Answer to the question no: 1                     Net sales of different years (1997-2010 in $ million)        Year        ...
=384668 $ million2.Plot:                                   Net Sales ($)      300,000                                     ...
Answer to the question no: 2                  Amount of Carbon Block imported in different years (1990-2006)              ...
Fig: Number of imported books are increasing at a increasing rate. This is an upward logarithmic trend.X-axis represents y...
Answer to the question no: 3Year             Production   4 Quarter         4 Quarter                                     ...
815   203.75     Spring   165                   207.625   0.794701987                     846    211.5     Summer   125   ...
1. Develop a seasonal index for each quarter andinterpret.                                                   Quarter      ...
Interpretation for spring: 80.81% (negative seasonal effect)The production of pine lumber during Spring quarter was 80.81%...
Summer             23             132    0.621628774                     212.3453827        Fall               24         ...
Spring           38            Summer           39            Fall             40        Y = 5.667x + 80.65        So the ...
700                             600   and deseasonalized data                             500                             ...
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Stat word-assign-

  1. 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 10 280,9001.The least square equation:Y= bx+aFrom scatter diagram Here, b=27093 a=5366 Y= 27093x + 5366Estimated sale for 2010: For 2010, X=14 Y= (27093*14) + 5366
  2. 2. =384668 $ million2.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. 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 135371.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. 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=0.157b= Antilog (0.157) =1.435489433G.M = 1.435489433-1 = 0.435489So 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. 5. Answer to the question no: 3Year Production 4 Quarter 4 Quarter Specific Quarter total Average Centered moving average Seasonal1998 Winter 90 Spring 85 333 83.25 Summer 56 86.375 0.648335745 358 89.5 Fall 102 90 1.133333333 362 90.51999 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 446 111.52000 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 689 172.252001 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 2002002 Winter 251 201.875 1.243343653
  6. 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 829 207.252003 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 881 220.252004 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 2332005 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 998 249.52006 Winter 290 253.25 1.145113524 1028 257 Spring 201 263.25 0.763532764 1078 269.5 Summer 187 Fall 400
  7. 7. 1. Develop a seasonal index for each quarter andinterpret. 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 0.763532764Total 9.78316198 6.416705328 4.935732468 10.69466207Average 1.222895248 0.802088166 0.616966559 1.336832758Adjusted 1.23213627 0.808149286 0.621628774 1.346934769Seasonal Index(%) 123.213627 80.81492856 62.16287743 134.6934769Correlation factor = (4/3.97) = 1.007557Interpretation: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 quarterannual average sales and it is 23.21%.
  8. 8. Interpretation for spring: 80.81% (negative seasonal effect)The production of pine lumber during Spring quarter was 80.81% lower than the spring quarterannual 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 summerquarter 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 quarterannual 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. 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 line1.Project the production for 2007: 2007 Winter 37
  10. 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 millionsBase year production: Y = 5.667*0 + 80.65 Y = 80.65 millions3. 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. 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 dataInterpretation:The data is Deseasonalize by dividing the observed value by its seasonal index. Thissmoothes the data by removing seasonal variation. Diamond shapes are representingproduction and square shapes are representing Deseasonalize data. Years are in X-axis andproduction and Deseasonalize data are in Y-axis. From the graph we can notice thatproduction data are more fluctuate then d Deseasonalize data from trend line becauseproduction data are not seasonally adjusted. After removing seasonal effect we findseasonally adjusted sales. From the graph we also find the trend line of sales. That is mucheasier for us to study on the trend and Deseasonalize data allow us to see better theunderlying pattern in the data. Seasonal adjustment may be a useful element in theproduction of short term forecasts of future values of a time series. From the graph we canmeasures of the extent of seasonality in the form of seasonal indexes.

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