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

=384668 $ million

2.Plot:

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.

y = 27093x + 5366.

0

50,000

100,000

150,000

200,000

250,000

300,000

0 5 10 15

Net Sales ($)

Net Sales ($)

Linear (Net Sales ($))

Answer to the question no: 2

Amount of Carbon Block imported in different years (1990-2006)

Year Code Log Y

Imports of Carbon Block

(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:

y = 0.157x + 2.033

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 2 4 6 8 10 12 14 16

Logarithmic trend

log Y

Linear (log Y)

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.

Answer to the question no: 3

Year

Quarter

Production 4 Quarter total

4 Quarter Average Centered moving average

Specific 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

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

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%.

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

Quarter Code Production

Seasonal

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

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

Fig: deseasonalize data and trend line

1.Project the production for 2007:

2007 Winter 37

y = 5.667x + 80.65

0

50

100

150

200

250

300

350

0 5 10 15 20 25 30 35 40

Deseasonalization

deseasonalization

Linear (deseasonalization)

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:

y = 5.789x + 78.97

y = 5.667x + 80.65

0

50

100

150

200

250

300

350

400

450

0 10 20 30 40

Production

deseasonalization

Linear (Production)

Linear (deseasonalization)

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.

y = 5.789x + 327.9

y = 5.872x + 328.9

0

100

200

300

400

500

600

700

0 5 10 15 20 25 30 35 40

pro

du

ctio

n

and

de

seas

on

aliz

ed

dat

a

year

Production

deseasonalization

Linear (Production)

Linear (deseasonalization)