Statystyczne modelowanie decyzji biznesowych
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w darmowym pakiecie R
Projekt „Nowa oferta edukacyjna Uniwersytetu Wrocławskiego odpowiedzią na współczesne potrzeby rynku pracy i gospodarki opartej na wiedzy”
Dane:
Eksploracja (mining)
Relacje między parami zmiennych
filled.contour(volcano, color.palette = terrain.colors, asp = 1)
title(main = "volcano data: filled contour map")
100 120 140 160 180
0.0 0.2 0.4 0.6 0.8 1.0 0.0
0.2 0.4 0.6 0.8 1.0
volcano data: filled contour map
Statystyczne modelowanie decyzji biznesowych
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w darmowym pakiecie R
plot(sales~marketvalue,pch=".")
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marketvalue
s a le s
Statystyczne modelowanie decyzji biznesowych
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w darmowym pakiecie R
hist(marketvalue) hist(log(marketvalue))
Histogram of log(marketvalue)
log(marketvalue)
F re q u e n c y
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Statystyczne modelowanie decyzji biznesowych
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w darmowym pakiecie R
plot(log(sales)~log(marketvalue),pch=".")
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log(marketvalue)
lo g (s a le s )
Statystyczne modelowanie decyzji biznesowych
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w darmowym pakiecie R
plot(log(sales)~log(marketvalue),col=rgb(0,0,0,0.1),pch=16)
Statystyczne modelowanie decyzji biznesowych
6
w darmowym pakiecie R
Drabina Tukeya
ladderTukey <- function(x,y){
qy <- fivenum(y)[1:3];qx <- fivenum(x)[1:3]
b1 <- (qy[2]-qy[1])/(qx[2]-qx[1]) b2 <- (qy[3]-qy[2])/(qx[3]-qx[2]) blad <- (b1-b2)/(b1+b2)
c(blad,b1,b2) }
ladderTukey(marketvalue,sales) -0.1313034 0.7425926 0.9670782
ladderTukey(marketvalue,log(sales)) 0.7213510 1.9651060 0.3181076
ladderTukey(log(marketvalue),log(sales)) -0.05713144 1.08002423 1.21090852
summary(lm(log(sales)~log(marketvalue)))
Call:
lm(formula = log(sales) ~ log(marketvalue)) Residuals:
Min 1Q Median 3Q Max -4.8400 -0.7255 0.0232 0.6890 3.9379 Coefficients:
Estimate Std. Error t value Pr(>|t|) (Intercept) 0.51153 0.03946 12.96 <2e-16 ***
log(marketvalue) 0.57885 0.01907 30.35 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 1.018 on 1998 degrees of freedom
Multiple R-squared: 0.3155, Adjusted R-squared: 0.3152 F-statistic: 920.9 on 1 and 1998 DF, p-value: < 2.2e-16
Statystyczne modelowanie decyzji biznesowych
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w darmowym pakiecie R
library(MASS)
plot(log(marketvalue),log(sales))
abline(coefficients(lm(log(sales)~log(marketvalue))),col="red") abline(coefficients(rlm(log(sales)~log(marketvalue))),col="blue")
lines(lowess(x = log(marketvalue), y = log(sales)), col = "green", lwd = 1)
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log(marketvalue)
lo g (s a le s )
Statystyczne modelowanie decyzji biznesowych
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w darmowym pakiecie R
library(calibrate)
orderProfits <- rev(order(profits)) profits50 <- profits[orderProfits][6:55]
assets50 <- assets[orderProfits][6:55]
abbreviateCountry <- abbreviate(country)
abbCountry50 <- abbreviateCountry[orderProfits][6:55]
plot(assets50,profits50,pch=20)
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assets50
p ro fi ts 5 0
Statystyczne modelowanie decyzji biznesowych
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w darmowym pakiecie R
ladderTukey(assets50,profits50) 0.15187330 0.03205128 0.02359943 ladderTukey(log(assets50),profits50) -0.1749298 1.2536184 1.7851981
ladderTukey(log(assets50),log(profits50)) -0.07235858 0.29215216 0.33772950
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log(assets50)
lo g (p ro fi ts 5 0 )
UntS
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Statystyczne modelowanie decyzji biznesowych
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w darmowym pakiecie R
#fragment danych bez brakujących
which(apply(Forbes2000,2,is.na)==T)
frb<-Forbes2000[!naProfits,c("sales","profits","assets","marketvalue")]
frbPlus <- frb[frb$profits>0,c("sales","profits","assets","marketvalue")]
pairs(frbPlus,pch=".")
sales
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0100250
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profits
assets
0600
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marketvalue
Statystyczne modelowanie decyzji biznesowych
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w darmowym pakiecie R
pairs(log(frbPlus),pch=".")
sales
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profits
assets
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marketvalue
Statystyczne modelowanie decyzji biznesowych
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w darmowym pakiecie R
#składowe główne
forbesPC <- princomp(log(frbPlus),cor=T)
plot(forbesPC$scores[,2] ~forbesPC$scores[,1],pch=20)
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forbesPC$scores[, 1]
fo rb e s P C $ s c o re s [, 2 ]
> summary(forbesPC)
Importance of components:
Comp.1 Comp.2 Comp.3 Comp.4 Standard deviation 1.6613196 0.7750725 0.6660821 0.44228306 Proportion of Variance 0.6899957 0.1501844 0.1109164 0.04890358 Cumulative Proportion 0.6899957 0.8401801 0.9510964 1.00000000
0.00.51.01.52.02.5
Ważność składowych (wariancje)
Statystyczne modelowanie decyzji biznesowych
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w darmowym pakiecie R
> forbesPC$loadings Loadings:
Comp.1 Comp.2 Comp.3 Comp.4 sales 0.488 -0.186 0.850 profits 0.523 0.466 -0.249 0.669 assets 0.446 -0.784 -0.431 marketvalue 0.538 0.365 -0.172 -0.740
> forbesPC$center
sales profits assets marketvalue 1.457143 -1.320061 2.296328 1.763937
> forbesPC$scale
sales profits assets marketvalue 1.234526 1.226756 1.326477 1.142203
> summary(forbesPC)
biplot(forbesPC)
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sales profits
assets
marketvalue
Statystyczne modelowanie decyzji biznesowych
14
w darmowym pakiecie R
library(FactoMineR)
result <- PCA(log(frbPlus)) # graphs generated automatically
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-2-10123
Individuals factor map (PCA)
Dim 1 (69%)
Dim 2 (15.02%)
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109310951092 1096
10971099 1100 1101
1102 1103 1104 1105
1106 11071108
1109
1110 1111
1112 1113 1116
1117 1118
1119 1120
1121 11221123 1125 1126
1127 11291128 11311130 1132
1133
1134 1135
11371138 1140 1141
1142 11441143
1145 1146
1147 1148
1149 11501152
1153 1154
1155
11581157 1159
1160
1161 1162 1163 1164
1165 1166
1167
1168 117011711169
11731172 1174
1175
1176 1177 1178
1179
1180 1181
1183 1184 11851186 1188
1189
1190 1191 1192 1193
1194
1195 119811991196
1200 1201
1202 1204
1205 1207 1208
1210
1211 1212
1213
1214 1215 1216
12181217 1220 1221
1222
1227 1228 12291230
1231
1232 1233
1235 1236
1238 1239 1240
1241 1243 1244 1246
1249 1250
1252 1253
1254 1255 1256 1257 1259
1261
1262 1264
1265
1266
1267 1269
1270 1271
1273
1274
1275 1276 1277
1279 1281
1282 1283
1284 1285 1286
1287 1288 1289
12911290 1292
1293 1294129612971295
1298 1299
1300 13041302 1305
1306 13071308
13091310
1311 1312
13141316 13181317
1320 1321
1323 1324 1325
1326 1327
1328 1329 1330
1331 1332
1333 1334 1336
1337 1338
1339 1340
1341
1342
1343 1344
13451346 1347
1348 1349 1351
1352 1353
1354 1355
1356 1358
1359
1360 1361
1362 1363 1364
1366 1367 1368
1369
1370 13721371
1373
1374
1375 1376 13801379
1381 1383
1384 1385
1387
1388
1390 1391
1392 1394 1395
13981396 1399
1400 1401 1402
1403
1405 1406 1407
1410 1412 1413
1414 1415 1416 1417
1418 1419 14201421
1423 1427 1428
1429 1430
14321431 1433
14351434 1436
1437
1438 1439 1440
14441445 1447 1448 1449
1451 1452
1453 1454 14571455
1460 1461
1462 1463 14641465
1467 14691470 1471 1472
1473 1474
14781475 1479
14801483 1484
1486
1487
1488 1491
149314941492 1495 1496
1498
1500 1501 1502
1503 1504
15061505 1507 1508
15091510 1511 1512
1513 1514
1515 1516 151815171519 1520
1521
1522 1523 15241525 1526
15281527 1529 1530 1531
15331532 1534
1535
1536 15371538 1539
1540 1541 1542
1543 1544
1545 1546
1547
1548 1549 1550 1551
1553 1555 1557
1558
1559
1561 1562
1563
1564 1565
1566 1567
1568 1569
1570
1571 1572 1573
1575 1576
1577 1578 1579
15811580
1582 1583 1584
1585 1587
1588
1589 15901592
15961595 1597
1598 1599 1601
16021603 1604
1605 16071606 1608
1609 1610
1611
16131612 1614
16151616 1617
1620
1621 1622
1623 16241625 1626
1627
1630 1631
1632 1633
1634 1636
1638
1639
1641 1642
1644 1645
1646
16491648 16501651
16521655 1656 1657 1661
1662 1663
16641665 1666
1667 1669
1671
1672 1673
1674 16761675 1677
16791678 1680 1681
1682 16841683
1685 1687
16881689 1690
16911694 1695
1696 1698 1699
17001701 1703 1704
1706
17091707 1710 1711
1712 1713 1714
1715 1716
17171718 1719 1721 1722 1723
1724
1725 1727 1728 1729
1730 1731 1732
1734
1735 1736
1737 1739
17401741 1742
1743 1744
1745 1746
17501748 1751 1752
1753 1754 1755 1756 1757
1758 1759
1761
1762
1763 1767 1769 1771
17731772 1777
1778 1779
1780
1783 1784
1785 1786 1787
1788
1789 1790
1792 1793
1794 1796
1797 1798 1799
1800
1801 1802
1803 1804
1805 1806 1808
1809 1810 1812
18151813 18161817 1818
1819 1820
1821 1823 1824 18251826
1827 1828
1830 1831
1832
1833
1834 1835
1836 1837 1838 1839 1841
1842 1843
1844
1845 1846 1847
1849 1850
18511852 18531854 1855
1856
1857 1858
1861
1862 1864
1866 1867
1869
1870
1871
1872
18741873 1876
1877 1878
1879 1881
1882 1883
1884 1886
1888 1889
18931894 1895 18981896
1899 1900
1901 1902
1903 1904 1907 1908
1911 1912
19131915 1916
1917 1918
19191920 1922 1923 1924
1925 1926 1930 1931
19321933 1934 1936
19371938
1939 1940
1941 1942
1943
1944 1945 1946
1947 1948
1951 1952
1953 1954
1955 1956 1957
1959 1960
1961
1962 1963
19651964 1967
1968 19701969
1971 1972
1973
1974 1975 1976
1977 1978
1979 1984
1985 1986
1987 1988
1989 1990
1991
1992 1995 1996
1998 2000
-1.0 -0.5 0.0 0.5 1.0
-1.0-0.50.00.51.0
Variables factor map (PCA)
Dim 1 (69%)
Dim 2 (15.02%)
sales
profits assets
marketvalue
Statystyczne modelowanie decyzji biznesowych
15
w darmowym pakiecie R
library(ade4)
forbesPCA<- dudi.pca(log(frbPlus), scan = T) # a normed PCA
> forbesPCA$c1
CS1 CS2 sales -0.4881373 -0.1864858 profits -0.5228124 0.4661999 assets -0.4457226 -0.7838260 marketvalue -0.5382570 0.3653730
s.corcircle(forbesPCA$co, lab = names(frbPlus))
sales profits
assets marketvalue
Pierwsza składowa główna a kolejność firm na liście Forbesa
> name[1:5]
[1] "Citigroup" "General Electric" "American Intl Group"
[4] "ExxonMobil" "BP"
> forbesPC$scores[,1][1:5]
1 2 3 4 5 6.422928 6.386240 5.554190 6.188101 5.701150
> name[6:10]
[1] "Bank of America" "HSBC Group" "Toyota Motor" "Fannie Mae"
[5] "Wal-Mart Stores"
> forbesPC$scores[,1][6:10]
6 7 8 9 10 5.401687 5.360522 5.177946 5.124337 5.668962
> name[1695:1705]
[1] "Kagoshima Bank" "Regal Entertainment Group"
[3] "Allergan" "Hong Leong Credit"
[5] "Washington Federal" "GTech Holdings"
[7] "Equifax" "Broadcom"
[9] "Dentsply Intl" "EMAP"
[11] "Neptune Orient Lines"
> forbesPC$scores[,1][1695:1705]
1986 1987 1988 1989 1990 1991 1992 1995 -3.041736 -1.948617 -2.145160 -1.529307 -1.805009 -1.666984 -1.495070 -2.109997 1996 1998 2000
-2.578421 -1.553430 -1.945621
Statystyczne modelowanie decyzji biznesowych
16
w darmowym pakiecie R
Druga składowa główna a kolejność firm na liście Forbesa
> forbesPC$scores[,2][1:5]
1 2 3 4 5 -0.5251281 -0.1341675 -0.5707036 0.6288218 0.1653822
> forbesPC$scores[,2][6:10]
6 7 8 9 10 -0.54508177 -0.59806428 0.04054584 -1.07973652 0.52226436
> forbesPC$scores[,2][1695:1705]
1986 1987 1988 1989 1990 1991 1992 -1.3132939 -0.3329063 -0.8525001 0.5921074 0.3627939 -0.6005488 0.4087964 1995 1996 1998 2000
-0.6535188 -1.1693902 0.5123731 -0.4417627
Statystyczne modelowanie decyzji biznesowych
17
w darmowym pakiecie R
Analiza czynnikowa
forbesFA <- factanal(log(frbPlus), 1, rotation="varimax")
> print(forbesFA, digits=2, cutoff=.3, sort=TRUE) Call:
factanal(x = log(frbPlus), factors = 1, rotation = "varimax") Uniquenesses:
sales profits assets marketvalue 0.54 0.25 0.66 0.16 Loadings:
[1] 0.68 0.86 0.58 0.92 Factor1 SS loadings 2.38 Proportion Var 0.60
Test of the hypothesis that 1 factor is sufficient.
The chi square statistic is 102.74 on 2 degrees of freedom.
The p-value is 4.91e-23
> load <- forbesFA$loadings[,1]
> plot(load,type="n") # set up plot
> text(load,labels=names(frbPlus),cex=.7) # add variable names
1.0 1.5 2.0 2.5 3.0 3.5 4.0
0 .6 0 0 .7 0 0 .8 0 0 .9 0
Index
lo a d
sales
profits
assets
marketvalue
