### PRACTICAL ACTUARIAL MODELLING.
# Import data
# Basic data analysis
# Modelling (regression,survival, time series etc)
# Statistics (ANOVA)
#libraries
library(tidyverse)
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.5
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 3.5.2 ✔ tibble 3.2.1
## ✔ lubridate 1.9.4 ✔ tidyr 1.3.1
## ✔ purrr 1.0.4
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
library(fGarch)
## NOTE: Packages 'fBasics', 'timeDate', and 'timeSeries' are no longer
## attached to the search() path when 'fGarch' is attached.
##
## If needed attach them yourself in your R script by e.g.,
## require("timeSeries")
library(rugarch)
## Loading required package: parallel
##
## Attaching package: 'rugarch'
##
## The following object is masked from 'package:purrr':
##
## reduce
##
## The following object is masked from 'package:stats':
##
## sigma
library(survival)
library(survminer)
## Loading required package: ggpubr
##
## Attaching package: 'survminer'
##
## The following object is masked from 'package:survival':
##
## myeloma
## Dataframes in R
x <- c(2, 4, 6, 8, 10)
y <- c(1, 3, 6, 9, 12)
z <- c(12, 4, 7, 1, 24)
Dataframe <- data.frame(x, y, z); Dataframe
## x y z
## 1 2 1 12
## 2 4 3 4
## 3 6 6 7
## 4 8 9 1
## 5 10 12 24
cor(x, y)
## [1] 0.9974587
cor(y,z)
## [1] 0.4085445
cor(x, z)
## [1] 0.3682511
# correlation between the two variables.
#regression analysis.
reg_1 <- lm(x~y); reg_1
##
## Call:
## lm(formula = x ~ y)
##
## Coefficients:
## (Intercept) y
## 1.5939 0.7107
reg_2 <- lm(x~y + z); reg_2
##
## Call:
## lm(formula = x ~ y + z)
##
## Coefficients:
## (Intercept) y z
## 1.66752 0.72438 -0.01653
# plot for individual variable.
plot(x)
hist(x)
# plot for linear model of the variables.
plot(reg_1)
plot(reg_2)
## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced
## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced
anova(reg_2)
## Analysis of Variance Table
##
## Response: x
## Df Sum Sq Mean Sq F value Pr(>F)
## y 1 39.797 39.797 616.7315 0.001618 **
## z 1 0.074 0.074 1.1466 0.396352
## Residuals 2 0.129 0.065
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(reg_2)
##
## Call:
## lm(formula = x ~ y + z)
##
## Residuals:
## 1 2 3 4 5
## -0.19359 0.22546 0.10191 -0.17037 0.03659
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.66752 0.22161 7.525 0.01721 *
## y 0.72438 0.03135 23.104 0.00187 **
## z -0.01653 0.01543 -1.071 0.39635
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.254 on 2 degrees of freedom
## Multiple R-squared: 0.9968, Adjusted R-squared: 0.9935
## F-statistic: 308.9 on 2 and 2 DF, p-value: 0.003226
## Importing data.
data <- read.csv("supermarket_sales.csv"); data
## Gender Invoice.ID Branch City Customer.type Product.line
## 1 Female 750-67-8428 A Yangon Member Health and beauty
## 2 Female 226-31-3081 C Naypyitaw Normal Electronic accessories
## 3 Female 355-53-5943 A Yangon Member Electronic accessories
## 4 Female 315-22-5665 C Naypyitaw Normal Home and lifestyle
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## 213 Female 394-30-3170 B Mandalay Member Sports and travel
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## Unit.price Quantity Tax.5. Sales
## 1 74.69 7 261.4150 522.83
## 2 15.28 5 3.8200 76.40
## 3 68.84 6 20.6520 413.04
## 4 73.56 10 36.7800 735.60
## 5 36.26 2 3.6260 72.52
## 6 54.84 3 8.2260 164.52
## 7 14.48 4 2.8960 57.92
## 8 46.95 5 11.7375 234.75
## 9 71.38 10 35.6900 713.80
## 10 93.72 6 28.1160 562.32
## 11 68.93 7 241.2550 482.51
## 12 40.30 2 4.0300 80.60
## 13 52.59 8 21.0360 420.72
## 14 87.67 2 8.7670 175.34
## 15 88.36 5 22.0900 441.80
## 16 99.42 4 19.8840 397.68
## 17 68.12 1 3.4060 68.12
## 18 60.88 9 27.3960 547.92
## 19 54.92 8 21.9680 439.36
## 20 86.72 1 4.3360 86.72
## 21 69.12 6 20.7360 414.72
## 22 98.70 8 39.4800 789.60
## 23 93.96 4 18.7920 375.84
## 24 20.01 9 9.1945 180.09
## 25 82.63 10 41.3150 826.30
## 26 44.59 5 11.1475 222.95
## 27 17.87 4 3.5740 71.48
## 28 85.98 8 34.3920 687.84
## 29 72.35 10 36.1750 723.50
## 30 24.74 3 3.7110 74.22
## 31 55.07 9 247.8150 495.63
## 32 33.47 2 3.3470 66.94
## 33 97.61 6 29.2830 585.66
## 34 18.33 1 9.1650 18.33
## 35 48.52 3 7.2780 145.56
## 36 75.91 6 22.7730 455.46
## 37 41.65 10 20.8250 416.50
## 38 20.01 9 9.1945 180.09
## 39 78.31 10 39.1550 783.10
## 40 20.38 5 5.0950 101.90
## 41 99.19 6 29.7570 595.14
## 42 96.68 3 14.5020 290.04
## 43 80.36 4 16.0720 321.44
## 44 83.06 7 29.0710 581.42
## 45 76.99 6 23.0970 461.94
## 46 47.38 4 9.4760 189.52
## 47 44.86 10 22.4300 448.60
## 48 21.98 7 7.6930 153.86
## 49 12.45 6 3.7350 74.70
## 50 23.07 9 10.3815 207.63
## 51 33.98 9 15.2910 305.82
## 52 16.49 2 1.6490 32.98
## 53 98.21 3 147.3150 294.63
## 54 72.84 7 25.4940 509.88
## 55 80.79 9 363.5550 727.11
## 56 27.02 3 4.0530 81.06
## 57 10.96 10 5.4800 109.60
## 58 99.56 8 39.8240 796.48
## 59 56.47 8 22.5880 451.76
## 60 93.69 7 327.9150 655.83
## 61 32.25 5 8.0625 161.25
## 62 31.73 9 142.7850 285.57
## 63 68.54 8 27.4160 548.32
## 64 90.28 9 40.6260 812.52
## 65 39.62 7 13.8670 277.34
## 66 92.13 6 27.6390 552.78
## 67 34.84 4 6.9680 139.36
## 68 81.30 6 24.3900 487.80
## 69 26.31 5 6.5775 131.55
## 70 34.42 6 10.3260 206.52
## 71 89.80 10 44.9000 898.00
## 72 68.60 10 34.3000 686.00
## 73 30.41 1 1.5205 30.41
## 74 77.95 6 23.3850 467.70
## 75 46.26 6 13.8780 277.56
## 76 30.14 10 15.0700 301.40
## 77 91.54 4 18.3080 366.16
## 78 16.48 6 4.9440 98.88
## 79 80.97 8 32.3880 647.76
## 80 43.18 8 17.2720 345.44
## 81 22.51 7 7.8785 157.57
## 82 12.34 7 4.3190 86.38
## 83 94.49 8 37.7960 755.92
## 84 69.81 4 13.9620 279.24
## 85 77.04 3 11.5560 231.12
## 86 73.52 2 7.3520 147.04
## 87 87.80 9 39.5100 790.20
## 88 74.29 1 3.7145 74.29
## 89 25.29 1 1.2645 25.29
## 90 71.39 5 178.4750 356.95
## 91 19.15 6 5.7450 114.90
## 92 57.49 4 11.4980 229.96
## 93 23.03 9 10.3635 207.27
## 94 66.65 9 299.9250 599.85
## 95 28.53 10 14.2650 285.30
## 96 30.37 3 4.5555 91.11
## 97 99.73 9 448.7850 897.57
## 98 93.26 9 41.9670 839.34
## 99 29.61 7 10.3635 207.27
## 100 24.77 5 6.1925 123.85
## 101 94.64 3 14.1960 283.92
## 102 57.34 3 8.6010 172.02
## 103 12.54 1 627.0000 12.54
## 104 87.16 2 8.7160 174.32
## 105 90.70 6 27.2100 544.20
## 106 63.42 8 25.3680 507.36
## 107 81.37 2 8.1370 162.74
## 108 10.59 3 1.5885 31.77
## 109 84.09 9 378.4050 756.81
## 110 93.14 2 9.3140 186.28
## 111 44.22 5 11.0550 221.10
## 112 13.22 5 3.3050 66.10
## 113 81.40 3 12.2100 244.20
## 114 14.39 2 1.4390 28.78
## 115 75.06 9 33.7770 675.54
## 116 16.45 4 3.2900 65.80
## 117 38.30 4 7.6600 153.20
## 118 22.24 10 11.1200 222.40
## 119 98.40 7 34.4400 688.80
## 120 74.60 10 37.3000 746.00
## 121 35.54 10 17.7700 355.40
## 122 67.43 5 168.5750 337.15
## 123 21.12 2 2.1120 42.24
## 124 21.54 9 9.6930 193.86
## 125 12.03 2 1.2030 24.06
## 126 99.71 6 29.9130 598.26
## 127 21.82 10 10.9100 218.20
## 128 95.42 4 19.0840 381.68
## 129 69.96 8 27.9840 559.68
## 130 15.34 1 767.0000 15.34
## 131 47.67 4 9.5340 190.68
## 132 23.75 9 10.6875 213.75
## 133 48.51 7 169.7850 339.57
## 134 94.88 7 33.2080 664.16
## 135 62.48 1 3.1240 62.48
## 136 36.36 2 3.6360 72.72
## 137 51.92 5 12.9800 259.60
## 138 88.61 1 4.4305 88.61
## 139 51.19 4 10.2380 204.76
## 140 14.96 8 5.9840 119.68
## 141 40.23 7 140.8050 281.61
## 142 88.79 8 35.5160 710.32
## 143 26.48 3 3.9720 79.44
## 144 81.91 2 8.1910 163.82
## 145 14.23 5 3.5575 71.15
## 146 15.55 9 6.9975 139.95
## 147 78.13 10 39.0650 781.30
## 148 21.08 3 3.1620 63.24
## 149 29.67 7 10.3845 207.69
## 150 22.93 9 10.3185 206.37
## 151 39.42 1 1.9710 39.42
## 152 61.77 5 154.4250 308.85
## 153 28.45 5 7.1125 142.25
## 154 57.95 6 17.3850 347.70
## 155 47.65 3 7.1475 142.95
## 156 42.82 9 19.2690 385.38
## 157 55.97 7 195.8950 391.79
## 158 76.90 7 26.9150 538.30
## 159 97.03 5 242.5750 485.15
## 160 77.93 9 350.6850 701.37
## 161 89.25 8 35.7000 714.00
## 162 13.50 10 6.7500 135.00
## 163 99.30 10 49.6500 993.00
## 164 54.73 7 191.5550 383.11
## 165 30.24 1 1.5120 30.24
## 166 89.14 4 17.8280 356.56
## 167 37.55 10 18.7750 375.50
## 168 95.44 10 47.7200 954.40
## 169 94.47 8 37.7880 755.76
## 170 41.24 4 8.2480 164.96
## 171 81.68 4 16.3360 326.72
## 172 51.32 9 23.0940 461.88
## 173 14.36 10 7.1800 143.60
## 174 26.26 7 9.1910 183.82
## 175 60.96 2 6.0960 121.92
## 176 70.11 6 21.0330 420.66
## 177 67.09 5 167.7250 335.45
## 178 96.70 5 24.1750 483.50
## 179 35.38 9 15.9210 318.42
## 180 23.65 4 4.7300 94.60
## 181 26.61 2 2.6610 53.22
## 182 99.69 5 249.2250 498.45
## 183 74.89 4 14.9780 299.56
## 184 40.94 5 10.2350 204.70
## 185 32.32 10 16.1600 323.20
## 186 54.07 9 243.3150 486.63
## 187 80.48 3 12.0720 241.44
## 188 37.95 10 18.9750 379.50
## 189 52.26 10 26.1300 522.60
## 190 79.74 1 3.9870 79.74
## 191 77.50 5 19.3750 387.50
## 192 54.27 5 135.6750 271.35
## 193 41.06 6 12.3180 246.36
## 194 39.43 6 11.8290 236.58
## 195 39.75 5 9.9375 198.75
## 196 97.79 7 342.2650 684.53
## 197 68.71 4 13.7420 274.84
## 198 56.53 4 11.3060 226.12
## 199 23.82 5 5.9550 119.10
## 200 34.21 10 17.1050 342.10
## 201 45.38 4 9.0760 181.52
## 202 81.51 1 4.0755 81.51
## 203 57.22 2 5.7220 114.44
## 204 25.22 7 8.8270 176.54
## 205 38.60 3 5.7900 115.80
## 206 84.05 3 12.6075 252.15
## 207 97.21 10 48.6050 972.10
## 208 20.87 3 3.1305 62.61
## 209 90.65 10 45.3250 906.50
## 210 23.46 6 7.0380 140.76
## 211 47.44 1 2.3720 47.44
## 212 40.86 8 16.3440 326.88
## 213 88.43 8 35.3720 707.44
## 214 89.21 9 401.4450 802.89
## 215 19.10 7 6.6850 133.70
## 216 19.15 1 9.5750 19.15
## 217 27.07 1 1.3535 27.07
## 218 39.12 1 1.9560 39.12
## 219 74.71 6 22.4130 448.26
## 220 63.61 5 159.0250 318.05
## 221 29.56 5 7.3900 147.80
## 222 77.40 9 34.8300 696.60
## 223 46.57 10 23.2850 465.70
## 224 73.05 10 36.5250 730.50
## 225 73.95 4 14.7900 295.80
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## 759 24.18 8 9.6720 193.44
## 760 61.29 5 153.2250 306.45
## 761 99.55 7 348.4250 696.85
## 762 58.39 7 204.3650 408.73
## 763 54.86 5 13.7150 274.30
## 764 39.39 5 9.8475 196.95
## 765 34.73 2 3.4730 69.46
## 766 71.92 5 17.9800 359.60
## 767 62.87 2 6.2870 125.74
## 768 81.71 6 24.5130 490.26
## 769 39.21 4 7.8420 156.84
## 770 59.86 2 5.9860 119.72
## 771 98.09 9 441.4050 882.81
## 772 25.43 6 7.6290 152.58
## 773 86.68 8 34.6720 693.44
## 774 22.95 10 11.4750 229.50
## 775 16.67 7 5.8345 116.69
## 776 97.94 1 4.8970 97.94
## 777 30.68 3 4.6020 92.04
## 778 75.88 1 3.7940 75.88
## 779 18.77 6 5.6310 112.62
## 780 38.81 4 7.7620 155.24
## 781 60.95 9 274.2750 548.55
## 782 57.27 3 8.5905 171.81
## 783 22.21 6 6.6630 133.26
## 784 19.32 7 6.7620 135.24
## 785 37.48 3 5.6220 112.44
## 786 41.66 6 12.4980 249.96
## 787 21.58 9 9.7110 194.22
## 788 89.20 10 44.6000 892.00
## 789 74.51 6 22.3530 447.06
## 790 99.25 2 9.9250 198.50
## 791 26.67 10 13.3350 266.70
## 792 10.13 7 3.5455 70.91
## 793 72.39 2 7.2390 144.78
## 794 85.91 5 214.7750 429.55
## 795 81.31 7 284.5850 569.17
## 796 60.30 4 12.0600 241.20
## 797 31.77 4 6.3540 127.08
## 798 69.51 2 6.9510 139.02
## 799 27.22 3 4.0830 81.66
## 800 63.06 3 9.4590 189.18
## 801 51.71 4 10.3420 206.84
## 802 59.61 10 29.8050 596.10
## 803 14.62 5 3.6550 73.10
## 804 46.53 6 13.9590 279.18
## 805 96.80 3 14.5200 290.40
## 806 14.82 3 2.2230 44.46
## 807 52.20 3 7.8300 156.60
## 808 83.08 1 4.1540 83.08
## 809 77.56 10 38.7800 775.60
## 810 31.75 4 6.3500 127.00
## 811 30.61 1 1.5305 30.61
## 812 57.89 2 5.7890 115.78
## 813 93.22 3 13.9830 279.66
## 814 80.93 1 4.0465 80.93
## 815 67.45 10 33.7250 674.50
## 816 72.60 6 21.7800 435.60
## 817 87.91 5 219.7750 439.55
## 818 98.53 6 29.5590 591.18
## 819 91.35 1 4.5675 91.35
## 820 60.87 2 6.0870 121.74
## 821 82.58 10 41.2900 825.80
## 822 53.30 3 7.9950 159.90
## 823 64.19 10 32.0950 641.90
## 824 78.31 3 11.7465 234.93
## 825 83.77 2 8.3770 167.54
## 826 99.70 3 14.9550 299.10
## 827 79.91 3 11.9865 239.73
## 828 66.47 10 33.2350 664.70
## 829 28.95 7 10.1325 202.65
## 830 52.42 3 7.8630 157.26
## 831 55.67 2 5.5670 111.34
## 832 12.05 5 3.0125 60.25
## 833 19.36 9 8.7120 174.24
## 834 70.21 6 21.0630 421.26
## 835 33.63 1 1.6815 33.63
## 836 24.74 10 12.3700 247.40
## 837 75.66 5 18.9150 378.30
## 838 72.78 10 36.3900 727.80
## 839 37.32 9 16.7940 335.88
## 840 60.18 4 12.0360 240.72
## 841 55.45 1 2.7725 55.45
## 842 17.14 7 5.9990 119.98
## 843 57.74 3 8.6610 173.22
## 844 56.04 10 28.0200 560.40
## 845 93.40 2 9.3400 186.80
## 846 33.64 8 13.4560 269.12
## 847 83.77 2 8.3770 167.54
## 848 58.95 10 29.4750 589.50
## 849 48.50 6 14.5500 291.00
## 850 21.48 2 2.1480 42.96
## 851 63.56 10 31.7800 635.60
## 852 72.88 2 7.2880 145.76
## 853 55.04 7 19.2640 385.28
## 854 48.63 10 24.3150 486.30
## 855 62.19 4 12.4380 248.76
## 856 69.58 9 31.3110 626.22
## 857 97.50 10 48.7500 975.00
## 858 32.32 3 4.8480 96.96
## 859 80.47 9 362.1150 724.23
## 860 71.77 7 251.1950 502.39
## 861 68.98 1 3.4490 68.98
## 862 15.62 8 6.2480 124.96
## 863 25.70 3 3.8550 77.10
## 864 80.62 6 24.1860 483.72
## 865 98.70 8 39.4800 789.60
## 866 11.94 3 1.7910 35.82
## 867 45.38 3 6.8070 136.14
## 868 44.12 3 6.6180 132.36
## 869 23.34 4 4.6680 93.36
## 870 55.57 3 8.3355 166.71
## 871 69.74 10 34.8700 697.40
## 872 97.26 4 19.4520 389.04
## 873 56.00 3 8.4000 168.00
## 874 19.70 1 985.0000 19.70
## 875 75.88 7 26.5580 531.16
## 876 53.72 1 2.6860 53.72
## 877 81.95 10 40.9750 819.50
## 878 58.76 10 29.3800 587.60
## 879 91.56 8 36.6240 732.48
## 880 93.96 9 42.2820 845.64
## 881 55.61 7 194.6350 389.27
## 882 84.83 1 4.2415 84.83
## 883 37.69 2 3.7690 75.38
## 884 65.23 10 32.6150 652.30
## 885 81.23 7 284.3050 568.61
## 886 73.28 5 18.3200 366.40
## 887 18.85 10 9.4250 188.50
## 888 72.13 10 36.0650 721.30
## 889 55.50 4 11.1000 222.00
## 890 13.69 6 4.1070 82.14
## 891 65.65 2 6.5650 131.30
## 892 65.31 7 228.5850 457.17
## 893 93.38 1 4.6690 93.38
## 894 25.25 5 6.3125 126.25
## 895 87.87 9 395.4150 790.83
## 896 21.80 8 8.7200 174.40
## 897 74.58 7 26.1030 522.06
## 898 71.89 8 28.7560 575.12
## 899 60.47 3 9.0705 181.41
## 900 58.91 7 206.1850 412.37
## 901 46.41 1 2.3205 46.41
## 902 68.55 4 13.7100 274.20
## 903 92.60 7 32.4100 648.20
## 904 27.18 2 2.7180 54.36
## 905 92.78 1 4.6390 92.78
## 906 86.69 5 216.7250 433.45
## 907 23.01 6 6.9030 138.06
## 908 67.39 7 235.8650 471.73
## 909 10.75 8 4.3000 86.00
## 910 95.15 1 4.7575 95.15
## 911 33.88 8 13.5520 271.04
## 912 96.16 4 19.2320 384.64
## 913 47.16 5 11.7900 235.80
## 914 52.89 4 10.5780 211.56
## 915 10.17 1 5.0850 10.17
## 916 41.28 3 6.1920 123.84
## 917 64.95 10 32.4750 649.50
## 918 10.56 8 4.2240 84.48
## 919 62.57 4 12.5140 250.28
## 920 91.30 1 4.5650 91.30
## 921 52.38 1 2.6190 52.38
## 922 38.54 5 9.6350 192.70
## 923 44.63 6 13.3890 267.78
## 924 55.87 10 27.9350 558.70
## 925 51.94 3 7.7910 155.82
## 926 60.30 1 3.0150 60.30
## 927 21.32 1 1.0660 21.32
## 928 93.78 3 14.0670 281.34
## 929 73.26 1 3.6630 73.26
## 930 74.10 1 3.7050 74.10
## 931 53.19 7 186.1650 372.33
## 932 21.12 8 8.4480 168.96
## 933 57.59 6 17.2770 345.54
## 934 12.76 2 1.2760 25.52
## 935 33.81 3 5.0715 101.43
## 936 90.53 8 36.2120 724.24
## 937 24.31 3 3.6465 72.93
## 938 64.59 4 12.9180 258.36
## 939 24.82 7 8.6870 173.74
## 940 56.50 1 2.8250 56.50
## 941 89.06 6 26.7180 534.36
## 942 23.29 4 4.6580 93.16
## 943 65.26 8 26.1040 522.08
## 944 52.35 1 2.6175 52.35
## 945 39.75 1 1.9875 39.75
## 946 31.99 10 15.9950 319.90
## 947 45.58 7 15.9530 319.06
## 948 87.90 1 4.3950 87.90
## 949 76.92 10 38.4600 769.20
## 950 28.38 5 7.0950 141.90
## 951 50.45 6 15.1350 302.70
## 952 99.16 8 39.6640 793.28
## 953 60.74 7 21.2590 425.18
## 954 85.60 7 29.9600 599.20
## 955 35.04 9 15.7680 315.36
## 956 45.97 4 9.1940 183.88
## 957 11.53 7 4.0355 80.71
## 958 84.61 10 42.3050 846.10
## 959 51.34 8 20.5360 410.72
## 960 42.85 1 2.1425 42.85
## 961 68.97 3 10.3455 206.91
## 962 88.31 1 4.4155 88.31
## 963 25.31 2 2.5310 50.62
## 964 99.92 6 29.9760 599.52
## 965 64.08 7 22.4280 448.56
## 966 85.72 3 12.8580 257.16
## 967 66.52 4 13.3040 266.08
## 968 99.82 9 44.9190 898.38
## 969 50.79 5 12.6975 253.95
## 970 10.08 7 3.5280 70.56
## 971 84.25 2 8.4250 168.50
## 972 53.78 1 2.6890 53.78
## 973 35.81 5 8.9525 179.05
## 974 39.91 3 5.9865 119.73
## 975 65.91 6 19.7730 395.46
## 976 50.49 9 227.2050 454.41
## 977 46.02 6 13.8060 276.12
## 978 91.98 1 4.5990 91.98
## 979 20.89 2 2.0890 41.78
## 980 96.82 3 14.5230 290.46
## 981 33.33 2 3.3330 66.66
## 982 81.01 3 12.1515 243.03
## 983 36.91 7 12.9185 258.37
## 984 87.08 7 30.4780 609.56
## 985 80.08 3 12.0120 240.24
## 986 86.13 2 8.6130 172.26
## 987 49.92 2 4.9920 99.84
## 988 26.60 6 7.9800 159.60
## 989 59.59 4 11.9180 238.36
## 990 58.15 4 11.6300 232.60
## 991 99.96 7 34.9860 699.72
## 992 96.37 7 337.2950 674.59
## 993 62.00 8 24.8000 496.00
## 994 82.34 10 41.1700 823.40
## 995 75.37 8 30.1480 602.96
## 996 58.03 2 5.8030 116.06
## 997 17.49 10 8.7450 174.90
## 998 40.35 1 2.0175 40.35
## 999 31.84 1 1.5920 31.84
## 1000 65.82 1 3.2910 65.82
View(data)
glimpse(data)
## Rows: 1,000
## Columns: 10
## $ Gender <chr> "Female", "Female", "Female", "Female", "Female", "Femal…
## $ Invoice.ID <chr> "750-67-8428", "226-31-3081", "355-53-5943", "315-22-566…
## $ Branch <chr> "A", "C", "A", "C", "A", "B", "B", "A", "A", "B", "A", "…
## $ City <chr> "Yangon", "Naypyitaw", "Yangon", "Naypyitaw", "Yangon", …
## $ Customer.type <chr> "Member", "Normal", "Member", "Normal", "Member", "Membe…
## $ Product.line <chr> "Health and beauty", "Electronic accessories", "Electron…
## $ Unit.price <dbl> 74.69, 15.28, 68.84, 73.56, 36.26, 54.84, 14.48, 46.95, …
## $ Quantity <int> 7, 5, 6, 10, 2, 3, 4, 5, 10, 6, 7, 2, 8, 2, 5, 4, 1, 9, …
## $ Tax.5. <dbl> 261.4150, 3.8200, 20.6520, 36.7800, 3.6260, 8.2260, 2.89…
## $ Sales <dbl> 522.83, 76.40, 413.04, 735.60, 72.52, 164.52, 57.92, 234…
sales <- data$Sales; sales # sales column.
## [1] 522.83 76.40 413.04 735.60 72.52 164.52 57.92 234.75 713.80 562.32
## [11] 482.51 80.60 420.72 175.34 441.80 397.68 68.12 547.92 439.36 86.72
## [21] 414.72 789.60 375.84 180.09 826.30 222.95 71.48 687.84 723.50 74.22
## [31] 495.63 66.94 585.66 18.33 145.56 455.46 416.50 180.09 783.10 101.90
## [41] 595.14 290.04 321.44 581.42 461.94 189.52 448.60 153.86 74.70 207.63
## [51] 305.82 32.98 294.63 509.88 727.11 81.06 109.60 796.48 451.76 655.83
## [61] 161.25 285.57 548.32 812.52 277.34 552.78 139.36 487.80 131.55 206.52
## [71] 898.00 686.00 30.41 467.70 277.56 301.40 366.16 98.88 647.76 345.44
## [81] 157.57 86.38 755.92 279.24 231.12 147.04 790.20 74.29 25.29 356.95
## [91] 114.90 229.96 207.27 599.85 285.30 91.11 897.57 839.34 207.27 123.85
## [101] 283.92 172.02 12.54 174.32 544.20 507.36 162.74 31.77 756.81 186.28
## [111] 221.10 66.10 244.20 28.78 675.54 65.80 153.20 222.40 688.80 746.00
## [121] 355.40 337.15 42.24 193.86 24.06 598.26 218.20 381.68 559.68 15.34
## [131] 190.68 213.75 339.57 664.16 62.48 72.72 259.60 88.61 204.76 119.68
## [141] 281.61 710.32 79.44 163.82 71.15 139.95 781.30 63.24 207.69 206.37
## [151] 39.42 308.85 142.25 347.70 142.95 385.38 391.79 538.30 485.15 701.37
## [161] 714.00 135.00 993.00 383.11 30.24 356.56 375.50 954.40 755.76 164.96
## [171] 326.72 461.88 143.60 183.82 121.92 420.66 335.45 483.50 318.42 94.60
## [181] 53.22 498.45 299.56 204.70 323.20 486.63 241.44 379.50 522.60 79.74
## [191] 387.50 271.35 246.36 236.58 198.75 684.53 274.84 226.12 119.10 342.10
## [201] 181.52 81.51 114.44 176.54 115.80 252.15 972.10 62.61 906.50 140.76
## [211] 47.44 326.88 707.44 802.89 133.70 19.15 27.07 39.12 448.26 318.05
## [221] 147.80 696.60 465.70 730.50 295.80 22.62 545.50 260.05 98.84 502.62
## [231] 160.20 322.20 166.30 328.00 369.80 197.96 410.90 699.12 69.40 196.60
## [241] 202.56 121.20 126.44 541.44 98.13 412.16 31.90 186.62 145.50 504.30
## [251] 95.70 635.18 214.55 379.96 51.47 137.13 499.02 224.64 457.05 543.60
## [261] 146.79 141.60 73.96 292.20 524.88 80.72 71.20 294.20 257.70 396.36
## [271] 488.79 524.16 144.08 985.20 217.26 339.36 812.10 493.30 591.66 559.02
## [281] 517.86 410.20 257.08 310.72 185.96 72.32 157.02 215.30 169.68 45.58
## [291] 225.60 419.94 184.25 140.64 64.99 327.06 363.23 375.55 199.16 28.96
## [301] 890.73 348.48 260.76 215.04 91.61 662.13 832.50 157.76 12.09 46.20
## [311] 88.15 296.37 708.40 580.16 30.98 334.86 47.07 99.69 264.45 139.65
## [321] 128.91 352.50 871.00 197.60 194.52 71.88 286.26 81.24 220.23 454.80
## [331] 448.56 293.88 39.48 34.81 295.92 138.48 98.20 129.66 201.30 631.71
## [341] 513.66 473.40 436.85 108.16 483.28 197.70 795.51 172.00 302.12 698.67
## [351] 124.65 178.40 500.22 104.88 178.92 815.67 257.39 228.00 365.26 89.28
## [361] 568.40 143.26 253.36 38.42 52.65 110.61 89.28 136.40 174.20 254.61
## [371] 778.32 285.92 579.12 221.56 772.00 511.04 53.45 763.68 228.18 382.56
## [381] 68.58 382.16 601.09 475.93 52.42 144.30 379.04 30.62 352.08 50.80
## [391] 54.95 973.70 93.22 60.87 244.90 241.60 440.64 680.31 309.88 186.36
## [401] 200.92 17.75 621.80 402.60 324.85 388.96 425.68 318.08 95.36 206.13
## [411] 420.56 88.04 648.99 742.20 94.80 285.11 175.32 78.94 29.74 22.38
## [421] 655.92 594.60 196.96 527.90 479.75 328.59 113.24 428.67 86.27 101.52
## [431] 357.49 238.77 125.64 214.30 720.16 96.80 332.10 81.44 206.52 166.68
## [441] 734.70 97.52 418.30 463.28 462.45 283.62 403.56 138.65 116.64 313.52
## [451] 414.40 159.08 490.10 87.45 224.52 744.96 298.80 212.94 378.68 78.78
## [461] 322.11 98.22 25.46 581.98 211.32 55.12 356.58 794.25 166.70 744.40
## [471] 378.90 552.23 447.40 276.27 343.74 456.80 657.16 211.44 65.70 251.40
## [481] 84.16 297.99 158.00 887.94 15.50 76.54 299.70 47.40 172.45 846.30
## [491] 298.64 25.45 67.77 877.32 318.55 29.52 282.80 766.00 60.95 973.80
## [501] 618.38 324.31 465.76 604.17 597.73 102.04 431.90 435.66 164.01 430.20
## [511] 263.94 66.40 172.80 265.89 33.52 224.01 470.65 702.63 670.24 193.16
## [521] 313.10 240.96 112.22 30.74 510.21 113.58 639.80 15.43 32.32 88.68
## [531] 716.80 183.66 334.38 158.10 302.96 158.70 787.70 894.80 621.20 672.03
## [541] 441.36 154.00 244.55 382.60 345.66 42.47 579.24 89.75 97.16 878.70
## [551] 158.25 496.20 48.71 706.95 349.56 212.45 886.70 164.28 372.78 819.70
## [561] 522.63 109.70 51.36 106.88 399.84 899.64 511.28 524.70 270.66 519.10
## [571] 580.00 905.00 264.56 574.88 259.68 241.92 749.16 461.45 72.17 251.40
## [581] 874.98 560.34 63.69 320.53 152.80 399.00 340.56 955.80 989.80 307.68
## [591] 486.64 350.05 400.25 166.80 317.34 158.32 304.56 177.36 443.28 260.40
## [601] 449.82 307.76 155.00 274.48 54.24 185.88 74.07 102.20 163.55 87.40
## [611] 166.00 429.87 259.00 88.85 236.07 461.80 139.26 18.28 758.96 272.10
## [621] 434.56 59.05 86.50 624.33 148.24 295.28 519.40 87.05 89.69 224.46
## [631] 119.54 186.40 250.60 750.96 380.72 89.70 310.88 511.42 418.95 351.90
## [641] 95.00 471.20 130.48 66.35 155.46 129.00 263.76 54.45 141.88 282.96
## [651] 335.79 709.90 440.20 37.00 598.98 333.40 74.86 403.00 194.95 181.10
## [661] 115.36 470.28 240.04 199.64 39.01 48.61 505.40 479.58 138.66 198.74
## [671] 373.95 176.28 91.56 129.12 390.96 498.90 377.04 204.52 145.44 198.18
## [681] 98.70 385.10 46.96 73.50 687.60 144.27 133.95 71.95 182.14 361.83
## [691] 243.00 82.50 74.97 647.68 199.58 439.32 263.76 193.50 252.48 668.43
## [701] 387.92 329.32 75.82 280.62 127.54 76.82 122.31 173.16 184.88 13.98
## [711] 269.04 68.95 43.74 104.85 77.52 407.44 96.11 203.36 16.28 365.49
## [721] 372.19 336.35 138.16 86.54 668.78 893.16 331.72 203.94 68.16 87.20
## [731] 12.78 276.60 137.22 132.06 25.00 83.08 793.90 35.89 202.60 256.70
## [741] 222.12 21.58 431.30 580.56 195.54 336.28 343.70 38.60 527.76 185.70
## [751] 603.80 148.60 22.96 199.78 607.36 73.97 138.80 88.45 193.44 306.45
## [761] 696.85 408.73 274.30 196.95 69.46 359.60 125.74 490.26 156.84 119.72
## [771] 882.81 152.58 693.44 229.50 116.69 97.94 92.04 75.88 112.62 155.24
## [781] 548.55 171.81 133.26 135.24 112.44 249.96 194.22 892.00 447.06 198.50
## [791] 266.70 70.91 144.78 429.55 569.17 241.20 127.08 139.02 81.66 189.18
## [801] 206.84 596.10 73.10 279.18 290.40 44.46 156.60 83.08 775.60 127.00
## [811] 30.61 115.78 279.66 80.93 674.50 435.60 439.55 591.18 91.35 121.74
## [821] 825.80 159.90 641.90 234.93 167.54 299.10 239.73 664.70 202.65 157.26
## [831] 111.34 60.25 174.24 421.26 33.63 247.40 378.30 727.80 335.88 240.72
## [841] 55.45 119.98 173.22 560.40 186.80 269.12 167.54 589.50 291.00 42.96
## [851] 635.60 145.76 385.28 486.30 248.76 626.22 975.00 96.96 724.23 502.39
## [861] 68.98 124.96 77.10 483.72 789.60 35.82 136.14 132.36 93.36 166.71
## [871] 697.40 389.04 168.00 19.70 531.16 53.72 819.50 587.60 732.48 845.64
## [881] 389.27 84.83 75.38 652.30 568.61 366.40 188.50 721.30 222.00 82.14
## [891] 131.30 457.17 93.38 126.25 790.83 174.40 522.06 575.12 181.41 412.37
## [901] 46.41 274.20 648.20 54.36 92.78 433.45 138.06 471.73 86.00 95.15
## [911] 271.04 384.64 235.80 211.56 10.17 123.84 649.50 84.48 250.28 91.30
## [921] 52.38 192.70 267.78 558.70 155.82 60.30 21.32 281.34 73.26 74.10
## [931] 372.33 168.96 345.54 25.52 101.43 724.24 72.93 258.36 173.74 56.50
## [941] 534.36 93.16 522.08 52.35 39.75 319.90 319.06 87.90 769.20 141.90
## [951] 302.70 793.28 425.18 599.20 315.36 183.88 80.71 846.10 410.72 42.85
## [961] 206.91 88.31 50.62 599.52 448.56 257.16 266.08 898.38 253.95 70.56
## [971] 168.50 53.78 179.05 119.73 395.46 454.41 276.12 91.98 41.78 290.46
## [981] 66.66 243.03 258.37 609.56 240.24 172.26 99.84 159.60 238.36 232.60
## [991] 699.72 674.59 496.00 823.40 602.96 116.06 174.90 40.35 31.84 65.82
head(sales) # getting the first values in the data.
## [1] 522.83 76.40 413.04 735.60 72.52 164.52
length(sales) # number of records.
## [1] 1000
#Basic Statistics.
min(sales)
## [1] 10.17
max(sales)
## [1] 993
mean(sales)
## [1] 307.5874
var(sales) # variance
## [1] 54838.64
sd(sales) # standard deviation
## [1] 234.1765
# visualization
hist(sales, col = "purple")
ts.plot(sales)
boxplot(sales)
summary(sales)# five number summary.
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 10.17 118.50 241.76 307.59 448.90 993.00
# Removing Outliers.
iqr <- IQR(sales); iqr
## [1] 330.4075
lower_bound <- quantile(sales, 0.25) - 1.5 * iqr ;lower_bound
## 25%
## -377.1138
upper_bound <- quantile(sales, 0.75) + 1.5 * iqr ;upper_bound
## 75%
## 944.5163
data_clean <- data[!(data$Sales < lower_bound | data$Sales > upper_bound), ];data_clean
## Gender Invoice.ID Branch City Customer.type Product.line
## 1 Female 750-67-8428 A Yangon Member Health and beauty
## 2 Female 226-31-3081 C Naypyitaw Normal Electronic accessories
## 3 Female 355-53-5943 A Yangon Member Electronic accessories
## 4 Female 315-22-5665 C Naypyitaw Normal Home and lifestyle
## 5 Female 665-32-9167 A Yangon Member Health and beauty
## 6 Female 692-92-5582 B Mandalay Member Food and beverages
## 7 Female 351-62-0822 B Mandalay Member Fashion accessories
## 8 Female 365-64-0515 A Yangon Normal Electronic accessories
## 9 Female 829-34-3910 A Yangon Normal Health and beauty
## 10 Female 299-46-1805 B Mandalay Member Sports and travel
## 11 Female 656-95-9349 A Yangon Member Health and beauty
## 12 Female 319-50-3348 B Mandalay Normal Home and lifestyle
## 13 Female 227-03-5010 A Yangon Member Home and lifestyle
## 14 Female 189-17-4241 A Yangon Normal Fashion accessories
## 15 Female 145-94-9061 B Mandalay Normal Food and beverages
## 16 Female 183-56-6882 C Naypyitaw Member Food and beverages
## 17 Female 232-16-2483 C Naypyitaw Member Sports and travel
## 18 Female 272-65-1806 A Yangon Normal Electronic accessories
## 19 Female 333-73-7901 C Naypyitaw Normal Health and beauty
## 20 Female 280-35-5823 B Mandalay Member Home and lifestyle
## 21 Female 354-25-5821 B Mandalay Member Sports and travel
## 22 Female 228-96-1411 C Naypyitaw Member Food and beverages
## 23 Female 132-32-9879 B Mandalay Member Electronic accessories
## 24 Female 727-46-3608 B Mandalay Member Food and beverages
## 25 Female 574-22-5561 C Naypyitaw Member Fashion accessories
## 26 Female 162-48-8011 A Yangon Member Food and beverages
## 27 Female 616-24-2851 B Mandalay Member Fashion accessories
## 28 Female 399-46-5918 C Naypyitaw Normal Electronic accessories
## 29 Female 817-48-8732 A Yangon Member Home and lifestyle
## 30 Female 285-68-5083 C Naypyitaw Member Sports and travel
## 31 Female 347-34-2234 B Mandalay Member Sports and travel
## 32 Female 838-78-4295 C Naypyitaw Normal Health and beauty
## 33 Female 109-28-2512 B Mandalay Member Fashion accessories
## 34 Female 382-03-4532 A Yangon Member Health and beauty
## 35 Female 510-95-6347 B Mandalay Member Food and beverages
## 36 Female 841-35-6630 C Naypyitaw Normal Electronic accessories
## 37 Female 732-94-0499 C Naypyitaw Normal Electronic accessories
## 38 Female 381-20-0914 A Yangon Member Fashion accessories
## 39 Female 829-49-1914 C Naypyitaw Member Food and beverages
## 40 Female 756-01-7507 C Naypyitaw Normal Health and beauty
## 41 Female 870-72-4431 C Naypyitaw Normal Health and beauty
## 42 Female 847-38-7188 B Mandalay Normal Food and beverages
## 43 Female 787-56-0757 C Naypyitaw Member Food and beverages
## 44 Female 730-50-9884 C Naypyitaw Normal Sports and travel
## 45 Female 318-68-5053 B Mandalay Normal Health and beauty
## 46 Female 565-80-5980 C Naypyitaw Member Home and lifestyle
## 47 Female 225-32-0908 C Naypyitaw Normal Sports and travel
## 48 Female 873-51-0671 A Yangon Member Sports and travel
## 49 Female 871-39-9221 C Naypyitaw Normal Electronic accessories
## 50 Female 551-21-3069 C Naypyitaw Normal Electronic accessories
## 51 Female 588-01-7461 C Naypyitaw Normal Food and beverages
## 52 Female 479-26-8945 B Mandalay Member Sports and travel
## 53 Female 210-67-5886 C Naypyitaw Member Health and beauty
## 54 Female 227-78-1148 B Mandalay Normal Fashion accessories
## 55 Female 237-01-6122 C Naypyitaw Member Home and lifestyle
## 56 Female 225-98-1496 C Naypyitaw Normal Fashion accessories
## 57 Female 642-32-2990 A Yangon Normal Food and beverages
## 58 Female 638-60-7125 A Yangon Normal Electronic accessories
## 59 Female 268-27-6179 B Mandalay Member Fashion accessories
## 60 Female 668-90-8900 A Yangon Normal Home and lifestyle
## 61 Female 870-54-3162 A Yangon Normal Sports and travel
## 62 Female 189-08-9157 C Naypyitaw Normal Fashion accessories
## 63 Female 663-86-9076 C Naypyitaw Member Food and beverages
## 64 Female 549-84-7482 B Mandalay Normal Sports and travel
## 65 Female 191-10-6171 B Mandalay Normal Fashion accessories
## 66 Female 802-70-5316 A Yangon Member Sports and travel
## 67 Female 695-51-0018 B Mandalay Normal Sports and travel
## 68 Female 483-71-1164 C Naypyitaw Normal Health and beauty
## 69 Female 700-81-1757 A Yangon Normal Electronic accessories
## 70 Female 354-39-5160 A Yangon Member Home and lifestyle
## 71 Female 731-81-9469 C Naypyitaw Member Sports and travel
## 72 Female 338-65-2210 C Naypyitaw Member Health and beauty
## 73 Female 488-25-4221 C Naypyitaw Member Food and beverages
## 74 Female 239-10-7476 A Yangon Normal Home and lifestyle
## 75 Female 458-41-1477 C Naypyitaw Normal Health and beauty
## 76 Female 685-64-1609 A Yangon Member Fashion accessories
## 77 Female 608-96-3517 B Mandalay Member Fashion accessories
## 78 Female 214-17-6927 C Naypyitaw Normal Food and beverages
## 79 Female 400-89-4171 C Naypyitaw Normal Sports and travel
## 80 Female 894-41-5205 C Naypyitaw Normal Food and beverages
## 81 Female 139-52-2867 C Naypyitaw Normal Fashion accessories
## 82 Female 586-25-0848 A Yangon Normal Sports and travel
## 83 Female 305-14-0245 B Mandalay Member Home and lifestyle
## 84 Female 593-65-1552 C Naypyitaw Normal Home and lifestyle
## 85 Female 284-34-9626 B Mandalay Normal Home and lifestyle
## 86 Female 437-58-8131 B Mandalay Normal Fashion accessories
## 87 Female 286-43-6208 C Naypyitaw Normal Food and beverages
## 88 Female 556-86-3144 C Naypyitaw Member Fashion accessories
## 89 Female 856-22-8149 A Yangon Normal Home and lifestyle
## 90 Female 420-11-4919 C Naypyitaw Member Food and beverages
## 91 Female 606-80-4905 C Naypyitaw Member Sports and travel
## 92 Female 542-41-0513 B Mandalay Member Electronic accessories
## 93 Female 749-24-1565 A Yangon Normal Health and beauty
## 94 Female 672-51-8681 C Naypyitaw Member Electronic accessories
## 95 Female 263-87-5680 C Naypyitaw Member Home and lifestyle
## 96 Female 573-58-9734 B Mandalay Normal Fashion accessories
## 97 Female 817-69-8206 B Mandalay Normal Electronic accessories
## 98 Female 677-11-0152 C Naypyitaw Normal Food and beverages
## 99 Female 891-58-8335 B Mandalay Member Sports and travel
## 100 Female 560-30-5617 B Mandalay Normal Sports and travel
## 101 Female 319-74-2561 A Yangon Member Electronic accessories
## 102 Female 790-29-1172 B Mandalay Normal Food and beverages
## 103 Female 279-62-1445 C Naypyitaw Member Fashion accessories
## 104 Female 746-68-6593 C Naypyitaw Member Sports and travel
## 105 Female 466-61-5506 B Mandalay Member Electronic accessories
## 106 Female 721-86-6247 A Yangon Normal Home and lifestyle
## 107 Female 289-65-5721 B Mandalay Normal Fashion accessories
## 108 Female 545-46-3100 B Mandalay Member Electronic accessories
## 109 Female 418-02-5978 B Mandalay Normal Health and beauty
## 110 Female 645-78-8093 A Yangon Normal Sports and travel
## 111 Female 755-12-3214 C Naypyitaw Member Fashion accessories
## 112 Female 346-84-3103 B Mandalay Member Electronic accessories
## 113 Female 866-05-7563 B Mandalay Member Electronic accessories
## 114 Female 883-17-4236 C Naypyitaw Normal Sports and travel
## 115 Female 850-41-9669 A Yangon Normal Electronic accessories
## 116 Female 821-07-3596 C Naypyitaw Normal Fashion accessories
## 117 Female 655-85-5130 B Mandalay Member Fashion accessories
## 118 Female 447-15-7839 A Yangon Member Sports and travel
## 119 Female 253-12-6086 A Yangon Member Sports and travel
## 120 Female 571-94-0759 B Mandalay Member Food and beverages
## 121 Female 731-14-2199 A Yangon Member Home and lifestyle
## 122 Female 783-09-1637 B Mandalay Normal Sports and travel
## 123 Female 687-15-1097 C Naypyitaw Member Health and beauty
## 124 Female 126-54-1082 A Yangon Member Home and lifestyle
## 125 Female 633-91-1052 A Yangon Normal Home and lifestyle
## 126 Female 477-24-6490 B Mandalay Normal Health and beauty
## 127 Female 526-86-8552 C Naypyitaw Member Home and lifestyle
## 128 Female 376-56-3573 C Naypyitaw Normal Fashion accessories
## 129 Female 136-08-6195 A Yangon Normal Home and lifestyle
## 130 Female 490-29-1201 A Yangon Normal Sports and travel
## 131 Female 565-17-3836 A Yangon Member Health and beauty
## 132 Female 226-71-3580 C Naypyitaw Normal Sports and travel
## 133 Female 283-79-9594 B Mandalay Normal Food and beverages
## 134 Female 430-60-3493 A Yangon Member Home and lifestyle
## 135 Female 278-97-7759 A Yangon Member Electronic accessories
## 136 Female 316-68-6352 A Yangon Member Food and beverages
## 137 Female 211-05-0490 C Naypyitaw Member Electronic accessories
## 138 Female 779-06-0012 C Naypyitaw Member Home and lifestyle
## 139 Female 439-54-7422 A Yangon Normal Electronic accessories
## 140 Female 396-90-2219 B Mandalay Normal Electronic accessories
## 141 Female 286-01-5402 A Yangon Normal Sports and travel
## 142 Female 803-17-8013 A Yangon Member Home and lifestyle
## 143 Female 512-98-1403 A Yangon Member Electronic accessories
## 144 Female 848-42-2560 A Yangon Normal Fashion accessories
## 145 Female 870-76-1733 A Yangon Member Food and beverages
## 146 Female 423-64-4619 A Yangon Member Health and beauty
## 147 Female 227-07-4446 C Naypyitaw Member Electronic accessories
## 148 Female 428-83-5800 C Naypyitaw Member Food and beverages
## 149 Female 704-20-4138 C Naypyitaw Member Health and beauty
## 150 Female 649-11-3678 C Naypyitaw Normal Food and beverages
## 151 Female 622-20-1945 C Naypyitaw Normal Health and beauty
## 152 Female 563-91-7120 A Yangon Normal Fashion accessories
## 153 Female 527-09-6272 A Yangon Member Electronic accessories
## 154 Female 692-27-8933 B Mandalay Normal Sports and travel
## 155 Female 633-09-3463 C Naypyitaw Normal Electronic accessories
## 156 Female 374-17-3652 B Mandalay Member Food and beverages
## 157 Female 433-75-6987 B Mandalay Member Health and beauty
## 158 Female 873-95-4984 B Mandalay Member Health and beauty
## 159 Female 416-13-5917 C Naypyitaw Normal Food and beverages
## 160 Female 135-84-8019 A Yangon Normal Fashion accessories
## 161 Female 725-96-3778 C Naypyitaw Member Home and lifestyle
## 162 Female 400-45-1220 B Mandalay Normal Health and beauty
## 164 Female 115-99-4379 B Mandalay Member Fashion accessories
## 165 Female 320-49-6392 C Naypyitaw Normal Electronic accessories
## 166 Female 889-04-9723 B Mandalay Member Food and beverages
## 167 Female 632-90-0281 C Naypyitaw Normal Fashion accessories
## 169 Female 605-72-4132 C Naypyitaw Normal Food and beverages
## 170 Female 272-27-9238 C Naypyitaw Normal Food and beverages
## 171 Female 834-25-9262 C Naypyitaw Normal Fashion accessories
## 172 Female 122-61-9553 C Naypyitaw Normal Electronic accessories
## 173 Female 613-59-9758 C Naypyitaw Normal Sports and travel
## 174 Female 201-86-2184 B Mandalay Member Electronic accessories
## 175 Female 261-12-8671 B Mandalay Normal Fashion accessories
## 176 Female 730-70-9830 C Naypyitaw Normal Home and lifestyle
## 177 Female 422-29-8786 A Yangon Normal Home and lifestyle
## 178 Female 667-23-5919 A Yangon Member Fashion accessories
## 179 Female 843-01-4703 B Mandalay Member Home and lifestyle
## 180 Female 182-69-8360 B Mandalay Normal Electronic accessories
## 181 Female 462-78-5240 C Naypyitaw Normal Electronic accessories
## 182 Female 868-52-7573 B Mandalay Normal Food and beverages
## 183 Female 153-58-4872 C Naypyitaw Member Food and beverages
## 184 Female 662-72-2873 A Yangon Normal Food and beverages
## 185 Female 725-56-0833 A Yangon Normal Health and beauty
## 186 Female 394-41-0748 C Naypyitaw Member Fashion accessories
## 187 Female 541-89-9860 C Naypyitaw Member Fashion accessories
## 188 Female 173-82-9529 B Mandalay Normal Fashion accessories
## 189 Female 308-47-4913 A Yangon Member Sports and travel
## 190 Female 885-17-6250 A Yangon Normal Health and beauty
## 191 Female 726-27-2396 A Yangon Normal Health and beauty
## 192 Female 316-01-3952 A Yangon Normal Food and beverages
## 193 Female 793-10-3222 B Mandalay Member Health and beauty
## 194 Female 110-05-6330 C Naypyitaw Normal Food and beverages
## 195 Female 831-64-0259 B Mandalay Normal Fashion accessories
## 196 Female 587-03-7455 C Naypyitaw Member Fashion accessories
## 197 Female 725-32-9708 B Mandalay Member Fashion accessories
## 198 Female 256-08-8343 A Yangon Normal Home and lifestyle
## 199 Female 372-26-1506 C Naypyitaw Normal Fashion accessories
## 200 Female 244-08-0162 B Mandalay Normal Health and beauty
## 201 Female 750-57-9686 C Naypyitaw Normal Home and lifestyle
## 202 Female 186-09-3669 C Naypyitaw Member Health and beauty
## 203 Female 848-07-1692 B Mandalay Normal Health and beauty
## 204 Female 745-71-3520 A Yangon Member Electronic accessories
## 205 Female 266-76-6436 C Naypyitaw Member Food and beverages
## 206 Female 740-22-2500 C Naypyitaw Normal Electronic accessories
## 208 Female 650-98-6268 B Mandalay Member Food and beverages
## 209 Female 325-77-6186 A Yangon Member Home and lifestyle
## 210 Female 459-50-7686 A Yangon Normal Electronic accessories
## 211 Female 837-55-7229 B Mandalay Normal Fashion accessories
## 212 Female 810-60-6344 C Naypyitaw Normal Electronic accessories
## 213 Female 394-30-3170 B Mandalay Member Sports and travel
## 214 Female 138-17-5109 A Yangon Member Home and lifestyle
## 215 Female 301-11-9629 A Yangon Normal Sports and travel
## 216 Female 390-80-5128 B Mandalay Member Health and beauty
## 217 Female 296-11-7041 B Mandalay Member Health and beauty
## 218 Female 449-27-2918 B Mandalay Member Sports and travel
## 219 Female 891-01-7034 B Mandalay Normal Electronic accessories
## 220 Female 727-17-0390 A Yangon Normal Food and beverages
## 221 Female 767-54-1907 B Mandalay Member Fashion accessories
## 222 Female 710-46-4433 B Mandalay Member Food and beverages
## 223 Female 325-90-8763 C Naypyitaw Member Electronic accessories
## 224 Female 234-03-4040 B Mandalay Member Food and beverages
## 225 Female 326-71-2155 C Naypyitaw Normal Sports and travel
## 226 Female 320-32-8842 C Naypyitaw Member Food and beverages
## 227 Female 878-30-2331 C Naypyitaw Member Sports and travel
## 228 Female 440-59-5691 C Naypyitaw Member Health and beauty
## 229 Female 233-34-0817 C Naypyitaw Member Electronic accessories
## 230 Female 767-05-1286 C Naypyitaw Member Home and lifestyle
## 231 Female 340-21-9136 A Yangon Member Sports and travel
## 232 Female 676-39-6028 A Yangon Member Electronic accessories
## 233 Female 485-30-8700 A Yangon Normal Sports and travel
## 234 Female 246-11-3901 C Naypyitaw Normal Electronic accessories
## 235 Female 493-65-6248 C Naypyitaw Member Sports and travel
## 236 Female 438-01-4015 B Mandalay Member Sports and travel
## 237 Female 709-58-4068 B Mandalay Normal Fashion accessories
## 238 Female 627-95-3243 B Mandalay Member Home and lifestyle
## 239 Female 686-41-0932 B Mandalay Normal Fashion accessories
## 240 Female 510-09-5628 A Yangon Member Fashion accessories
## 241 Female 608-04-3797 B Mandalay Member Health and beauty
## 242 Female 148-82-2527 C Naypyitaw Member Home and lifestyle
## 243 Female 556-97-7101 C Naypyitaw Normal Electronic accessories
## 244 Female 862-59-8517 C Naypyitaw Normal Food and beverages
## 245 Female 401-18-8016 B Mandalay Member Sports and travel
## 246 Female 420-18-8989 A Yangon Member Sports and travel
## 247 Female 573-98-8548 C Naypyitaw Member Fashion accessories
## 248 Female 282-35-2475 B Mandalay Normal Sports and travel
## 249 Female 387-49-4215 B Mandalay Member Sports and travel
## 250 Female 862-17-9201 B Mandalay Normal Food and beverages
## 251 Female 602-80-9671 C Naypyitaw Member Home and lifestyle
## 252 Female 347-72-6115 B Mandalay Member Sports and travel
## 253 Female 209-61-0206 A Yangon Normal Home and lifestyle
## 254 Female 595-27-4851 A Yangon Normal Fashion accessories
## 255 Female 413-20-6708 C Naypyitaw Member Fashion accessories
## 256 Female 734-91-1155 B Mandalay Normal Electronic accessories
## 257 Female 451-28-5717 C Naypyitaw Member Home and lifestyle
## 258 Female 609-81-8548 A Yangon Member Home and lifestyle
## 259 Female 719-89-8991 A Yangon Member Sports and travel
## 260 Female 827-44-5872 B Mandalay Member Food and beverages
## 261 Female 236-27-1144 C Naypyitaw Normal Food and beverages
## 262 Female 892-05-6689 A Yangon Normal Home and lifestyle
## 263 Female 339-12-4827 B Mandalay Member Fashion accessories
## 264 Female 308-81-0538 A Yangon Normal Fashion accessories
## 265 Female 358-88-9262 C Naypyitaw Member Food and beverages
## 266 Female 173-50-1108 B Mandalay Member Sports and travel
## 267 Female 841-18-8232 B Mandalay Normal Food and beverages
## 268 Female 647-50-1224 A Yangon Normal Fashion accessories
## 269 Female 539-21-7227 B Mandalay Normal Sports and travel
## 270 Female 213-32-1216 A Yangon Normal Electronic accessories
## 271 Female 582-52-8065 B Mandalay Normal Fashion accessories
## 272 Female 210-57-1719 B Mandalay Normal Health and beauty
## 273 Female 198-66-9832 B Mandalay Member Fashion accessories
## 275 Female 218-59-9410 A Yangon Member Home and lifestyle
## 276 Female 134-54-4720 B Mandalay Normal Electronic accessories
## 277 Female 698-98-5964 A Yangon Normal Food and beverages
## 278 Female 718-57-9773 C Naypyitaw Normal Sports and travel
## 279 Female 651-88-7328 A Yangon Normal Fashion accessories
## 280 Female 241-11-2261 B Mandalay Normal Fashion accessories
## 281 Female 408-26-9866 C Naypyitaw Normal Sports and travel
## 282 Female 834-83-1826 B Mandalay Member Home and lifestyle
## 283 Female 797-88-0493 A Yangon Normal Health and beauty
## 284 Female 443-82-0585 A Yangon Member Health and beauty
## 285 Female 339-18-7061 C Naypyitaw Member Fashion accessories
## 286 Female 359-90-3665 B Mandalay Member Fashion accessories
## 287 Female 278-86-2735 A Yangon Normal Food and beverages
## 288 Female 695-28-6250 A Yangon Normal Sports and travel
## 289 Female 788-07-8452 C Naypyitaw Member Home and lifestyle
## 290 Female 560-49-6611 A Yangon Member Sports and travel
## 291 Female 880-35-0356 A Yangon Member Sports and travel
## 292 Female 123-35-4896 C Naypyitaw Normal Sports and travel
## 293 Female 258-69-7810 C Naypyitaw Normal Fashion accessories
## 294 Female 334-64-2006 A Yangon Member Home and lifestyle
## 295 Female 881-41-7302 C Naypyitaw Normal Fashion accessories
## 296 Female 642-30-6693 B Mandalay Normal Sports and travel
## 297 Female 484-22-8230 C Naypyitaw Member Fashion accessories
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## 299 Female 544-32-5024 C Naypyitaw Member Food and beverages
## 300 Female 421-95-9805 A Yangon Normal Electronic accessories
## 301 Female 277-35-5865 C Naypyitaw Member Food and beverages
## 302 Female 509-29-3912 A Yangon Member Sports and travel
## 303 Female 641-96-3695 C Naypyitaw Member Fashion accessories
## 304 Female 420-97-3340 A Yangon Normal Food and beverages
## 305 Female 436-54-4512 A Yangon Member Food and beverages
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## 310 Female 318-81-2368 C Naypyitaw Normal Electronic accessories
## 311 Female 364-33-8584 B Mandalay Member Food and beverages
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## 316 Female 563-47-4072 B Mandalay Normal Health and beauty
## 317 Female 169-52-4504 A Yangon Normal Electronic accessories
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## 319 Female 562-12-5430 A Yangon Member Fashion accessories
## 320 Female 816-72-8853 A Yangon Member Sports and travel
## 321 Female 322-02-2271 B Mandalay Normal Sports and travel
## 322 Female 725-67-2480 B Mandalay Member Fashion accessories
## 323 Female 641-51-2661 C Naypyitaw Member Food and beverages
## 324 Female 714-02-3114 C Naypyitaw Normal Sports and travel
## 325 Female 518-17-2983 A Yangon Normal Fashion accessories
## 326 Female 190-14-3147 B Mandalay Normal Health and beauty
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## 328 Female 679-22-6530 B Mandalay Normal Sports and travel
## 329 Female 576-31-4774 B Mandalay Normal Health and beauty
## 330 Female 811-03-8790 A Yangon Normal Electronic accessories
## 331 Female 752-23-3760 B Mandalay Member Sports and travel
## 332 Female 274-05-5470 A Yangon Member Food and beverages
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## 334 Female 320-85-2052 B Mandalay Normal Sports and travel
## 335 Female 370-96-0655 C Naypyitaw Normal Fashion accessories
## 336 Female 510-79-0415 B Mandalay Member Sports and travel
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## 338 Female 767-97-4650 B Mandalay Member Sports and travel
## 339 Female 305-03-2383 A Yangon Normal Food and beverages
## 340 Female 394-55-6384 C Naypyitaw Member Sports and travel
## 341 Female 196-01-2849 C Naypyitaw Member Fashion accessories
## 342 Female 372-62-5264 C Naypyitaw Normal Food and beverages
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## 345 Female 626-43-7888 C Naypyitaw Normal Fashion accessories
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## 349 Female 728-88-7867 C Naypyitaw Member Home and lifestyle
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## 351 Female 268-20-3585 C Naypyitaw Normal Health and beauty
## 352 Female 258-92-7466 A Yangon Normal Health and beauty
## 353 Female 857-16-3520 A Yangon Member Fashion accessories
## 354 Female 821-14-9046 B Mandalay Member Fashion accessories
## 355 Female 418-05-0656 B Mandalay Normal Fashion accessories
## 356 Female 678-79-0726 C Naypyitaw Member Sports and travel
## 357 Female 592-46-1692 C Naypyitaw Member Food and beverages
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## 364 Female 390-17-5806 C Naypyitaw Member Food and beverages
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## 368 Female 585-86-8361 A Yangon Normal Food and beverages
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## 371 Female 652-43-6591 A Yangon Normal Fashion accessories
## 372 Female 785-96-0615 B Mandalay Member Electronic accessories
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## 374 Female 156-95-3964 A Yangon Normal Food and beverages
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## 376 Female 410-67-1709 A Yangon Member Fashion accessories
## 377 Female 587-73-4862 A Yangon Member Health and beauty
## 378 Female 593-14-4239 B Mandalay Normal Home and lifestyle
## 379 Female 801-88-0346 C Naypyitaw Normal Fashion accessories
## 380 Female 711-31-1234 B Mandalay Normal Electronic accessories
## 381 Female 886-54-6089 A Yangon Normal Home and lifestyle
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## 384 Female 201-63-8275 C Naypyitaw Member Sports and travel
## 385 Female 471-06-8611 C Naypyitaw Normal Food and beverages
## 386 Female 120-54-2248 B Mandalay Normal Food and beverages
## 387 Female 534-53-3526 A Yangon Normal Sports and travel
## 388 Female 307-04-2070 A Yangon Member Fashion accessories
## 389 Female 468-99-7231 C Naypyitaw Normal Home and lifestyle
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## 397 Female 759-29-9521 A Yangon Member Fashion accessories
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## 399 Female 220-68-6701 A Yangon Normal Home and lifestyle
## 400 Female 618-34-8551 A Yangon Normal Sports and travel
## 401 Female 257-60-7754 A Yangon Normal Electronic accessories
## 402 Female 559-61-5987 B Mandalay Normal Health and beauty
## 403 Female 189-55-2313 C Naypyitaw Normal Fashion accessories
## 404 Female 380-60-5336 A Yangon Normal Electronic accessories
## 405 Female 815-04-6282 C Naypyitaw Member Sports and travel
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## 407 Female 499-27-7781 B Mandalay Normal Food and beverages
## 408 Female 477-59-2456 C Naypyitaw Normal Fashion accessories
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## 412 Female 569-76-2760 A Yangon Member Sports and travel
## 413 Female 222-42-0244 B Mandalay Member Health and beauty
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## Unit.price Quantity Tax.5. Sales
## 1 74.69 7 261.4150 522.83
## 2 15.28 5 3.8200 76.40
## 3 68.84 6 20.6520 413.04
## 4 73.56 10 36.7800 735.60
## 5 36.26 2 3.6260 72.52
## 6 54.84 3 8.2260 164.52
## 7 14.48 4 2.8960 57.92
## 8 46.95 5 11.7375 234.75
## 9 71.38 10 35.6900 713.80
## 10 93.72 6 28.1160 562.32
## 11 68.93 7 241.2550 482.51
## 12 40.30 2 4.0300 80.60
## 13 52.59 8 21.0360 420.72
## 14 87.67 2 8.7670 175.34
## 15 88.36 5 22.0900 441.80
## 16 99.42 4 19.8840 397.68
## 17 68.12 1 3.4060 68.12
## 18 60.88 9 27.3960 547.92
## 19 54.92 8 21.9680 439.36
## 20 86.72 1 4.3360 86.72
## 21 69.12 6 20.7360 414.72
## 22 98.70 8 39.4800 789.60
## 23 93.96 4 18.7920 375.84
## 24 20.01 9 9.1945 180.09
## 25 82.63 10 41.3150 826.30
## 26 44.59 5 11.1475 222.95
## 27 17.87 4 3.5740 71.48
## 28 85.98 8 34.3920 687.84
## 29 72.35 10 36.1750 723.50
## 30 24.74 3 3.7110 74.22
## 31 55.07 9 247.8150 495.63
## 32 33.47 2 3.3470 66.94
## 33 97.61 6 29.2830 585.66
## 34 18.33 1 9.1650 18.33
## 35 48.52 3 7.2780 145.56
## 36 75.91 6 22.7730 455.46
## 37 41.65 10 20.8250 416.50
## 38 20.01 9 9.1945 180.09
## 39 78.31 10 39.1550 783.10
## 40 20.38 5 5.0950 101.90
## 41 99.19 6 29.7570 595.14
## 42 96.68 3 14.5020 290.04
## 43 80.36 4 16.0720 321.44
## 44 83.06 7 29.0710 581.42
## 45 76.99 6 23.0970 461.94
## 46 47.38 4 9.4760 189.52
## 47 44.86 10 22.4300 448.60
## 48 21.98 7 7.6930 153.86
## 49 12.45 6 3.7350 74.70
## 50 23.07 9 10.3815 207.63
## 51 33.98 9 15.2910 305.82
## 52 16.49 2 1.6490 32.98
## 53 98.21 3 147.3150 294.63
## 54 72.84 7 25.4940 509.88
## 55 80.79 9 363.5550 727.11
## 56 27.02 3 4.0530 81.06
## 57 10.96 10 5.4800 109.60
## 58 99.56 8 39.8240 796.48
## 59 56.47 8 22.5880 451.76
## 60 93.69 7 327.9150 655.83
## 61 32.25 5 8.0625 161.25
## 62 31.73 9 142.7850 285.57
## 63 68.54 8 27.4160 548.32
## 64 90.28 9 40.6260 812.52
## 65 39.62 7 13.8670 277.34
## 66 92.13 6 27.6390 552.78
## 67 34.84 4 6.9680 139.36
## 68 81.30 6 24.3900 487.80
## 69 26.31 5 6.5775 131.55
## 70 34.42 6 10.3260 206.52
## 71 89.80 10 44.9000 898.00
## 72 68.60 10 34.3000 686.00
## 73 30.41 1 1.5205 30.41
## 74 77.95 6 23.3850 467.70
## 75 46.26 6 13.8780 277.56
## 76 30.14 10 15.0700 301.40
## 77 91.54 4 18.3080 366.16
## 78 16.48 6 4.9440 98.88
## 79 80.97 8 32.3880 647.76
## 80 43.18 8 17.2720 345.44
## 81 22.51 7 7.8785 157.57
## 82 12.34 7 4.3190 86.38
## 83 94.49 8 37.7960 755.92
## 84 69.81 4 13.9620 279.24
## 85 77.04 3 11.5560 231.12
## 86 73.52 2 7.3520 147.04
## 87 87.80 9 39.5100 790.20
## 88 74.29 1 3.7145 74.29
## 89 25.29 1 1.2645 25.29
## 90 71.39 5 178.4750 356.95
## 91 19.15 6 5.7450 114.90
## 92 57.49 4 11.4980 229.96
## 93 23.03 9 10.3635 207.27
## 94 66.65 9 299.9250 599.85
## 95 28.53 10 14.2650 285.30
## 96 30.37 3 4.5555 91.11
## 97 99.73 9 448.7850 897.57
## 98 93.26 9 41.9670 839.34
## 99 29.61 7 10.3635 207.27
## 100 24.77 5 6.1925 123.85
## 101 94.64 3 14.1960 283.92
## 102 57.34 3 8.6010 172.02
## 103 12.54 1 627.0000 12.54
## 104 87.16 2 8.7160 174.32
## 105 90.70 6 27.2100 544.20
## 106 63.42 8 25.3680 507.36
## 107 81.37 2 8.1370 162.74
## 108 10.59 3 1.5885 31.77
## 109 84.09 9 378.4050 756.81
## 110 93.14 2 9.3140 186.28
## 111 44.22 5 11.0550 221.10
## 112 13.22 5 3.3050 66.10
## 113 81.40 3 12.2100 244.20
## 114 14.39 2 1.4390 28.78
## 115 75.06 9 33.7770 675.54
## 116 16.45 4 3.2900 65.80
## 117 38.30 4 7.6600 153.20
## 118 22.24 10 11.1200 222.40
## 119 98.40 7 34.4400 688.80
## 120 74.60 10 37.3000 746.00
## 121 35.54 10 17.7700 355.40
## 122 67.43 5 168.5750 337.15
## 123 21.12 2 2.1120 42.24
## 124 21.54 9 9.6930 193.86
## 125 12.03 2 1.2030 24.06
## 126 99.71 6 29.9130 598.26
## 127 21.82 10 10.9100 218.20
## 128 95.42 4 19.0840 381.68
## 129 69.96 8 27.9840 559.68
## 130 15.34 1 767.0000 15.34
## 131 47.67 4 9.5340 190.68
## 132 23.75 9 10.6875 213.75
## 133 48.51 7 169.7850 339.57
## 134 94.88 7 33.2080 664.16
## 135 62.48 1 3.1240 62.48
## 136 36.36 2 3.6360 72.72
## 137 51.92 5 12.9800 259.60
## 138 88.61 1 4.4305 88.61
## 139 51.19 4 10.2380 204.76
## 140 14.96 8 5.9840 119.68
## 141 40.23 7 140.8050 281.61
## 142 88.79 8 35.5160 710.32
## 143 26.48 3 3.9720 79.44
## 144 81.91 2 8.1910 163.82
## 145 14.23 5 3.5575 71.15
## 146 15.55 9 6.9975 139.95
## 147 78.13 10 39.0650 781.30
## 148 21.08 3 3.1620 63.24
## 149 29.67 7 10.3845 207.69
## 150 22.93 9 10.3185 206.37
## 151 39.42 1 1.9710 39.42
## 152 61.77 5 154.4250 308.85
## 153 28.45 5 7.1125 142.25
## 154 57.95 6 17.3850 347.70
## 155 47.65 3 7.1475 142.95
## 156 42.82 9 19.2690 385.38
## 157 55.97 7 195.8950 391.79
## 158 76.90 7 26.9150 538.30
## 159 97.03 5 242.5750 485.15
## 160 77.93 9 350.6850 701.37
## 161 89.25 8 35.7000 714.00
## 162 13.50 10 6.7500 135.00
## 164 54.73 7 191.5550 383.11
## 165 30.24 1 1.5120 30.24
## 166 89.14 4 17.8280 356.56
## 167 37.55 10 18.7750 375.50
## 169 94.47 8 37.7880 755.76
## 170 41.24 4 8.2480 164.96
## 171 81.68 4 16.3360 326.72
## 172 51.32 9 23.0940 461.88
## 173 14.36 10 7.1800 143.60
## 174 26.26 7 9.1910 183.82
## 175 60.96 2 6.0960 121.92
## 176 70.11 6 21.0330 420.66
## 177 67.09 5 167.7250 335.45
## 178 96.70 5 24.1750 483.50
## 179 35.38 9 15.9210 318.42
## 180 23.65 4 4.7300 94.60
## 181 26.61 2 2.6610 53.22
## 182 99.69 5 249.2250 498.45
## 183 74.89 4 14.9780 299.56
## 184 40.94 5 10.2350 204.70
## 185 32.32 10 16.1600 323.20
## 186 54.07 9 243.3150 486.63
## 187 80.48 3 12.0720 241.44
## 188 37.95 10 18.9750 379.50
## 189 52.26 10 26.1300 522.60
## 190 79.74 1 3.9870 79.74
## 191 77.50 5 19.3750 387.50
## 192 54.27 5 135.6750 271.35
## 193 41.06 6 12.3180 246.36
## 194 39.43 6 11.8290 236.58
## 195 39.75 5 9.9375 198.75
## 196 97.79 7 342.2650 684.53
## 197 68.71 4 13.7420 274.84
## 198 56.53 4 11.3060 226.12
## 199 23.82 5 5.9550 119.10
## 200 34.21 10 17.1050 342.10
## 201 45.38 4 9.0760 181.52
## 202 81.51 1 4.0755 81.51
## 203 57.22 2 5.7220 114.44
## 204 25.22 7 8.8270 176.54
## 205 38.60 3 5.7900 115.80
## 206 84.05 3 12.6075 252.15
## 208 20.87 3 3.1305 62.61
## 209 90.65 10 45.3250 906.50
## 210 23.46 6 7.0380 140.76
## 211 47.44 1 2.3720 47.44
## 212 40.86 8 16.3440 326.88
## 213 88.43 8 35.3720 707.44
## 214 89.21 9 401.4450 802.89
## 215 19.10 7 6.6850 133.70
## 216 19.15 1 9.5750 19.15
## 217 27.07 1 1.3535 27.07
## 218 39.12 1 1.9560 39.12
## 219 74.71 6 22.4130 448.26
## 220 63.61 5 159.0250 318.05
## 221 29.56 5 7.3900 147.80
## 222 77.40 9 34.8300 696.60
## 223 46.57 10 23.2850 465.70
## 224 73.05 10 36.5250 730.50
## 225 73.95 4 14.7900 295.80
## 226 22.62 1 1.1310 22.62
## 227 54.55 10 27.2750 545.50
## 228 37.15 7 130.0250 260.05
## 229 98.84 1 4.9420 98.84
## 230 83.77 6 25.1310 502.62
## 231 40.05 4 8.0100 160.20
## 232 64.44 5 16.1100 322.20
## 233 33.26 5 8.3150 166.30
## 234 32.80 10 16.4000 328.00
## 235 36.98 10 18.4900 369.80
## 236 49.49 4 9.8980 197.96
## 237 41.09 10 20.5450 410.90
## 238 77.68 9 34.9560 699.12
## 239 34.70 2 3.4700 69.40
## 240 19.66 10 9.8300 196.60
## 241 25.32 8 10.1280 202.56
## 242 12.12 10 6.0600 121.20
## 243 63.22 2 6.3220 126.44
## 244 90.24 6 27.0720 541.44
## 245 98.13 1 4.9065 98.13
## 246 51.52 8 20.6080 412.16
## 247 31.90 1 1.5950 31.90
## 248 93.31 2 9.3310 186.62
## 249 48.50 3 7.2750 145.50
## 250 84.05 6 25.2150 504.30
## 251 15.95 6 4.7850 95.70
## 252 90.74 7 31.7590 635.18
## 253 42.91 5 10.7275 214.55
## 254 54.28 7 18.9980 379.96
## 255 51.47 1 2.5735 51.47
## 256 45.71 3 6.8565 137.13
## 257 83.17 6 24.9510 499.02
## 258 37.44 6 11.2320 224.64
## 259 91.41 5 228.5250 457.05
## 260 54.36 10 27.1800 543.60
## 261 16.31 9 7.3395 146.79
## 262 28.32 5 7.0800 141.60
## 263 73.96 1 3.6980 73.96
## 264 73.05 4 14.6100 292.20
## 265 87.48 6 26.2440 524.88
## 266 20.18 4 4.0360 80.72
## 267 71.20 1 3.5600 71.20
## 268 29.42 10 14.7100 294.20
## 269 51.54 5 12.8850 257.70
## 270 66.06 6 19.8180 396.36
## 271 54.31 9 244.3950 488.79
## 272 58.24 9 26.2080 524.16
## 273 72.04 2 7.2040 144.08
## 275 72.42 3 10.8630 217.26
## 276 42.42 8 16.9680 339.36
## 277 81.21 10 40.6050 812.10
## 278 49.33 10 24.6650 493.30
## 279 65.74 9 29.5830 591.66
## 280 79.86 7 27.9510 559.02
## 281 73.98 7 25.8930 517.86
## 282 82.04 5 20.5100 410.20
## 283 64.27 4 12.8540 257.08
## 284 77.68 4 15.5360 310.72
## 285 92.98 2 9.2980 185.96
## 286 18.08 4 3.6160 72.32
## 287 52.34 3 7.8510 157.02
## 288 43.06 5 10.7650 215.30
## 289 24.24 7 8.4840 169.68
## 290 45.58 1 2.2790 45.58
## 291 75.20 3 11.2800 225.60
## 292 46.66 9 20.9970 419.94
## 293 36.85 5 9.2125 184.25
## 294 70.32 2 7.0320 140.64
## 295 64.99 1 3.2495 64.99
## 296 54.51 6 16.3530 327.06
## 297 51.89 7 181.6150 363.23
## 298 53.65 7 187.7750 375.55
## 299 49.79 4 9.9580 199.16
## 300 28.96 1 1.4480 28.96
## 301 98.97 9 445.3650 890.73
## 302 38.72 9 17.4240 348.48
## 303 43.46 6 13.0380 260.76
## 304 71.68 3 10.7520 215.04
## 305 91.61 1 4.5805 91.61
## 306 94.59 7 331.0650 662.13
## 307 83.25 10 41.6250 832.50
## 308 78.88 2 7.8880 157.76
## 309 12.09 1 6.0450 12.09
## 310 46.20 1 2.3100 46.20
## 311 17.63 5 4.4075 88.15
## 312 98.79 3 148.1850 296.37
## 313 88.55 8 35.4200 708.40
## 314 72.52 8 29.0080 580.16
## 315 15.49 2 1.5490 30.98
## 316 55.81 6 16.7430 334.86
## 317 15.69 3 2.3535 47.07
## 318 99.69 1 4.9845 99.69
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## 850 21.48 2 2.1480 42.96
## 851 63.56 10 31.7800 635.60
## 852 72.88 2 7.2880 145.76
## 853 55.04 7 19.2640 385.28
## 854 48.63 10 24.3150 486.30
## 855 62.19 4 12.4380 248.76
## 856 69.58 9 31.3110 626.22
## 858 32.32 3 4.8480 96.96
## 859 80.47 9 362.1150 724.23
## 860 71.77 7 251.1950 502.39
## 861 68.98 1 3.4490 68.98
## 862 15.62 8 6.2480 124.96
## 863 25.70 3 3.8550 77.10
## 864 80.62 6 24.1860 483.72
## 865 98.70 8 39.4800 789.60
## 866 11.94 3 1.7910 35.82
## 867 45.38 3 6.8070 136.14
## 868 44.12 3 6.6180 132.36
## 869 23.34 4 4.6680 93.36
## 870 55.57 3 8.3355 166.71
## 871 69.74 10 34.8700 697.40
## 872 97.26 4 19.4520 389.04
## 873 56.00 3 8.4000 168.00
## 874 19.70 1 985.0000 19.70
## 875 75.88 7 26.5580 531.16
## 876 53.72 1 2.6860 53.72
## 877 81.95 10 40.9750 819.50
## 878 58.76 10 29.3800 587.60
## 879 91.56 8 36.6240 732.48
## 880 93.96 9 42.2820 845.64
## 881 55.61 7 194.6350 389.27
## 882 84.83 1 4.2415 84.83
## 883 37.69 2 3.7690 75.38
## 884 65.23 10 32.6150 652.30
## 885 81.23 7 284.3050 568.61
## 886 73.28 5 18.3200 366.40
## 887 18.85 10 9.4250 188.50
## 888 72.13 10 36.0650 721.30
## 889 55.50 4 11.1000 222.00
## 890 13.69 6 4.1070 82.14
## 891 65.65 2 6.5650 131.30
## 892 65.31 7 228.5850 457.17
## 893 93.38 1 4.6690 93.38
## 894 25.25 5 6.3125 126.25
## 895 87.87 9 395.4150 790.83
## 896 21.80 8 8.7200 174.40
## 897 74.58 7 26.1030 522.06
## 898 71.89 8 28.7560 575.12
## 899 60.47 3 9.0705 181.41
## 900 58.91 7 206.1850 412.37
## 901 46.41 1 2.3205 46.41
## 902 68.55 4 13.7100 274.20
## 903 92.60 7 32.4100 648.20
## 904 27.18 2 2.7180 54.36
## 905 92.78 1 4.6390 92.78
## 906 86.69 5 216.7250 433.45
## 907 23.01 6 6.9030 138.06
## 908 67.39 7 235.8650 471.73
## 909 10.75 8 4.3000 86.00
## 910 95.15 1 4.7575 95.15
## 911 33.88 8 13.5520 271.04
## 912 96.16 4 19.2320 384.64
## 913 47.16 5 11.7900 235.80
## 914 52.89 4 10.5780 211.56
## 915 10.17 1 5.0850 10.17
## 916 41.28 3 6.1920 123.84
## 917 64.95 10 32.4750 649.50
## 918 10.56 8 4.2240 84.48
## 919 62.57 4 12.5140 250.28
## 920 91.30 1 4.5650 91.30
## 921 52.38 1 2.6190 52.38
## 922 38.54 5 9.6350 192.70
## 923 44.63 6 13.3890 267.78
## 924 55.87 10 27.9350 558.70
## 925 51.94 3 7.7910 155.82
## 926 60.30 1 3.0150 60.30
## 927 21.32 1 1.0660 21.32
## 928 93.78 3 14.0670 281.34
## 929 73.26 1 3.6630 73.26
## 930 74.10 1 3.7050 74.10
## 931 53.19 7 186.1650 372.33
## 932 21.12 8 8.4480 168.96
## 933 57.59 6 17.2770 345.54
## 934 12.76 2 1.2760 25.52
## 935 33.81 3 5.0715 101.43
## 936 90.53 8 36.2120 724.24
## 937 24.31 3 3.6465 72.93
## 938 64.59 4 12.9180 258.36
## 939 24.82 7 8.6870 173.74
## 940 56.50 1 2.8250 56.50
## 941 89.06 6 26.7180 534.36
## 942 23.29 4 4.6580 93.16
## 943 65.26 8 26.1040 522.08
## 944 52.35 1 2.6175 52.35
## 945 39.75 1 1.9875 39.75
## 946 31.99 10 15.9950 319.90
## 947 45.58 7 15.9530 319.06
## 948 87.90 1 4.3950 87.90
## 949 76.92 10 38.4600 769.20
## 950 28.38 5 7.0950 141.90
## 951 50.45 6 15.1350 302.70
## 952 99.16 8 39.6640 793.28
## 953 60.74 7 21.2590 425.18
## 954 85.60 7 29.9600 599.20
## 955 35.04 9 15.7680 315.36
## 956 45.97 4 9.1940 183.88
## 957 11.53 7 4.0355 80.71
## 958 84.61 10 42.3050 846.10
## 959 51.34 8 20.5360 410.72
## 960 42.85 1 2.1425 42.85
## 961 68.97 3 10.3455 206.91
## 962 88.31 1 4.4155 88.31
## 963 25.31 2 2.5310 50.62
## 964 99.92 6 29.9760 599.52
## 965 64.08 7 22.4280 448.56
## 966 85.72 3 12.8580 257.16
## 967 66.52 4 13.3040 266.08
## 968 99.82 9 44.9190 898.38
## 969 50.79 5 12.6975 253.95
## 970 10.08 7 3.5280 70.56
## 971 84.25 2 8.4250 168.50
## 972 53.78 1 2.6890 53.78
## 973 35.81 5 8.9525 179.05
## 974 39.91 3 5.9865 119.73
## 975 65.91 6 19.7730 395.46
## 976 50.49 9 227.2050 454.41
## 977 46.02 6 13.8060 276.12
## 978 91.98 1 4.5990 91.98
## 979 20.89 2 2.0890 41.78
## 980 96.82 3 14.5230 290.46
## 981 33.33 2 3.3330 66.66
## 982 81.01 3 12.1515 243.03
## 983 36.91 7 12.9185 258.37
## 984 87.08 7 30.4780 609.56
## 985 80.08 3 12.0120 240.24
## 986 86.13 2 8.6130 172.26
## 987 49.92 2 4.9920 99.84
## 988 26.60 6 7.9800 159.60
## 989 59.59 4 11.9180 238.36
## 990 58.15 4 11.6300 232.60
## 991 99.96 7 34.9860 699.72
## 992 96.37 7 337.2950 674.59
## 993 62.00 8 24.8000 496.00
## 994 82.34 10 41.1700 823.40
## 995 75.37 8 30.1480 602.96
## 996 58.03 2 5.8030 116.06
## 997 17.49 10 8.7450 174.90
## 998 40.35 1 2.0175 40.35
## 999 31.84 1 1.5920 31.84
## 1000 65.82 1 3.2910 65.82
boxplot(data_clean$Sales)
pacf(data_clean$Sales)
acf(data_clean$Sales)
# Modelling using garch model.
model_1 <- garchFit(formula = ~garch(1,1), data = sales, trace = F); model_1
##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~garch(1, 1), data = sales, trace = F)
##
## Mean and Variance Equation:
## data ~ garch(1, 1)
## <environment: 0x0000021bb0631108>
## [data = sales]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu omega alpha1 beta1
## 3.0704e+02 2.3472e+03 6.5592e-03 9.5053e-01
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu 3.070e+02 7.437e+00 41.286 <2e-16 ***
## omega 2.347e+03 2.244e+03 1.046 0.296
## alpha1 6.559e-03 1.010e-02 0.649 0.516
## beta1 9.505e-01 4.289e-02 22.164 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## -6874.28 normalized: -6.87428
##
## Description:
## Wed May 7 17:50:49 2025 by user: Administrator
model_2 <- garchFit(formula = ~garch(1,0), data = sales, trace = F); model_2
##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~garch(1, 0), data = sales, trace = F)
##
## Mean and Variance Equation:
## data ~ garch(1, 0)
## <environment: 0x0000021baf973fb8>
## [data = sales]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu omega alpha1
## 3.0759e+02 5.4782e+04 3.1829e-05
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu 3.076e+02 7.403e+00 41.547 <2e-16 ***
## omega 5.478e+04 2.954e+03 18.542 <2e-16 ***
## alpha1 3.183e-05 3.014e-02 0.001 0.999
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## -6874.513 normalized: -6.874513
##
## Description:
## Wed May 7 17:50:50 2025 by user: Administrator
model_3 <- garchFit(formula = ~garch(2,1), data = sales, trace = F); model_3
##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~garch(2, 1), data = sales, trace = F)
##
## Mean and Variance Equation:
## data ~ garch(2, 1)
## <environment: 0x0000021ba86a3890>
## [data = sales]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu omega alpha1 alpha2 beta1
## 3.0700e+02 2.8958e+03 1.0000e-08 8.4130e-03 9.3867e-01
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu 3.070e+02 7.437e+00 41.282 <2e-16 ***
## omega 2.896e+03 3.454e+03 0.838 0.402
## alpha1 1.000e-08 3.095e-02 0.000 1.000
## alpha2 8.413e-03 3.225e-02 0.261 0.794
## beta1 9.387e-01 6.694e-02 14.023 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## -6874.231 normalized: -6.874231
##
## Description:
## Wed May 7 17:50:50 2025 by user: Administrator
model_4 <- garchFit(formula = ~garch(2,2), data = sales, trace = F); model_4
## Warning in sqrt(diag(fit$cvar)): NaNs produced
##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~garch(2, 2), data = sales, trace = F)
##
## Mean and Variance Equation:
## data ~ garch(2, 2)
## <environment: 0x0000021bafcb3040>
## [data = sales]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu omega alpha1 alpha2 beta1 beta2
## 3.0727e+02 3.1120e+03 1.0000e-08 1.2441e-02 1.0000e-08 9.3057e-01
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu 3.073e+02 7.423e+00 41.394 < 2e-16 ***
## omega 3.112e+03 3.242e+03 0.960 0.337
## alpha1 1.000e-08 NaN NaN NaN
## alpha2 1.244e-02 1.755e-03 7.088 1.36e-12 ***
## beta1 1.000e-08 NaN NaN NaN
## beta2 9.306e-01 NaN NaN NaN
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## -6873.81 normalized: -6.87381
##
## Description:
## Wed May 7 17:50:50 2025 by user: Administrator
model_5 <- garchFit(formula = ~garch(1,2), data = sales, trace = F); model_5
##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~garch(1, 2), data = sales, trace = F)
##
## Mean and Variance Equation:
## data ~ garch(1, 2)
## <environment: 0x0000021ba687fe68>
## [data = sales]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu omega alpha1 beta1 beta2
## 3.0704e+02 2.3353e+03 6.5565e-03 9.5074e-01 1.0000e-08
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu 3.070e+02 7.438e+00 41.282 <2e-16 ***
## omega 2.335e+03 2.256e+03 1.035 0.301
## alpha1 6.557e-03 1.255e-02 0.522 0.601
## beta1 9.507e-01 3.915e+00 0.243 0.808
## beta2 1.000e-08 3.900e+00 0.000 1.000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## -6874.279 normalized: -6.874279
##
## Description:
## Wed May 7 17:50:50 2025 by user: Administrator
summary(model_1) # AIC = 13.75656 **
##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~garch(1, 1), data = sales, trace = F)
##
## Mean and Variance Equation:
## data ~ garch(1, 1)
## <environment: 0x0000021bb0631108>
## [data = sales]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu omega alpha1 beta1
## 3.0704e+02 2.3472e+03 6.5592e-03 9.5053e-01
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu 3.070e+02 7.437e+00 41.286 <2e-16 ***
## omega 2.347e+03 2.244e+03 1.046 0.296
## alpha1 6.559e-03 1.010e-02 0.649 0.516
## beta1 9.505e-01 4.289e-02 22.164 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## -6874.28 normalized: -6.87428
##
## Description:
## Wed May 7 17:50:49 2025 by user: Administrator
##
##
## Standardised Residuals Tests:
## Statistic p-Value
## Jarque-Bera Test R Chi^2 132.2638357 0.0000000
## Shapiro-Wilk Test R W 0.9090713 0.0000000
## Ljung-Box Test R Q(10) 11.2074753 0.3415840
## Ljung-Box Test R Q(15) 15.2634071 0.4326152
## Ljung-Box Test R Q(20) 16.4030459 0.6913262
## Ljung-Box Test R^2 Q(10) 13.6386024 0.1901233
## Ljung-Box Test R^2 Q(15) 16.1769402 0.3703906
## Ljung-Box Test R^2 Q(20) 21.7162724 0.3561028
## LM Arch Test R TR^2 14.3027783 0.2817928
##
## Information Criterion Statistics:
## AIC BIC SIC HQIC
## 13.75656 13.77619 13.75653 13.76402
summary(model_2) # AIC = 13.75503 * -least AIC
##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~garch(1, 0), data = sales, trace = F)
##
## Mean and Variance Equation:
## data ~ garch(1, 0)
## <environment: 0x0000021baf973fb8>
## [data = sales]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu omega alpha1
## 3.0759e+02 5.4782e+04 3.1829e-05
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu 3.076e+02 7.403e+00 41.547 <2e-16 ***
## omega 5.478e+04 2.954e+03 18.542 <2e-16 ***
## alpha1 3.183e-05 3.014e-02 0.001 0.999
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## -6874.513 normalized: -6.874513
##
## Description:
## Wed May 7 17:50:50 2025 by user: Administrator
##
##
## Standardised Residuals Tests:
## Statistic p-Value
## Jarque-Bera Test R Chi^2 132.69957 0.0000000
## Shapiro-Wilk Test R W 0.90876 0.0000000
## Ljung-Box Test R Q(10) 11.44954 0.3235827
## Ljung-Box Test R Q(15) 15.64770 0.4058440
## Ljung-Box Test R Q(20) 16.80830 0.6653842
## Ljung-Box Test R^2 Q(10) 14.68733 0.1438838
## Ljung-Box Test R^2 Q(15) 17.31148 0.3005876
## Ljung-Box Test R^2 Q(20) 22.86667 0.2953889
## LM Arch Test R TR^2 15.41636 0.2194525
##
## Information Criterion Statistics:
## AIC BIC SIC HQIC
## 13.75503 13.76975 13.75501 13.76062
summary(model_3) # AIC = 13.75846 ***
##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~garch(2, 1), data = sales, trace = F)
##
## Mean and Variance Equation:
## data ~ garch(2, 1)
## <environment: 0x0000021ba86a3890>
## [data = sales]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu omega alpha1 alpha2 beta1
## 3.0700e+02 2.8958e+03 1.0000e-08 8.4130e-03 9.3867e-01
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu 3.070e+02 7.437e+00 41.282 <2e-16 ***
## omega 2.896e+03 3.454e+03 0.838 0.402
## alpha1 1.000e-08 3.095e-02 0.000 1.000
## alpha2 8.413e-03 3.225e-02 0.261 0.794
## beta1 9.387e-01 6.694e-02 14.023 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## -6874.231 normalized: -6.874231
##
## Description:
## Wed May 7 17:50:50 2025 by user: Administrator
##
##
## Standardised Residuals Tests:
## Statistic p-Value
## Jarque-Bera Test R Chi^2 132.5221631 0.0000000
## Shapiro-Wilk Test R W 0.9089859 0.0000000
## Ljung-Box Test R Q(10) 11.1966170 0.3424064
## Ljung-Box Test R Q(15) 15.2042237 0.4368091
## Ljung-Box Test R Q(20) 16.3230319 0.6963925
## Ljung-Box Test R^2 Q(10) 13.3143288 0.2066244
## Ljung-Box Test R^2 Q(15) 15.9548990 0.3850554
## Ljung-Box Test R^2 Q(20) 21.4389681 0.3717123
## LM Arch Test R TR^2 13.9074370 0.3066582
##
## Information Criterion Statistics:
## AIC BIC SIC HQIC
## 13.75846 13.78300 13.75841 13.76779
summary(model_4) # AIC = 13.75962 ***** - highest AIC
##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~garch(2, 2), data = sales, trace = F)
##
## Mean and Variance Equation:
## data ~ garch(2, 2)
## <environment: 0x0000021bafcb3040>
## [data = sales]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu omega alpha1 alpha2 beta1 beta2
## 3.0727e+02 3.1120e+03 1.0000e-08 1.2441e-02 1.0000e-08 9.3057e-01
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu 3.073e+02 7.423e+00 41.394 < 2e-16 ***
## omega 3.112e+03 3.242e+03 0.960 0.337
## alpha1 1.000e-08 NaN NaN NaN
## alpha2 1.244e-02 1.755e-03 7.088 1.36e-12 ***
## beta1 1.000e-08 NaN NaN NaN
## beta2 9.306e-01 NaN NaN NaN
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## -6873.81 normalized: -6.87381
##
## Description:
## Wed May 7 17:50:50 2025 by user: Administrator
##
##
## Standardised Residuals Tests:
## Statistic p-Value
## Jarque-Bera Test R Chi^2 131.4401826 0.0000000
## Shapiro-Wilk Test R W 0.9096346 0.0000000
## Ljung-Box Test R Q(10) 11.3797540 0.3287068
## Ljung-Box Test R Q(15) 15.4002409 0.4229897
## Ljung-Box Test R Q(20) 16.4875445 0.6859546
## Ljung-Box Test R^2 Q(10) 10.8549220 0.3689321
## Ljung-Box Test R^2 Q(15) 13.4400930 0.5683452
## Ljung-Box Test R^2 Q(20) 19.1212070 0.5139604
## LM Arch Test R TR^2 11.5537987 0.4821461
##
## Information Criterion Statistics:
## AIC BIC SIC HQIC
## 13.75962 13.78907 13.75955 13.77081
summary(model_5) # AIC = 13.75856 ****
##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~garch(1, 2), data = sales, trace = F)
##
## Mean and Variance Equation:
## data ~ garch(1, 2)
## <environment: 0x0000021ba687fe68>
## [data = sales]
##
## Conditional Distribution:
## norm
##
## Coefficient(s):
## mu omega alpha1 beta1 beta2
## 3.0704e+02 2.3353e+03 6.5565e-03 9.5074e-01 1.0000e-08
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu 3.070e+02 7.438e+00 41.282 <2e-16 ***
## omega 2.335e+03 2.256e+03 1.035 0.301
## alpha1 6.557e-03 1.255e-02 0.522 0.601
## beta1 9.507e-01 3.915e+00 0.243 0.808
## beta2 1.000e-08 3.900e+00 0.000 1.000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## -6874.279 normalized: -6.874279
##
## Description:
## Wed May 7 17:50:50 2025 by user: Administrator
##
##
## Standardised Residuals Tests:
## Statistic p-Value
## Jarque-Bera Test R Chi^2 132.2637328 0.0000000
## Shapiro-Wilk Test R W 0.9090745 0.0000000
## Ljung-Box Test R Q(10) 11.2065380 0.3416549
## Ljung-Box Test R Q(15) 15.2626026 0.4326721
## Ljung-Box Test R Q(20) 16.4021060 0.6913859
## Ljung-Box Test R^2 Q(10) 13.6401550 0.1900469
## Ljung-Box Test R^2 Q(15) 16.1790656 0.3702517
## Ljung-Box Test R^2 Q(20) 21.7191580 0.3559423
## LM Arch Test R TR^2 14.3038753 0.2817258
##
## Information Criterion Statistics:
## AIC BIC SIC HQIC
## 13.75856 13.78310 13.75851 13.76788
## Forecasting.
# variance models- gjrgarch, sgarch, egarch,
# distribution models - ged, std, norm
m1 <- ugarchspec(variance.model = list(model="gjrGARCH",garchOrder= c(1,1)),
mean.model = list(armaOrder= c(1,1),include.mean=F),
distribution.model= "norm");m1 # optimal model
##
## *---------------------------------*
## * GARCH Model Spec *
## *---------------------------------*
##
## Conditional Variance Dynamics
## ------------------------------------
## GARCH Model : gjrGARCH(1,1)
## Variance Targeting : FALSE
##
## Conditional Mean Dynamics
## ------------------------------------
## Mean Model : ARFIMA(1,0,1)
## Include Mean : FALSE
## GARCH-in-Mean : FALSE
##
## Conditional Distribution
## ------------------------------------
## Distribution : norm
## Includes Skew : FALSE
## Includes Shape : FALSE
## Includes Lambda : FALSE
m1fit <- ugarchfit(data=sales , spec = m1); m1fit
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(1,0,1)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## ar1 0.999463 0.000015 65987.0886 0
## ma1 -0.956083 0.004655 -205.3694 0
## omega 382.599397 5.792923 66.0460 0
## alpha1 0.000197 0.000032 6.2635 0
## beta1 1.000000 0.000003 337347.4495 0
## gamma1 -0.021702 0.000842 -25.7836 0
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## ar1 0.999463 0.000006 159558.4149 0
## ma1 -0.956083 0.003733 -256.1449 0
## omega 382.599397 8.854180 43.2112 0
## alpha1 0.000197 0.000026 7.4548 0
## beta1 1.000000 0.000001 821135.4905 0
## gamma1 -0.021702 0.000909 -23.8670 0
##
## LogLikelihood : -6889.597
##
## Information Criteria
## ------------------------------------
##
## Akaike 13.791
## Bayes 13.821
## Shibata 13.791
## Hannan-Quinn 13.802
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.2116 0.6455
## Lag[2*(p+q)+(p+q)-1][5] 2.9347 0.5134
## Lag[4*(p+q)+(p+q)-1][9] 4.9948 0.4548
## d.o.f=2
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.4808 0.4881
## Lag[2*(p+q)+(p+q)-1][5] 1.1363 0.8281
## Lag[4*(p+q)+(p+q)-1][9] 8.5698 0.0994
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.3789 0.500 2.000 0.53821
## ARCH Lag[5] 1.2002 1.440 1.667 0.67458
## ARCH Lag[7] 10.0638 2.315 1.543 0.01779
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 4.3664
## Individual Statistics:
## ar1 0.08956
## ma1 0.28628
## omega 0.08263
## alpha1 0.08582
## beta1 0.08874
## gamma1 0.08550
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.49 1.68 2.12
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.5144 0.6071
## Negative Sign Bias 0.4312 0.6664
## Positive Sign Bias 0.4506 0.6524
## Joint Effect 1.1611 0.7624
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 307.5 5.850e-54
## 2 30 342.5 2.838e-55
## 3 40 347.8 3.308e-51
## 4 50 364.0 1.070e-49
##
##
## Elapsed time : 0.5322881
summary(m1)
## Length Class Mode
## 1 uGARCHspec S4
# AIC = 13.797, sgarch,(1,1),ged **
# AIC = 13.799, sgarch,(1,2),ged
# AIC = 13.800, sgarch,(2, 1),ged
# AIC = 13.800 sgarch, (2,2) ,ged
# AIC = 13.793, gjrgarch,(1, 1),std **
# AIC = 14.077, gjrgarch,(2, 0),std
# AIC = 13.803, gjrgarch,(2, 1),std
# AIC = 13.796, gjrgarch,(2, 1), norm
# AIC = 13.791, gjrgarch,(1, 1), norm **
## Forecsting.
forecast <- ugarchforecast(m1fit, n.ahead = 60); forecast
##
## *------------------------------------*
## * GARCH Model Forecast *
## *------------------------------------*
## Model: gjrGARCH
## Horizon: 60
## Roll Steps: 0
## Out of Sample: 0
##
## 0-roll forecast [T0=1972-09-27]:
## Series Sigma
## T+1 283.6 230.3
## T+2 283.4 229.9
## T+3 283.3 229.5
## T+4 283.1 229.1
## T+5 283.0 228.7
## T+6 282.8 228.3
## T+7 282.7 228.0
## T+8 282.5 227.6
## T+9 282.4 227.2
## T+10 282.2 226.8
## T+11 282.1 226.5
## T+12 281.9 226.1
## T+13 281.8 225.8
## T+14 281.6 225.4
## T+15 281.5 225.1
## T+16 281.3 224.7
## T+17 281.2 224.4
## T+18 281.0 224.0
## T+19 280.8 223.7
## T+20 280.7 223.3
## T+21 280.5 223.0
## T+22 280.4 222.7
## T+23 280.2 222.3
## T+24 280.1 222.0
## T+25 279.9 221.7
## T+26 279.8 221.4
## T+27 279.6 221.1
## T+28 279.5 220.8
## T+29 279.3 220.4
## T+30 279.2 220.1
## T+31 279.0 219.8
## T+32 278.9 219.5
## T+33 278.7 219.2
## T+34 278.6 218.9
## T+35 278.4 218.6
## T+36 278.3 218.4
## T+37 278.1 218.1
## T+38 278.0 217.8
## T+39 277.9 217.5
## T+40 277.7 217.2
## T+41 277.6 216.9
## T+42 277.4 216.7
## T+43 277.3 216.4
## T+44 277.1 216.1
## T+45 277.0 215.9
## T+46 276.8 215.6
## T+47 276.7 215.3
## T+48 276.5 215.1
## T+49 276.4 214.8
## T+50 276.2 214.6
## T+51 276.1 214.3
## T+52 275.9 214.1
## T+53 275.8 213.8
## T+54 275.6 213.6
## T+55 275.5 213.3
## T+56 275.3 213.1
## T+57 275.2 212.9
## T+58 275.0 212.6
## T+59 274.9 212.4
## T+60 274.7 212.2
forc1 <- ugarchforecast(m1fit, n.ahead = 60, method= c("Partial", "Full")[1]); forc1
##
## *------------------------------------*
## * GARCH Model Forecast *
## *------------------------------------*
## Model: gjrGARCH
## Horizon: 60
## Roll Steps: 0
## Out of Sample: 0
##
## 0-roll forecast [T0=1972-09-27]:
## Series Sigma
## T+1 283.6 230.3
## T+2 283.4 229.9
## T+3 283.3 229.5
## T+4 283.1 229.1
## T+5 283.0 228.7
## T+6 282.8 228.3
## T+7 282.7 228.0
## T+8 282.5 227.6
## T+9 282.4 227.2
## T+10 282.2 226.8
## T+11 282.1 226.5
## T+12 281.9 226.1
## T+13 281.8 225.8
## T+14 281.6 225.4
## T+15 281.5 225.1
## T+16 281.3 224.7
## T+17 281.2 224.4
## T+18 281.0 224.0
## T+19 280.8 223.7
## T+20 280.7 223.3
## T+21 280.5 223.0
## T+22 280.4 222.7
## T+23 280.2 222.3
## T+24 280.1 222.0
## T+25 279.9 221.7
## T+26 279.8 221.4
## T+27 279.6 221.1
## T+28 279.5 220.8
## T+29 279.3 220.4
## T+30 279.2 220.1
## T+31 279.0 219.8
## T+32 278.9 219.5
## T+33 278.7 219.2
## T+34 278.6 218.9
## T+35 278.4 218.6
## T+36 278.3 218.4
## T+37 278.1 218.1
## T+38 278.0 217.8
## T+39 277.9 217.5
## T+40 277.7 217.2
## T+41 277.6 216.9
## T+42 277.4 216.7
## T+43 277.3 216.4
## T+44 277.1 216.1
## T+45 277.0 215.9
## T+46 276.8 215.6
## T+47 276.7 215.3
## T+48 276.5 215.1
## T+49 276.4 214.8
## T+50 276.2 214.6
## T+51 276.1 214.3
## T+52 275.9 214.1
## T+53 275.8 213.8
## T+54 275.6 213.6
## T+55 275.5 213.3
## T+56 275.3 213.1
## T+57 275.2 212.9
## T+58 275.0 212.6
## T+59 274.9 212.4
## T+60 274.7 212.2
## visualizing the prediction
plot(forecast, which = 1)
plot(forecast, which = 3)
plot(forc1, which = 1)
plot(forc1, which = 3)
## Survival Model Analysis.
# using the rats data on our notes.
d1 <- data.frame(time=c(3, 4, 6, 11, 17, 21, 24, 25, 26, 30),
event=c(1, 1, 0, 0, 0, 1, 0, 0, 1, 0)); d1
## time event
## 1 3 1
## 2 4 1
## 3 6 0
## 4 11 0
## 5 17 0
## 6 21 1
## 7 24 0
## 8 25 0
## 9 26 1
## 10 30 0
kaplan_m_curv <- with(d1, Surv(time, event)); kaplan_m_curv
## [1] 3 4 6+ 11+ 17+ 21 24+ 25+ 26 30+
summary(kaplan_m_curv)
## time status
## Min. : 3.00 Min. :0.0
## 1st Qu.: 7.25 1st Qu.:0.0
## Median :19.00 Median :0.0
## Mean :16.70 Mean :0.4
## 3rd Qu.:24.75 3rd Qu.:1.0
## Max. :30.00 Max. :1.0
plot(kaplan_m_curv) # the vertical axis indicates the survival probabilities.
plot(kaplan_m_curv, fun="cumhaz")
