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8/3/2019 Assignment 1 Stat 217 Shatil Ff
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Lab Assignment – 1
STA 217
Sec – 4
Submit to : Basanta Kumar Barmon
Department of Business Economic
East West University
Submit by : Shatil Sharyer
ID no. 2007-1-10-081
Date of Submission: March 27, 2011
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Answer to question no. 1
YearNetSales Time(X)
New NetSales(Y)
1997 50600 1 50681
1998 67300 2 67381
1999 80800 3 80881
2000 98100 4 98181
2001 124400 5 124481
2002 156700 6 156781
2003 201400 7 201481
2004 227300 8 227381
2005 256300 9 256381
2006 280900 10 280981
i) Here, by using statistical software MS Excel,
Coefficients Standar d Error t Stat P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0 %
Intercept 5447.667 8377.1820.65029
80.53372
5 -13870.224765.
5 -13870.2 24765
X-Variable 27093.33 1350.10520.0675
7 3.97E-0823979.9
830206.
723979.9
8 30207
Here we find the least square equation,
Y = a + b(t)
Y = 5447.667 + 27093.33(t)
On the Basis of this information,
Here, for 2010 t will be 14
So, The estimated sales for 2010, Y = 5447.667 + 27093.33(14)
= $ 384754.3
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ii) Here is the net sales & trend line,
Answer to question no. 2
Year Import Time(X)Newimport(Y) Log(Y)
1990 124 1 205 2.311754
1991 175 2 256 2.408241992 306 3 387 2.587711
1993 524 4 605 2.781755
1994 714 5 795 2.900367
1995 1052 6 1133 3.05423
1996 1638 7 1719 3.235276
1997 2463 8 2544 3.405517
1998 3358 9 3439 3.536432
1999 4781 10 4862 3.686815
2000 5388 11 5469 3.737908
2001 8027 12 8108 3.908914
2002 10587 13 10668 4.028083
2003 13537 14 13618 4.134113
Net Sales & Trend Line
0
200000
400000
1 2 3 4 5 6 7 8 9 1
Time
N e t S a l e s
Y
Predicted Y
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i) Here, by using statistical software MS Excel,
Coefficient s
Standard Error t Stat P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept 2.1834980.02601
283.9428
25.45E-
182.12682
42.24017
32.1268
22.24017
3
X Variable 0.1442680.00305
547.2247
45.31E-
150.13761
20.15092
40.1376
10.15092
4
here we find the logarithmic trend,
Y* = log a + log b(t)
Y* = 2.183498 + 0.144268(t)
ii) Here, the annual rate of increase is,
log b = 0.144268
b = antilog(0.144268) - 1
=1.394017 - 1
=.394017
=39.4017%
So, the imports of Carbon block increase at a rate 39.4017% by increasing year by a
unit.
iii) On the Basis of this information,
For 2006, here t will be 17
So, The estimated sales for 2006, log Y = 2.183498 + 0.144268(17)
log Y = 4.636054
Y= antilog(4.636054)
Y = 43256.76 thousands of ton
So, The estimated sales for 2006 will be 43256.76 thousands of ton.
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Answer to question no. 3
i) Develop a Seasonalize index for each quarter.
Computation of Seasonal Index:
Year Quarter ProductionNewProduction
4 quarterMovingAvg.
Centeredmovingaverage
SpecificSeasonal
Winter 90 171
Spring 85 166
1998 164.25
Summer 56 137 167.375 0.818521
170.5
Fall 102 183 171 1.070175
171.5
Winter 115 196 172.125 1.138707172.75
Spring 89 170 173.75 0.978417
1999 174.75
Summer 61 142 181 0.78453
187.25
Fall 110 191 189.875 1.005925
192.5
Winter 165 246 197.125 1.247939
201.75
Spring 110 191 219 0.872146
2000 236.25
Summer 98 179 240.75 0.74351245.25
Fall 248 329 249.25 1.31996
253.25
Winter 201 282 254.75 1.106968
256.25
Spring 142 223 259.5 0.859345
2001 262.75
Summer 110 191 269 0.710037
275.25
Fall 274 355 278.125 1.276404
281
Winter 251 332 282.875 1.173663
284.75
Spring 165 246 288.625 0.852317
2002 292.5
Summer 125 206 291.25 0.707296
290
Fall 305 386 289.125 1.335063288.25
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Winter 241 322 289.125 1.113705
290
Spring 158 239 289.25 0.826275
2003 288.5
Summer 132 213 291.5 0.730703
294.5
Fall 299 380 297.875 1.275703
301.25
Winter 265 346 302.5 1.143802
303.75
Spring 185 266 308 0.863636
2004 312.25
Summer 142 223 314.375 0.709344
316.5
Fall 333 414 315.25 1.313243
314
Winter 282 363 315.875 1.149189
317.75Spring 175 256 319.875 0.800313
2005 322
Summer 157 238 323 0.736842
324
Fall 350 431 327.25 1.317036
330.5
Winter 290 371 334.25 1.109948
338
Spring 201 282 344.25 0.819172
2006 350.5
Summer 187 268
Fall 400 481
Calculation of Seasonal Index :
Year Winter Spring Summer Fall
1998 0.8185213 1.070175
1999 1.138707 0.978417 0.7845304 1.005925
2000 1.247939 0.872146 0.7435099 1.31996
2001 1.106968 0.859345 0.7100372 1.276404
2002 1.173663 0.852317 0.7072961 1.335063
2003 1.113705 0.826275 0.7307033 1.275703
2004 1.143802 0.863636 0.7093439 1.3132432005 1.149189 0.800313 0.7368421 1.317036
2006 1.109948 0.819172
Total 9.183921 6.871621 5.9407841 9.91351 Total
Mean 1.14799 0.858953 0.742598 1.2391893.98872946
Adjusted Mean 1.151234 0.86138 0.7446963 1.24269 4
Index 115.1234 86.13797 74.46963 124.269
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Correction factor for adjusting quarterly means:
Correction factor =
=
= 1.002826
Adjusted Mean = Mean * Correction Factor
Mean Adjusted Mean Index
Winter 1.14799007 1.151233827 115.123383
Spring 0.858952656 0.86137971 86.137971
Summer 0.742598019 0.744696301 74.4696301
Fall 1.239188714 1.242690162 124.269016
Interpretation : The production of Winter quarter are 15.12% above the typical quarter, The production
of Spring quarter are 13.87% below the typical quarter, The production of Summer quarter are 25.54%
below the typical quarter, The production of Fall quarter are 24.26% above the typical quarter.
ii) Production for 2007 for different quarters:
Estimated Sale:
Intercept = 5.5629X variable (a) = 163.71
Y = a + b(t)
Y = 163.71 + 5.5629(t)
Quarterly forecast production = Estimated sale(Y) * Seasonal Index
Quarter Time(t)Estimatedsale(Y)
SeasonalIndex
Quarterlyforecastproduction
Winter 37 369.5373 1.151234 425.4238
Spring 38 375.1002 0.86138 323.1037
Summer 39 380.6631 0.744696 283.4784
Fall 40 386.226 1.24269 479.9593
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iii) Plot of original data and deseasonalize data :
Deseanolizes Production =
Year Quarter Production
New
Production Code(t)
Seasonal
Index
Deseanolizes
ProductionWinter 90 171 1 1.151233827 148.5362886
1998 Spring 85 166 2 0.86137971 192.7140819
Summer 56 137 3 0.744696301 183.9676117
Fall 102 183 4 1.242690162 147.2611642
Winter 115 196 5 1.151233827 170.2521203
1999 Spring 89 170 6 0.86137971 197.3577948
Summer 61 142 7 0.744696301 190.6817581
Fall 110 191 8 1.242690162 153.6988108
Winter 165 246 9 1.151233827 213.6837836
2000 Spring 110 191 10 0.86137971 221.737287
Summer 98 179 11 0.744696301 240.3664416
Fall 248 329 12 1.242690162 264.7482133
Winter 201 282 13 1.151233827 244.9545813
2001 Spring 142 223 14 0.86137971 258.8869896
Summer 110 191 15 0.744696301 256.4803929
Fall 274 355 16 1.242690162 285.6705645
Winter 251 332 17 1.151233827 288.3862446
2002 Spring 165 246 18 0.86137971 285.5883383
Summer 125 206 19 0.744696301 276.6228322
Fall 305 386 20 1.242690162 310.6164448
Winter 241 322 21 1.151233827 279.6999119
2003 Spring 158 239 22 0.86137971 277.4618409
Summer 132 213 23 0.744696301 286.0226372Fall 299 380 24 1.242690162 305.7882099
Winter 265 346 25 1.151233827 300.5471103
2004 Spring 185 266 26 0.86137971 308.8069024
Summer 142 223 27 0.744696301 299.45093
Fall 333 414 28 1.242690162 333.1482076
Winter 282 363 29 1.151233827 315.3138759
2005 Spring 175 256 30 0.86137971 297.1976203
Summer 157 238 31 0.744696301 319.5933692
Fall 350 431 32 1.242690162 346.8282065
Winter 290 371 33 1.151233827 322.262942
2006 Spring 201 282 34 0.86137971 327.3817537
Summer 187 268 35 0.744696301 359.8782477
Fall 400 481 36 1.242690162 387.0634972
Interpretation : We get the deseanolize data in by dividing the New production by seasonalize index. As
a result we remove the new seasonality from the production.
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Using of Deseasonalize Data to Forecast y = 5.5629x + 163.71
R 2
= 0.8864
0
100
200
300
400
500
0 10 20 30 40
Deseasonalized
Index
Linear (Deseasonalized
Index)
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Answer to question no. 4
i) Here, we select a random sample of 50 cases from 105 cases.
When k = 6,
> 50 or, 64> 50
Class interval range =
=
= 343.23 = 400
confidance Interval
3 6.0 6.0 6.0
22 44.0 44.0 50.0
12 24.0 24.0 74.0
7 14.0 14.0 88.0
5 10.0 10.0 98.0
1 2.0 2.0 100.0
50 100.0 100.0
1300-1700
1700-2100
2100-2500
2500-2900
2900-3300
3300-3700
Total
ValidFrequency Percent Valid Percent
Cumulative
Percent
Confidance Interval
50 0
1.1843
5.00
1.00
6.00
Valid Missing
N
Std. Deviation
Range
Minimum
Maximum
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ii)
iii) Bar Diagram for Variable “Confidance Interval” :
confidance Interval
confidance Interval
3300-37002900-33002500-29002100-25001700-21001300-1700
30
20
10
0
confidance Interval
50
0
Valid
Missing
N
Selling Price
50
0
2224.4520
2110.6500
2090.30 a
467.7359
218776.9
2059.40
1710.1400
1875.4000
2110.6500
2525.3000
2938.3100
Valid
Missing
N
Mean
Median
Mode
Std. Deviation
Variance
Range
10
25
50
75
90
Percentiles
Multiple modes exist. The smallest value is shown a.
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Comment: From the Bar diagram, we find, the the majority number of selling price (22) in 1700-2100
class interval. and fewer number of selling price (01) is in 3300-3700 class interval.
iv)
Bar Diagram for Variable “Township” :
Comment: From the Bar diagram, we find, the the majority number of apartment situated in Dhanmondi
(14) and fewer apartment is situated in Banani (6).
Pie chart for Variable “Township” :
Comment: From the Pie chart, we find, the the majority portion of apartment situated in Dhanmondi
(28.0%) and fewer apartment is situated in Banani (12.0%).
Statistics
Tow nship
50
0
Valid
Missing
N
Township
Township
BananiDhanmondiDOHSUttaraGulshan
16
14
12
10
8
6
4
2
0
Township
12.0%
28.0%
22.0%
18.0%
20.0%
Banani
Dhanmondi
DOHS
Uttara
Gulshan
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v) Develop a box plot for variable “Distance”
Comment : a) The distribution is negatively skewed.b) Mean < Median
c) There is no outlier.
Answer to question no. 5
i) Determining the coefficient of skewness for variable “ Selling Price”
Comment : A positive skewness indicates a greater number of smaller values, and a negative value
indicates a greater number of larger values. The coefficient of skewness is .696 .So the distribution
is positively skewed. And mean > median .
Case Process ing Summ ary
50 100.0% 0 .0% 50 100.0%Distance from the
centre of the city
N Percent N Percent N Percent
Valid Missing Total
Cases
Distance from the ce
3020100
Selling Price
50 0
.696
.337
Valid
Missing
N
Skewness
Std. Error of Skewness
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ii)
Comment : From the box plot, we find, there are no Outlier. And the distribution is positivelyskewed. And mean > median .
Case Process ing Summ ary
50 100.0% 0 .0% 50 100.0%Selling Price
N Percent N Percent N Percent
Valid Missing Total
Cases
Selling Price
4000300020001000