index Deseasonalization
1998 Winter 1 90 1.23213627 73.04386879
Spring 2 85 0.808149286 105.1785871
Summer 3 56 0.621628774 90.08591995
Fall 4 102 1.346934769 75.72749797
1999 Winter 5 115 1.23213627 93.33383234
Spring 6 89 0.808149286 110.1281676
Summer 7 61 0.621628774 98.12930566
Fall 8 110 1.346934769 81.66690958
2000 Winter 9 165 1.23213627 133.9137594
Spring 10 110 0.808149286 136.1134656
Summer 11 98 0.621628774 157.6503599
Fall 12 248 1.346934769 184.1217598
2001 Winter 13 201 1.23213627 163.131307
Spring 14 142 0.808149286 175.7101102
Summer 15 110 0.621628774 176.9544856
Fall 16 274 1.346934769 203.4248475
2002 Winter 17 251 1.23213627 203.7112341
Spring 18 165 0.808149286 204.1701984
Summer 19 125 0.621628774 201.0846427
Fall 20 305 1.346934769 226.4400675
2003 Winter 21 241 1.23213627 195.5952486
Spring 22 158 0.808149286 195.5084324

9. Summer 23 132 0.621628774 212.3453827
Fall 24 299 1.346934769 221.9855088
2004 Winter 25 265 1.23213627 215.0736136
Spring 26 185 0.808149286 228.9181013
Summer 27 142 0.621628774 228.4321541
Fall 28 333 1.346934769 247.2280081
2005 Winter 29 282 1.23213627 228.8707889
Spring 30 175 0.808149286 216.5441499
Summer 31 157 0.621628774 252.5623113
Fall 32 350 1.346934769 259.8492577
2006 Winter 33 290 1.23213627 235.3635772
Spring 34 201 0.808149286 248.7164235
Summer 35 187 0.621628774 300.8226255
Fall 36 400 1.346934769 296.9705803
Deseasonalization
350
y = 5.667x + 80.65
300
250
200
deseasonalization
150 Linear (deseasonalization)
100
50
0
0 5 10 15 20 25 30 35 40
Fig: deseasonalize data and trend line
1.Project the production for 2007:
2007 Winter 37

10. Spring 38
Summer 39
Fall 40
Y = 5.667x + 80.65
So the new production in,
Winter = 5.667*37 + 80.65= 290.329 millions
Spring = 5.667*38 + 80.65= 295.996 millions
Fall =5.667*39+ 80.65=301.663 millions
Summer =5.667*40+ 80.65= 307.33 millions
Base year production:
Y = 5.667*0 + 80.65
Y = 80.65 millions
3. Plot the original data:
450
400
350
Production
300 y = 5.789x + 78.97
250 deseasonalization
200 y = 5.667x + 80.65
Linear (Production)
150
100 Linear
50 (deseasonalization)
0
0 10 20 30 40

11. 700
600
and deseasonalized data
500
y = 5.789x + 327.9
Production
production
400
300
deseasonalization
y = 5.872x + 328.9
200
100 Linear (Production)
0
0 5 10 15 20 25 30 35 40 Linear (deseasonalization)
year
fig: comparison between actual production data and deseasonalize data
Interpretation:
The data is Deseasonalize by dividing the observed value by its seasonal index. This
smoothes the data by removing seasonal variation. Diamond shapes are representing
production and square shapes are representing Deseasonalize data. Years are in X-axis and
production and Deseasonalize data are in Y-axis. From the graph we can notice that
production data are more fluctuate then d Deseasonalize data from trend line because
production data are not seasonally adjusted. After removing seasonal effect we find
seasonally adjusted sales. From the graph we also find the trend line of sales. That is much
easier for us to study on the trend and Deseasonalize data allow us to see better the
underlying pattern in the data. Seasonal adjustment may be a useful element in the
production of short term forecasts of future values of a time series. From the graph we can
measures of the extent of seasonality in the form of seasonal indexes.