NikhilBharadwaj_DA_E3
2024-02-14
13. This question should be answered using the Weekly data set, which is part of the ISLR2 package. This data is similar in nature to the Smarket data from this chapter’s lab, except that it contains 1,089 weekly returns for 21 years, from the beginning of 1990 to the end of 2010.
(a) Produce some numerical and graphical summaries of the Weekly data. Do there appear to be any patterns?
library(ISLR2)
library(psych)
Weekly## Year Lag1 Lag2 Lag3 Lag4 Lag5 Volume Today Direction
## 1 1990 0.816 1.572 -3.936 -0.229 -3.484 0.1549760 -0.270 Down
## 2 1990 -0.270 0.816 1.572 -3.936 -0.229 0.1485740 -2.576 Down
## 3 1990 -2.576 -0.270 0.816 1.572 -3.936 0.1598375 3.514 Up
## 4 1990 3.514 -2.576 -0.270 0.816 1.572 0.1616300 0.712 Up
## 5 1990 0.712 3.514 -2.576 -0.270 0.816 0.1537280 1.178 Up
## 6 1990 1.178 0.712 3.514 -2.576 -0.270 0.1544440 -1.372 Down
## 7 1990 -1.372 1.178 0.712 3.514 -2.576 0.1517220 0.807 Up
## 8 1990 0.807 -1.372 1.178 0.712 3.514 0.1323100 0.041 Up
## 9 1990 0.041 0.807 -1.372 1.178 0.712 0.1439720 1.253 Up
## 10 1990 1.253 0.041 0.807 -1.372 1.178 0.1336350 -2.678 Down
## 11 1990 -2.678 1.253 0.041 0.807 -1.372 0.1490240 -1.793 Down
## 12 1990 -1.793 -2.678 1.253 0.041 0.807 0.1357900 2.820 Up
## 13 1990 2.820 -1.793 -2.678 1.253 0.041 0.1398980 4.022 Up
## 14 1990 4.022 2.820 -1.793 -2.678 1.253 0.1643420 0.750 Up
## 15 1990 0.750 4.022 2.820 -1.793 -2.678 0.1756480 -0.017 Down
## 16 1990 -0.017 0.750 4.022 2.820 -1.793 0.1634700 2.420 Up
## 17 1990 2.420 -0.017 0.750 4.022 2.820 0.1726250 -1.225 Down
## 18 1990 -1.225 2.420 -0.017 0.750 4.022 0.1684460 1.171 Up
## 19 1990 1.171 -1.225 2.420 -0.017 0.750 0.1552920 -2.061 Down
## 20 1990 -2.061 1.171 -1.225 2.420 -0.017 0.1433920 0.729 Up
## 21 1990 0.729 -2.061 1.171 -1.225 2.420 0.1405540 0.112 Up
## 22 1990 0.112 0.729 -2.061 1.171 -1.225 0.1250750 2.480 Up
## 23 1990 2.480 0.112 0.729 -2.061 1.171 0.1716040 -1.552 Down
## 24 1990 -1.552 2.480 0.112 0.729 -2.061 0.1669560 -2.259 Down
## 25 1990 -2.259 -1.552 2.480 0.112 0.729 0.1717180 -2.428 Down
## 26 1990 -2.428 -2.259 -1.552 2.480 0.112 0.2098160 -2.708 Down
## 27 1990 -2.708 -2.428 -2.259 -1.552 2.480 0.1927060 -2.292 Down
## 28 1990 -2.292 -2.708 -2.428 -2.259 -1.552 0.1482520 -4.978 Down
## 29 1990 -4.978 -2.292 -2.708 -2.428 -2.259 0.1898580 3.547 Up
## 30 1990 3.547 -4.978 -2.292 -2.708 -2.428 0.1278840 0.260 Up
## 31 1990 0.260 3.547 -4.978 -2.292 -2.708 0.1157425 -2.032 Down
## 32 1990 -2.032 0.260 3.547 -4.978 -2.292 0.1239240 -1.739 Down
## 33 1990 -1.739 -2.032 0.260 3.547 -4.978 0.1490820 -1.693 Down
## 34 1990 -1.693 -1.739 -2.032 0.260 3.547 0.1718560 1.781 Up
## 35 1990 1.781 -1.693 -1.739 -2.032 0.260 0.1649700 -3.682 Down
## 36 1990 -3.682 1.781 -1.693 -1.739 -2.032 0.1564540 4.150 Up
## 37 1990 4.150 -3.682 1.781 -1.693 -1.739 0.1802800 -2.487 Down
## 38 1990 -2.487 4.150 -3.682 1.781 -1.693 0.1439780 2.343 Up
## 39 1990 2.343 -2.487 4.150 -3.682 1.781 0.1542920 0.606 Up
## 40 1990 0.606 2.343 -2.487 4.150 -3.682 0.1480060 1.077 Up
## 41 1990 1.077 0.606 2.343 -2.487 4.150 0.1635500 -0.637 Down
## 42 1990 -0.637 1.077 0.606 2.343 -2.487 0.1265325 2.260 Up
## 43 1990 2.260 -0.637 1.077 0.606 2.343 0.1515780 1.716 Up
## 44 1990 1.716 2.260 -0.637 1.077 0.606 0.1979940 -0.284 Down
## 45 1990 -0.284 1.716 2.260 -0.637 1.077 0.1558740 1.508 Up
## 46 1990 1.508 -0.284 1.716 2.260 -0.637 0.1767000 -0.913 Down
## 47 1990 -0.913 1.508 -0.284 1.716 2.260 0.0874650 -2.349 Down
## 48 1991 -2.349 -0.913 1.508 -0.284 1.716 0.1306700 -1.798 Down
## 49 1991 -1.798 -2.349 -0.913 1.508 -0.284 0.1425320 5.393 Up
## 50 1991 5.393 -1.798 -2.349 -0.913 1.508 0.1822480 1.156 Up
## 51 1991 1.156 5.393 -1.798 -2.349 -0.913 0.1798940 2.077 Up
## 52 1991 2.077 1.156 5.393 -1.798 -2.349 0.1949980 4.751 Up
## 53 1991 4.751 2.077 1.156 5.393 -1.798 0.2596560 2.702 Up
## 54 1991 2.702 4.751 2.077 1.156 5.393 0.2381400 -0.924 Down
## 55 1991 -0.924 2.702 4.751 2.077 1.156 0.1937775 1.318 Up
## 56 1991 1.318 -0.924 2.702 4.751 2.077 0.2027840 1.209 Up
## 57 1991 1.209 1.318 -0.924 2.702 4.751 0.2239460 -0.363 Down
## 58 1991 -0.363 1.209 1.318 -0.924 2.702 0.1967520 -1.635 Down
## 59 1991 -1.635 -0.363 1.209 1.318 -0.924 0.1795400 2.106 Up
## 60 1991 2.106 -1.635 -0.363 1.209 1.318 0.1763050 0.037 Up
## 61 1991 0.037 2.106 -1.635 -0.363 1.209 0.1865580 1.343 Up
## 62 1991 1.343 0.037 2.106 -1.635 -0.363 0.1743280 0.999 Up
## 63 1991 0.999 1.343 0.037 2.106 -1.635 0.2072280 -1.348 Down
## 64 1991 -1.348 0.999 1.343 0.037 2.106 0.1641080 0.470 Up
## 65 1991 0.470 -1.348 0.999 1.343 0.037 0.1766460 -1.329 Down
## 66 1991 -1.329 0.470 -1.348 0.999 1.343 0.1585660 -0.892 Down
## 67 1991 -0.892 -1.329 0.470 -1.348 0.999 0.1718580 1.370 Up
## 68 1991 1.370 -0.892 -1.329 0.470 -1.348 0.1486320 3.269 Up
## 69 1991 3.269 1.370 -0.892 -1.329 0.470 0.2043200 -2.668 Down
## 70 1991 -2.668 3.269 1.370 -0.892 -1.329 0.1757660 0.754 Up
## 71 1991 0.754 -2.668 3.269 1.370 -0.892 0.1538140 -1.188 Down
## 72 1991 -1.188 0.754 -2.668 3.269 1.370 0.1606320 -1.745 Down
## 73 1991 -1.745 -1.188 0.754 -2.668 3.269 0.1615340 0.787 Up
## 74 1991 0.787 -1.745 -1.188 0.754 -2.668 0.1338150 1.649 Up
## 75 1991 1.649 0.787 -1.745 -1.188 0.754 0.1602280 1.044 Up
## 76 1991 1.044 1.649 0.787 -1.745 -1.188 0.1863660 -0.856 Down
## 77 1991 -0.856 1.044 1.649 0.787 -1.745 0.1483000 1.641 Up
## 78 1991 1.641 -0.856 1.044 1.649 0.787 0.1609440 -0.015 Down
## 79 1991 -0.015 1.641 -0.856 1.044 1.649 0.1564720 -0.398 Down
## 80 1991 -0.398 -0.015 1.641 -0.856 1.044 0.1693200 2.228 Up
## 81 1991 2.228 -0.398 -0.015 1.641 -0.856 0.2018520 0.320 Up
## 82 1991 0.320 2.228 -0.398 -0.015 1.641 0.1485440 -1.601 Down
## 83 1991 -1.601 0.320 2.228 -0.398 -0.015 0.1600150 -1.416 Down
## 84 1991 -1.416 -1.601 0.320 2.228 -0.398 0.1473080 1.129 Up
## 85 1991 1.129 -1.416 -1.601 0.320 2.228 0.1895540 -0.521 Down
## 86 1991 -0.521 1.129 -1.416 -1.601 0.320 0.1579680 -1.205 Down
## 87 1991 -1.205 -0.521 1.129 -1.416 -1.601 0.1630180 0.052 Up
## 88 1991 0.052 -1.205 -0.521 1.129 -1.416 0.1650700 2.897 Up
## 89 1991 2.897 0.052 -1.205 -0.521 1.129 0.1958320 -2.115 Down
## 90 1991 -2.115 2.897 0.052 -1.205 -0.521 0.1760080 1.853 Up
## 91 1991 1.853 -2.115 2.897 0.052 -1.205 0.1870600 0.401 Up
## 92 1991 0.401 1.853 -2.115 2.897 0.052 0.1767860 -2.614 Down
## 93 1991 -2.614 0.401 1.853 -2.115 2.897 0.1903460 -1.694 Down
## 94 1991 -1.694 -2.614 0.401 1.853 -2.115 0.2123900 -0.245 Down
## 95 1991 -0.245 -1.694 -2.614 0.401 1.853 0.1585575 1.034 Up
## 96 1991 1.034 -0.245 -1.694 -2.614 0.401 0.1858220 1.417 Up
## 97 1991 1.417 1.034 -0.245 -1.694 -2.614 0.1925060 0.668 Up
## 98 1991 0.668 1.417 1.034 -0.245 -1.694 0.2144540 5.018 Up
## 99 1991 5.018 0.668 1.417 1.034 -0.245 0.1746800 3.169 Up
## 100 1992 3.169 5.018 0.668 1.417 1.034 0.2311300 -1.011 Down
## 101 1992 -1.011 3.169 5.018 0.668 1.417 0.2646440 0.906 Up
## 102 1992 0.906 -1.011 3.169 5.018 0.668 0.2809220 -0.807 Down
## 103 1992 -0.807 0.906 -1.011 3.169 5.018 0.2152000 -1.613 Down
## 104 1992 -1.613 -0.807 0.906 -1.011 3.169 0.2101220 0.565 Up
## 105 1992 0.565 -1.613 -0.807 0.906 -1.011 0.2309160 0.338 Up
## 106 1992 0.338 0.565 -1.613 -0.807 0.906 0.2133280 -0.255 Down
## 107 1992 -0.255 0.338 0.565 -1.613 -0.807 0.2498925 0.309 Up
## 108 1992 0.309 -0.255 0.338 0.565 -1.613 0.2093640 -2.001 Down
## 109 1992 -2.001 0.309 -0.255 0.338 0.565 0.1958180 0.346 Up
## 110 1992 0.346 -2.001 0.309 -0.255 0.338 0.1816380 1.345 Up
## 111 1992 1.345 0.346 -2.001 0.309 -0.255 0.1956880 -1.896 Down
## 112 1992 -1.896 1.345 0.346 -2.001 0.309 0.1768340 -0.483 Down
## 113 1992 -0.483 -1.896 1.345 0.346 -2.001 0.1753340 0.682 Up
## 114 1992 0.682 -0.483 -1.896 1.345 0.346 0.2130720 2.906 Up
## 115 1992 2.906 0.682 -0.483 -1.896 1.345 0.2093025 -1.687 Down
## 116 1992 -1.687 2.906 0.682 -0.483 -1.896 0.2120920 0.858 Up
## 117 1992 0.858 -1.687 2.906 0.682 -0.483 0.1939760 0.853 Up
## 118 1992 0.853 0.858 -1.687 2.906 0.682 0.1825480 -1.433 Down
## 119 1992 -1.433 0.853 0.858 -1.687 2.906 0.1812680 0.958 Up
## 120 1992 0.958 -1.433 0.853 0.858 -1.687 0.1736520 0.321 Up
## 121 1992 0.321 0.958 -1.433 0.853 0.858 0.1948125 -0.450 Down
## 122 1992 -0.450 0.321 0.958 -1.433 0.853 0.2005260 -0.900 Down
## 123 1992 -0.900 -0.450 0.321 0.958 -1.433 0.1899600 -1.486 Down
## 124 1992 -1.486 -0.900 -0.450 0.321 0.958 0.2090600 -0.054 Down
## 125 1992 -0.054 -1.486 -0.900 -0.450 0.321 0.1779640 2.062 Up
## 126 1992 2.062 -0.054 -1.486 -0.900 -0.450 0.2016825 0.692 Up
## 127 1992 0.692 2.062 -0.054 -1.486 -0.900 0.1973500 0.241 Up
## 128 1992 0.241 0.692 2.062 -0.054 -1.486 0.1900040 -0.967 Down
## 129 1992 -0.967 0.241 0.692 2.062 -0.054 0.1738120 3.064 Up
## 130 1992 3.064 -0.967 0.241 0.692 2.062 0.2049880 -1.256 Down
## 131 1992 -1.256 3.064 -0.967 0.241 0.692 0.1751500 0.246 Up
## 132 1992 0.246 -1.256 3.064 -0.967 0.241 0.1691100 -1.205 Down
## 133 1992 -1.205 0.246 -1.256 3.064 -0.967 0.1799740 -0.002 Down
## 134 1992 -0.002 -1.205 0.246 -1.256 3.064 0.1742340 0.540 Up
## 135 1992 0.540 -0.002 -1.205 0.246 -1.256 0.1717040 0.599 Up
## 136 1992 0.599 0.540 -0.002 -1.205 0.246 0.1856975 0.798 Up
## 137 1992 0.798 0.599 0.540 -0.002 -1.205 0.2239920 -2.029 Down
## 138 1992 -2.029 0.798 0.599 0.540 -0.002 0.1900160 -0.936 Down
## 139 1992 -0.936 -2.029 0.798 0.599 0.540 0.1813580 -1.903 Down
## 140 1992 -1.903 -0.936 -2.029 0.798 0.599 0.2116740 2.253 Up
## 141 1992 2.253 -1.903 -0.936 -2.029 0.798 0.1877460 0.576 Up
## 142 1992 0.576 2.253 -1.903 -0.936 -2.029 0.2229840 1.106 Up
## 143 1992 1.106 0.576 2.253 -1.903 -0.936 0.2004360 -0.263 Down
## 144 1992 -0.263 1.106 0.576 2.253 -1.903 0.2061720 1.161 Up
## 145 1992 1.161 -0.263 1.106 0.576 2.253 0.2166900 0.999 Up
## 146 1992 0.999 1.161 -0.263 1.106 0.576 0.2113040 0.823 Up
## 147 1992 0.823 0.999 1.161 -0.263 1.106 0.1869475 0.442 Up
## 148 1992 0.442 0.823 0.999 1.161 -0.263 0.2418440 0.387 Up
## 149 1992 0.387 0.442 0.823 0.999 1.161 0.2174480 1.741 Up
## 150 1992 1.741 0.387 0.442 0.823 0.999 0.2595760 -0.342 Down
## 151 1992 -0.342 1.741 0.387 0.442 0.823 0.2011225 -0.923 Down
## 152 1993 -0.923 -0.342 1.741 0.387 0.442 0.1768675 -1.529 Down
## 153 1993 -1.529 -0.923 -0.342 1.741 0.387 0.2610240 1.888 Up
## 154 1993 1.888 -1.529 -0.923 -0.342 1.741 0.2585360 -0.238 Down
## 155 1993 -0.238 1.888 -1.529 -0.923 -0.342 0.2598000 0.612 Up
## 156 1993 0.612 -0.238 1.888 -1.529 -0.923 0.2768100 2.313 Up
## 157 1993 2.313 0.612 -0.238 1.888 -1.529 0.3062780 -0.969 Down
## 158 1993 -0.969 2.313 0.612 -0.238 1.888 0.2419440 -2.330 Down
## 159 1993 -2.330 -0.969 2.313 0.612 -0.238 0.3142350 2.110 Up
## 160 1993 2.110 -2.330 -0.969 2.313 0.612 0.2888800 0.616 Up
## 161 1993 0.616 2.110 -2.330 -0.969 2.313 0.2534580 0.834 Up
## 162 1993 0.834 0.616 2.110 -2.330 -0.969 0.2668100 0.078 Up
## 163 1993 0.078 0.834 0.616 2.110 -2.330 0.2473720 -0.533 Down
## 164 1993 -0.533 0.078 0.834 0.616 2.110 0.2436800 -1.427 Down
## 165 1993 -1.427 -0.533 0.078 0.834 0.616 0.2536420 0.102 Up
## 166 1993 0.102 -1.427 -0.533 0.078 0.834 0.2935325 1.607 Up
## 167 1993 1.607 0.102 -1.427 -0.533 0.078 0.2736760 -2.653 Down
## 168 1993 -2.653 1.607 0.102 -1.427 -0.533 0.2840400 0.723 Up
## 169 1993 0.723 -2.653 1.607 0.102 -1.427 0.2665200 0.482 Up
## 170 1993 0.482 0.723 -2.653 1.607 0.102 0.2493100 -0.622 Down
## 171 1993 -0.622 0.482 0.723 -2.653 1.607 0.2513140 1.429 Up
## 172 1993 1.429 -0.622 0.482 0.723 -2.653 0.2805160 0.976 Up
## 173 1993 0.976 1.429 -0.622 0.482 0.723 0.2405880 -0.029 Down
## 174 1993 -0.029 0.976 1.429 -0.622 0.482 0.2593150 -0.622 Down
## 175 1993 -0.622 -0.029 0.976 1.429 -0.622 0.2431880 -0.800 Down
## 176 1993 -0.800 -0.622 -0.029 0.976 1.429 0.2504720 0.884 Up
## 177 1993 0.884 -0.800 -0.622 -0.029 0.976 0.2478640 -0.393 Down
## 178 1993 -0.393 0.884 -0.800 -0.622 -0.029 0.2624620 0.509 Up
## 179 1993 0.509 -0.393 0.884 -0.800 -0.622 0.2515250 -0.527 Down
## 180 1993 -0.527 0.509 -0.393 0.884 -0.800 0.2554740 0.303 Up
## 181 1993 0.303 -0.527 0.509 -0.393 0.884 0.2488360 0.230 Up
## 182 1993 0.230 0.303 -0.527 0.509 -0.393 0.2536180 0.123 Up
## 183 1993 0.123 0.230 0.303 -0.527 0.509 0.2393200 0.325 Up
## 184 1993 0.325 0.123 0.230 0.303 -0.527 0.2499000 1.337 Up
## 185 1993 1.337 0.325 0.123 0.230 0.303 0.2756060 0.960 Up
## 186 1993 0.960 1.337 0.325 0.123 0.230 0.2470120 0.174 Up
## 187 1993 0.174 0.960 1.337 0.325 0.123 0.2298160 0.082 Up
## 188 1993 0.082 0.174 0.960 1.337 0.325 0.2601550 -0.626 Down
## 189 1993 -0.626 0.082 0.174 0.960 1.337 0.2818200 -0.262 Down
## 190 1993 -0.262 -0.626 0.082 0.174 0.960 0.2708040 0.798 Up
## 191 1993 0.798 -0.262 -0.626 0.082 0.174 0.2607580 -0.210 Down
## 192 1993 -0.210 0.798 -0.262 -0.626 0.082 0.2599660 1.996 Up
## 193 1993 1.996 -0.210 0.798 -0.262 -0.626 0.2913200 -1.327 Down
## 194 1993 -1.327 1.996 -0.210 0.798 -0.262 0.3061380 0.984 Up
## 195 1993 0.984 -1.327 1.996 -0.210 0.798 0.2792920 -1.766 Down
## 196 1993 -1.766 0.984 -1.327 1.996 -0.210 0.3126480 1.266 Up
## 197 1993 1.266 -1.766 0.984 -1.327 1.996 0.2808420 -0.599 Down
## 198 1993 -0.599 1.266 -1.766 0.984 -1.327 0.2976820 0.099 Up
## 199 1993 0.099 -0.599 1.266 -1.766 0.984 0.2153450 0.395 Up
## 200 1993 0.395 0.099 -0.599 1.266 -1.766 0.2755940 -0.207 Down
## 201 1993 -0.207 0.395 0.099 -0.599 1.266 0.2851420 0.528 Up
## 202 1993 0.528 -0.207 0.395 0.099 -0.599 0.3023540 0.214 Up
## 203 1993 0.214 0.528 -0.207 0.395 0.099 0.2572375 -0.199 Down
## 204 1994 -0.199 0.214 0.528 -0.207 0.395 0.2012360 0.740 Up
## 205 1994 0.740 -0.199 0.214 0.528 -0.207 0.3375300 1.066 Up
## 206 1994 1.066 0.740 -0.199 0.214 0.528 0.3037120 -0.040 Down
## 207 1994 -0.040 1.066 0.740 -0.199 0.214 0.3021980 0.838 Up
## 208 1994 0.838 -0.040 1.066 0.740 -0.199 0.3174640 -1.857 Down
## 209 1994 -1.857 0.838 -0.040 1.066 0.740 0.3342140 0.079 Up
## 210 1994 0.079 -1.857 0.838 -0.040 1.066 0.3080220 -0.530 Down
## 211 1994 -0.530 0.079 -1.857 0.838 -0.040 0.2997340 -0.346 Down
## 212 1994 -0.346 -0.530 0.079 -1.857 0.838 0.2993575 -0.285 Down
## 213 1994 -0.285 -0.346 -0.530 0.079 -1.857 0.3075820 0.366 Up
## 214 1994 0.366 -0.285 -0.346 -0.530 0.079 0.3133540 0.990 Up
## 215 1994 0.990 0.366 -0.285 -0.346 -0.530 0.3275420 -2.225 Down
## 216 1994 -2.225 0.990 0.366 -0.285 -0.346 0.2729000 -3.216 Down
## 217 1994 -3.216 -2.225 0.990 0.366 -0.285 0.3467025 0.298 Up
## 218 1994 0.298 -3.216 -2.225 0.990 0.366 0.3131500 -0.206 Down
## 219 1994 -0.206 0.298 -3.216 -2.225 0.990 0.2727760 0.325 Up
## 220 1994 0.325 -0.206 0.298 -3.216 -2.225 0.3271540 0.733 Up
## 221 1994 0.733 0.325 -0.206 0.298 -3.216 0.2924025 -0.685 Down
## 222 1994 -0.685 0.733 0.325 -0.206 0.298 0.2799880 -0.822 Down
## 223 1994 -0.822 -0.685 0.733 0.325 -0.206 0.2701540 2.427 Up
## 224 1994 2.427 -0.822 -0.685 0.733 0.325 0.2965020 0.530 Up
## 225 1994 0.530 2.427 -0.822 -0.685 0.733 0.2452100 0.612 Up
## 226 1994 0.612 0.530 2.427 -0.822 -0.685 0.2599325 -0.317 Down
## 227 1994 -0.317 0.612 0.530 2.427 -0.822 0.2450220 -0.048 Down
## 228 1994 -0.048 -0.317 0.612 0.530 2.427 0.2863540 -3.414 Down
## 229 1994 -3.414 -0.048 -0.317 0.612 0.530 0.2594200 0.768 Up
## 230 1994 0.768 -3.414 -0.048 -0.317 0.612 0.2549380 0.751 Up
## 231 1994 0.751 0.768 -3.414 -0.048 -0.317 0.2319750 1.025 Up
## 232 1994 1.025 0.751 0.768 -3.414 -0.048 0.2678500 -0.231 Down
## 233 1994 -0.231 1.025 0.751 0.768 -3.414 0.2601100 1.137 Up
## 234 1994 1.137 -0.231 1.025 0.751 0.768 0.2426740 -0.255 Down
## 235 1994 -0.255 1.137 -0.231 1.025 0.751 0.2712360 1.061 Up
## 236 1994 1.061 -0.255 1.137 -0.231 1.025 0.2562580 0.377 Up
## 237 1994 0.377 1.061 -0.255 1.137 -0.231 0.2806120 2.183 Up
## 238 1994 2.183 0.377 1.061 -0.255 1.137 0.2885940 -0.593 Down
## 239 1994 -0.593 2.183 0.377 1.061 -0.255 0.2828460 -0.597 Down
## 240 1994 -0.597 -0.593 2.183 0.377 1.061 0.2695925 0.643 Up
## 241 1994 0.643 -0.597 -0.593 2.183 0.377 0.3056400 -2.445 Down
## 242 1994 -2.445 0.643 -0.597 -0.593 2.183 0.3120520 0.661 Up
## 243 1994 0.661 -2.445 0.643 -0.597 -0.593 0.2974120 -1.645 Down
## 244 1994 -1.645 0.661 -2.445 0.643 -0.597 0.3022540 3.076 Up
## 245 1994 3.076 -1.645 0.661 -2.445 0.643 0.2855740 -0.897 Down
## 246 1994 -0.897 3.076 -1.645 0.661 -2.445 0.2924040 1.910 Up
## 247 1994 1.910 -0.897 3.076 -1.645 0.661 0.3281440 -2.425 Down
## 248 1994 -2.425 1.910 -0.897 3.076 -1.645 0.3029700 0.015 Up
## 249 1994 0.015 -2.425 1.910 -0.897 3.076 0.2770760 -0.190 Down
## 250 1994 -0.190 0.015 -2.425 1.910 -0.897 0.3147460 -1.989 Down
## 251 1994 -1.989 -0.190 0.015 -2.425 1.910 0.3073375 0.223 Up
## 252 1994 0.223 -1.989 -0.190 0.015 -2.425 0.2842840 -1.399 Down
## 253 1994 -1.399 0.223 -1.989 -0.190 0.015 0.3079280 2.649 Up
## 254 1994 2.649 -1.399 0.223 -1.989 -0.190 0.3524980 0.224 Up
## 255 1994 0.224 2.649 -1.399 0.223 -1.989 0.3028760 -0.122 Down
## 256 1995 -0.122 0.224 2.649 -1.399 0.223 0.2410875 0.307 Up
## 257 1995 0.307 -0.122 0.224 2.649 -1.399 0.2997700 1.148 Up
## 258 1995 1.148 0.307 -0.122 0.224 2.649 0.3254660 -0.255 Down
## 259 1995 -0.255 1.148 0.307 -0.122 0.224 0.3334800 1.207 Up
## 260 1995 1.207 -0.255 1.148 0.307 -0.122 0.3256220 1.756 Up
## 261 1995 1.756 1.207 -0.255 1.148 0.307 0.3777120 0.587 Up
## 262 1995 0.587 1.756 1.207 -0.255 1.148 0.3159840 0.106 Up
## 263 1995 0.106 0.587 1.756 1.207 -0.255 0.3287980 1.274 Up
## 264 1995 1.274 0.106 0.587 1.756 1.207 0.3361900 -0.551 Down
## 265 1995 -0.551 1.274 0.106 0.587 1.756 0.3252960 0.855 Up
## 266 1995 0.855 -0.551 1.274 0.106 0.587 0.3412920 1.215 Up
## 267 1995 1.215 0.855 -0.551 1.274 0.106 0.3370060 1.100 Up
## 268 1995 1.100 1.215 0.855 -0.551 1.274 0.3317740 -0.052 Down
## 269 1995 -0.052 1.100 1.215 0.855 -0.551 0.3437140 1.140 Up
## 270 1995 1.140 -0.052 1.100 1.215 0.855 0.3154800 0.555 Up
## 271 1995 0.555 1.140 -0.052 1.100 1.215 0.3002750 -0.145 Down
## 272 1995 -0.145 0.555 1.140 -0.052 1.100 0.3656720 1.223 Up
## 273 1995 1.223 -0.145 0.555 1.140 -0.052 0.3400340 1.051 Up
## 274 1995 1.051 1.223 -0.145 0.555 1.140 0.3538260 1.044 Up
## 275 1995 1.044 1.051 1.223 -0.145 0.555 0.3472000 -1.210 Down
## 276 1995 -1.210 1.044 1.051 1.223 -0.145 0.3472520 0.859 Up
## 277 1995 0.859 -1.210 1.044 1.051 1.223 0.3346200 1.692 Up
## 278 1995 1.692 0.859 -1.210 1.044 1.051 0.3382800 -0.858 Down
## 279 1995 -0.858 1.692 0.859 -1.210 1.044 0.3246500 2.252 Up
## 280 1995 2.252 -0.858 1.692 0.859 -1.210 0.3475580 1.830 Up
## 281 1995 1.830 2.252 -0.858 1.692 0.859 0.3692460 -0.902 Down
## 282 1995 -0.902 1.830 2.252 -0.858 1.692 0.3272920 2.133 Up
## 283 1995 2.133 -0.902 1.830 2.252 -0.858 0.3406975 0.633 Up
## 284 1995 0.633 2.133 -0.902 1.830 2.252 0.3806520 -1.120 Down
## 285 1995 -1.120 0.633 2.133 -0.902 1.830 0.3999660 1.682 Up
## 286 1995 1.682 -1.120 0.633 2.133 -0.902 0.3500260 -0.709 Down
## 287 1995 -0.709 1.682 -1.120 0.633 2.133 0.3332680 -0.685 Down
## 288 1995 -0.685 -0.709 1.682 -1.120 0.633 0.2922080 0.739 Up
## 289 1995 0.739 -0.685 -0.709 1.682 -1.120 0.3320220 0.159 Up
## 290 1995 0.159 0.739 -0.685 -0.709 1.682 0.2882340 0.668 Up
## 291 1995 0.668 0.159 0.739 -0.685 -0.709 0.2933280 1.568 Up
## 292 1995 1.568 0.668 0.159 0.739 -0.685 0.3354675 1.863 Up
## 293 1995 1.863 1.568 0.668 0.159 0.739 0.3736020 -0.278 Down
## 294 1995 -0.278 1.863 1.568 0.668 0.159 0.3670400 0.461 Up
## 295 1995 0.461 -0.278 1.863 1.568 0.668 0.3502040 -0.329 Down
## 296 1995 -0.329 0.461 -0.278 1.863 1.568 0.3422940 0.345 Up
## 297 1995 0.345 -0.329 0.461 -0.278 1.863 0.3495020 0.506 Up
## 298 1995 0.506 0.345 -0.329 0.461 -0.278 0.3728760 -1.321 Down
## 299 1995 -1.321 0.506 0.345 -0.329 0.461 0.4046820 1.875 Up
## 300 1995 1.875 -1.321 0.506 0.345 -0.329 0.3640420 0.364 Up
## 301 1995 0.364 1.875 -1.321 0.506 0.345 0.3426020 1.240 Up
## 302 1995 1.240 0.364 1.875 -1.321 0.506 0.3773680 -0.017 Down
## 303 1995 -0.017 1.240 0.364 1.875 -1.321 0.3180800 1.168 Up
## 304 1995 1.168 -0.017 1.240 0.364 1.875 0.3999260 1.730 Up
## 305 1995 1.730 1.168 -0.017 1.240 0.364 0.3935560 -0.185 Down
## 306 1995 -0.185 1.730 1.168 -0.017 1.240 0.4418640 -0.712 Down
## 307 1995 -0.712 -0.185 1.730 1.168 -0.017 0.4095280 0.650 Up
## 308 1996 0.650 -0.712 -0.185 1.730 1.168 0.2698725 0.127 Up
## 309 1996 0.127 0.650 -0.712 -0.185 1.730 0.4457050 -2.416 Down
## 310 1996 -2.416 0.127 0.650 -0.712 -0.185 0.3673580 1.665 Up
## 311 1996 1.665 -2.416 0.127 0.650 -0.712 0.4276500 1.600 Up
## 312 1996 1.600 1.665 -2.416 0.127 0.650 0.4260600 2.288 Up
## 313 1996 2.288 1.600 1.665 -2.416 0.127 0.4362680 3.229 Up
## 314 1996 3.229 2.288 1.600 1.665 -2.416 0.4518080 -1.278 Down
## 315 1996 -1.278 3.229 2.288 1.600 1.665 0.4244220 1.713 Up
## 316 1996 1.713 -1.278 3.229 2.288 1.600 0.4389325 -2.232 Down
## 317 1996 -2.232 1.713 -1.278 3.229 2.288 0.4406220 -1.687 Down
## 318 1996 -1.687 -2.232 1.713 -1.278 3.229 0.4527060 1.252 Up
## 319 1996 1.252 -1.687 -2.232 1.713 -1.278 0.4680220 1.433 Up
## 320 1996 1.433 1.252 -1.687 -2.232 1.713 0.3963500 -0.787 Down
## 321 1996 -0.787 1.433 1.252 -1.687 -2.232 0.3854660 1.605 Up
## 322 1996 1.605 -0.787 1.433 1.252 -1.687 0.3921950 -2.920 Down
## 323 1996 -2.920 1.605 -0.787 1.433 1.252 0.4493460 1.313 Up
## 324 1996 1.313 -2.920 1.605 -0.787 1.433 0.4231440 1.301 Up
## 325 1996 1.301 1.313 -2.920 1.605 -0.787 0.4413860 -1.810 Down
## 326 1996 -1.810 1.301 1.313 -2.920 1.605 0.4038020 1.630 Up
## 327 1996 1.630 -1.810 1.301 1.313 -2.920 0.4229460 2.579 Up
## 328 1996 2.579 1.630 -1.810 1.301 1.313 0.4247240 1.435 Up
## 329 1996 1.435 2.579 1.630 -1.810 1.301 0.3958560 -1.384 Down
## 330 1996 -1.384 1.435 2.579 1.630 -1.810 0.3554800 0.626 Up
## 331 1996 0.626 -1.384 1.435 2.579 1.630 0.3995040 -1.108 Down
## 332 1996 -1.108 0.626 -1.384 1.435 2.579 0.3856620 0.149 Up
## 333 1996 0.149 -1.108 0.626 -1.384 1.435 0.4033420 0.568 Up
## 334 1996 0.568 0.149 -1.108 0.626 -1.384 0.3976600 -1.967 Down
## 335 1996 -1.967 0.568 0.149 -1.108 0.626 0.3128700 -1.711 Down
## 336 1996 -1.711 -1.967 0.568 0.149 -1.108 0.4212580 -1.154 Down
## 337 1996 -1.154 -1.711 -1.967 0.568 0.149 0.4996720 -0.443 Down
## 338 1996 -0.443 -1.154 -1.711 -1.967 0.568 0.3935040 4.181 Up
## 339 1996 4.181 -0.443 -1.154 -1.711 -1.967 0.3814800 -0.059 Down
## 340 1996 -0.059 4.181 -0.443 -1.154 -1.711 0.3421440 0.470 Up
## 341 1996 0.470 -0.059 4.181 -0.443 -1.154 0.3359400 0.274 Up
## 342 1996 0.274 0.470 -0.059 4.181 -0.443 0.3281640 -2.255 Down
## 343 1996 -2.255 0.274 0.470 -0.059 4.181 0.2935780 0.566 Up
## 344 1996 0.566 -2.255 0.274 0.470 -0.059 0.3517925 3.791 Up
## 345 1996 3.791 0.566 -2.255 0.274 0.470 0.3897100 0.954 Up
## 346 1996 0.954 3.791 0.566 -2.255 0.274 0.4389060 -0.122 Down
## 347 1996 -0.122 0.954 3.791 0.566 -2.255 0.4250500 2.225 Up
## 348 1996 2.225 -0.122 0.954 3.791 0.566 0.4201380 -0.114 Down
## 349 1996 -0.114 2.225 -0.122 0.954 3.791 0.4030540 1.450 Up
## 350 1996 1.450 -0.114 2.225 -0.122 0.954 0.4347920 -1.393 Down
## 351 1996 -1.393 1.450 -0.114 2.225 -0.122 0.4108400 0.407 Up
## 352 1996 0.407 -1.393 1.450 -0.114 2.225 0.4427260 3.844 Up
## 353 1996 3.844 0.407 -1.393 1.450 -0.114 0.4599800 0.930 Up
## 354 1996 0.930 3.844 0.407 -1.393 1.450 0.4529980 1.506 Up
## 355 1996 1.506 0.930 3.844 0.407 -1.393 0.4676080 1.107 Up
## 356 1996 1.107 1.506 0.930 3.844 0.407 0.3488525 -2.301 Down
## 357 1996 -2.301 1.107 1.506 0.930 3.844 0.4822980 -1.482 Down
## 358 1996 -1.482 -2.301 1.107 1.506 0.930 0.4546720 2.776 Up
## 359 1996 2.776 -1.482 -2.301 1.107 1.506 0.5297280 1.058 Up
## 360 1996 1.058 2.776 -1.482 -2.301 1.107 0.2542150 -1.158 Down
## 361 1997 -1.158 1.058 2.776 -1.482 -2.301 0.4137550 1.533 Up
## 362 1997 1.533 -1.158 1.058 2.776 -1.482 0.5456600 2.195 Up
## 363 1997 2.195 1.533 -1.158 1.058 2.776 0.5147840 -0.728 Down
## 364 1997 -0.728 2.195 1.533 -1.158 1.058 0.5657940 2.030 Up
## 365 1997 2.030 -0.728 2.195 1.533 -1.158 0.5176880 0.432 Up
## 366 1997 0.432 2.030 -0.728 2.195 1.533 0.5222440 2.396 Up
## 367 1997 2.396 0.432 2.030 -0.728 2.195 0.5207640 -0.830 Down
## 368 1997 -0.830 2.396 0.432 2.030 -0.728 0.4910325 -1.366 Down
## 369 1997 -1.366 -0.830 2.396 0.432 2.030 0.5073520 1.789 Up
## 370 1997 1.789 -1.366 -0.830 2.396 0.432 0.5112380 -1.466 Down
## 371 1997 -1.466 1.789 -1.366 -0.830 2.396 0.4902660 -1.144 Down
## 372 1997 -1.144 -1.466 1.789 -1.366 -0.830 0.5268820 -1.303 Down
## 373 1997 -1.303 -1.144 -1.466 1.789 -1.366 0.4807375 -2.065 Down
## 374 1997 -2.065 -1.303 -1.144 -1.466 1.789 0.5184900 -2.672 Down
## 375 1997 -2.672 -2.065 -1.303 -1.144 -1.466 0.4444500 3.889 Up
## 376 1997 3.889 -2.672 -2.065 -1.303 -1.144 0.4771380 -0.127 Down
## 377 1997 -0.127 3.889 -2.672 -2.065 -1.303 0.4604280 6.219 Up
## 378 1997 6.219 -0.127 3.889 -2.672 -2.065 0.4936760 1.453 Up
## 379 1997 1.453 6.219 -0.127 3.889 -2.672 0.5286960 0.603 Up
## 380 1997 0.603 1.453 6.219 -0.127 3.889 0.4798080 2.083 Up
## 381 1997 2.083 0.603 1.453 6.219 -0.127 0.4361380 0.148 Up
## 382 1997 0.148 2.083 0.603 1.453 6.219 0.4808225 1.147 Up
## 383 1997 1.147 0.148 2.083 0.603 1.453 0.4742620 4.110 Up
## 384 1997 4.110 1.147 0.148 2.083 0.603 0.5350140 0.608 Up
## 385 1997 0.608 4.110 1.147 0.148 2.083 0.5278160 -1.268 Down
## 386 1997 -1.268 0.608 4.110 1.147 0.148 0.5221900 3.338 Up
## 387 1997 3.338 -1.268 0.608 4.110 1.147 0.5018450 -0.026 Down
## 388 1997 -0.026 3.338 -1.268 0.608 4.110 0.5370580 -0.151 Down
## 389 1997 -0.151 -0.026 3.338 -1.268 0.608 0.5901360 2.566 Up
## 390 1997 2.566 -0.151 -0.026 3.338 -1.268 0.5497100 0.889 Up
## 391 1997 0.889 2.566 -0.151 -0.026 3.338 0.5283020 -1.436 Down
## 392 1997 -1.436 0.889 2.566 -0.151 -0.026 0.5372720 -3.506 Down
## 393 1997 -3.506 -1.436 0.889 2.566 -0.151 0.5270280 2.523 Up
## 394 1997 2.523 -3.506 -1.436 0.889 2.566 0.5080780 -2.606 Down
## 395 1997 -2.606 2.523 -3.506 -1.436 0.889 0.4460920 3.289 Up
## 396 1997 3.289 -2.606 2.523 -3.506 -1.436 0.5341600 -0.553 Down
## 397 1997 -0.553 3.289 -2.606 2.523 -3.506 0.5210840 2.879 Up
## 398 1997 2.879 -0.553 3.289 -2.606 2.523 0.5785660 -0.557 Down
## 399 1997 -0.557 2.879 -0.553 3.289 -2.606 0.5367020 2.096 Up
## 400 1997 2.096 -0.557 2.879 -0.553 3.289 0.5522780 0.202 Up
## 401 1997 0.202 2.096 -0.557 2.879 -0.553 0.5346440 -2.360 Down
## 402 1997 -2.360 0.202 2.096 -0.557 2.879 0.5184860 -0.267 Down
## 403 1997 -0.267 -2.360 0.202 2.096 -0.557 0.6061160 -2.869 Down
## 404 1997 -2.869 -0.267 -2.360 0.202 2.096 0.8048480 1.409 Up
## 405 1997 1.409 -2.869 -0.267 -2.360 0.202 0.5529760 0.091 Up
## 406 1997 0.091 1.409 -2.869 -0.267 -2.360 0.5549720 3.742 Up
## 407 1997 3.742 0.091 1.409 -2.869 -0.267 0.5708500 -0.798 Down
## 408 1997 -0.798 3.742 0.091 1.409 -2.869 0.4449075 2.972 Up
## 409 1997 2.972 -0.798 3.742 0.091 1.409 0.5976180 -3.090 Down
## 410 1997 -3.090 2.972 -0.798 3.742 0.091 0.5685580 -0.693 Down
## 411 1997 -0.693 -3.090 2.972 -0.798 3.742 0.6502880 -1.090 Down
## 412 1997 -1.090 -0.693 -3.090 2.972 -0.798 0.3666550 4.120 Up
## 413 1998 4.120 -1.090 -0.693 -3.090 2.972 0.4441675 -4.856 Down
## 414 1998 -4.856 4.120 -1.090 -0.693 -3.090 0.6624760 3.646 Up
## 415 1998 3.646 -4.856 4.120 -1.090 -0.693 0.6389200 -0.408 Down
## 416 1998 -0.408 3.646 -4.856 4.120 -1.090 0.6383225 2.369 Up
## 417 1998 2.369 -0.408 3.646 -4.856 4.120 0.6613660 3.283 Up
## 418 1998 3.283 2.369 -0.408 3.646 -4.856 0.6770980 0.754 Up
## 419 1998 0.754 3.283 2.369 -0.408 3.646 0.5820660 1.384 Up
## 420 1998 1.384 0.754 3.283 2.369 -0.408 0.5970025 1.463 Up
## 421 1998 1.463 1.384 0.754 3.283 2.369 0.5945440 0.605 Up
## 422 1998 0.605 1.463 1.384 0.754 3.283 0.6323760 1.224 Up
## 423 1998 1.224 0.605 1.463 1.384 0.754 0.6209240 2.859 Up
## 424 1998 2.859 1.224 0.605 1.463 1.384 0.6356360 -0.338 Down
## 425 1998 -0.338 2.859 1.224 0.605 1.463 0.6205160 2.488 Up
## 426 1998 2.488 -0.338 2.859 1.224 0.605 0.6355720 -1.072 Down
## 427 1998 -1.072 2.488 -0.338 2.859 1.224 0.6154600 1.085 Up
## 428 1998 1.085 -1.072 2.488 -0.338 2.859 0.6470180 -1.320 Down
## 429 1998 -1.320 1.085 -1.072 2.488 -0.338 0.6509300 1.182 Up
## 430 1998 1.182 -1.320 1.085 -1.072 2.488 0.6561840 -1.147 Down
## 431 1998 -1.147 1.182 -1.320 1.085 -1.072 0.5784000 0.053 Up
## 432 1998 0.053 -1.147 1.182 -1.320 1.085 0.5931280 0.157 Up
## 433 1998 0.157 0.053 -1.147 1.182 -1.320 0.5336800 -1.770 Down
## 434 1998 -1.770 0.157 0.053 -1.147 1.182 0.5922825 2.112 Up
## 435 1998 2.112 -1.770 0.157 0.053 -1.147 0.5697960 -1.348 Down
## 436 1998 -1.348 2.112 -1.770 0.157 0.053 0.5954360 0.165 Up
## 437 1998 0.165 -1.348 2.112 -1.770 0.157 0.6621520 2.957 Up
## 438 1998 2.957 0.165 -1.348 2.112 -1.770 0.6187000 1.167 Up
## 439 1998 1.167 2.957 0.165 -1.348 2.112 0.6333400 1.562 Up
## 440 1998 1.562 1.167 2.957 0.165 -1.348 0.5973100 1.926 Up
## 441 1998 1.926 1.562 1.167 2.957 0.165 0.6589820 -3.872 Down
## 442 1998 -3.872 1.926 1.562 1.167 2.957 0.6800560 -1.765 Down
## 443 1998 -1.765 -3.872 1.926 1.562 1.167 0.6602500 -2.786 Down
## 444 1998 -2.786 -1.765 -3.872 1.926 1.562 0.7704200 -2.451 Down
## 445 1998 -2.451 -2.786 -1.765 -3.872 1.926 0.6740020 1.740 Up
## 446 1998 1.740 -2.451 -2.786 -1.765 -3.872 0.6511880 -5.004 Down
## 447 1998 -5.004 1.740 -2.451 -2.786 -1.765 0.7352000 -5.184 Down
## 448 1998 -5.184 -5.004 1.740 -2.451 -2.786 0.9379000 3.611 Up
## 449 1998 3.611 -5.184 -5.004 1.740 -2.451 0.8046250 1.093 Up
## 450 1998 1.093 3.611 -5.184 -5.004 1.740 0.7451400 2.417 Up
## 451 1998 2.417 1.093 3.611 -5.184 -5.004 0.7494360 -4.034 Down
## 452 1998 -4.034 2.417 1.093 3.611 -5.184 0.8106600 -1.816 Down
## 453 1998 -1.816 -4.034 2.417 1.093 3.611 0.9265800 7.317 Up
## 454 1998 7.317 -1.816 -4.034 2.417 1.093 0.8390800 1.349 Up
## 455 1998 1.349 7.317 -1.816 -4.034 2.417 0.7668880 2.615 Up
## 456 1998 2.615 1.349 7.317 -1.816 -4.034 0.7072620 3.854 Up
## 457 1998 3.854 2.615 1.349 7.317 -1.816 0.7545000 -1.340 Down
## 458 1998 -1.340 3.854 2.615 1.349 7.317 0.6489120 3.361 Up
## 459 1998 3.361 -1.340 3.854 2.615 1.349 0.6730980 2.473 Up
## 460 1998 2.473 3.361 -1.340 3.854 2.615 0.5952075 -1.308 Down
## 461 1998 -1.308 2.473 3.361 -1.340 3.854 0.7426600 -0.874 Down
## 462 1998 -0.874 -1.308 2.473 3.361 -1.340 0.7061200 1.849 Up
## 463 1998 1.849 -0.874 -1.308 2.473 3.361 0.7648400 3.219 Up
## 464 1998 3.219 1.849 -0.874 -1.308 2.473 0.5924450 0.241 Up
## 465 1999 0.241 3.219 1.849 -0.874 -1.308 0.6078675 3.731 Up
## 466 1999 3.731 0.241 3.219 1.849 -0.874 0.8879400 -2.496 Down
## 467 1999 -2.496 3.731 0.241 3.219 1.849 0.8290000 -1.453 Down
## 468 1999 -1.453 -2.496 3.731 0.241 3.219 0.8372250 4.444 Up
## 469 1999 4.444 -1.453 -2.496 3.731 0.241 0.8559800 -3.145 Down
## 470 1999 -3.145 4.444 -1.453 -2.496 3.731 0.8495600 -0.748 Down
## 471 1999 -0.748 -3.145 4.444 -1.453 -2.496 0.7340200 0.739 Up
## 472 1999 0.739 -0.748 -3.145 4.444 -1.453 0.7078150 -0.072 Down
## 473 1999 -0.072 0.739 -0.748 -3.145 4.444 0.7613400 2.999 Up
## 474 1999 2.999 -0.072 0.739 -0.748 -3.145 0.7621200 1.499 Up
## 475 1999 1.499 2.999 -0.072 0.739 -0.748 0.8181600 0.363 Up
## 476 1999 0.363 1.499 2.999 -0.072 0.739 0.7954200 -1.269 Down
## 477 1999 -1.269 0.363 1.499 2.999 -0.072 0.7445600 0.851 Up
## 478 1999 0.851 -1.269 0.363 1.499 2.999 0.7760500 4.223 Up
## 479 1999 4.223 0.851 -1.269 0.363 1.499 0.7732600 -2.177 Down
## 480 1999 -2.177 4.223 0.851 -1.269 0.363 0.9331600 2.870 Up
## 481 1999 2.870 -2.177 4.223 0.851 -1.269 0.9585200 -1.597 Down
## 482 1999 -1.597 2.870 -2.177 4.223 0.851 0.8991000 0.735 Up
## 483 1999 0.735 -1.597 2.870 -2.177 4.223 0.8696600 -0.535 Down
## 484 1999 -0.535 0.735 -1.597 2.870 -2.177 0.7919200 -0.561 Down
## 485 1999 -0.561 -0.535 0.735 -1.597 2.870 0.7317600 -2.139 Down
## 486 1999 -2.139 -0.561 -0.535 0.735 -1.597 0.7827120 1.990 Up
## 487 1999 1.990 -2.139 -0.561 -0.535 0.735 0.7064750 -2.569 Down
## 488 1999 -2.569 1.990 -2.139 -0.561 -0.535 0.6853800 3.803 Up
## 489 1999 3.803 -2.569 1.990 -2.139 -0.561 0.7575200 -2.050 Down
## 490 1999 -2.050 3.803 -2.569 1.990 -2.139 0.6897520 5.771 Up
## 491 1999 5.771 -2.050 3.803 -2.569 1.990 0.8093960 0.867 Up
## 492 1999 0.867 5.771 -2.050 3.803 -2.569 0.7614250 1.105 Up
## 493 1999 1.105 0.867 5.771 -2.050 3.803 0.7420600 -4.359 Down
## 494 1999 -4.359 1.105 0.867 5.771 -2.050 0.7169820 -2.080 Down
## 495 1999 -2.080 -4.359 1.105 0.867 5.771 0.7070100 -2.140 Down
## 496 1999 -2.140 -2.080 -4.359 1.105 0.867 0.7473300 2.106 Up
## 497 1999 2.106 -2.140 -2.080 -4.359 1.105 0.7500200 0.673 Up
## 498 1999 0.673 2.106 -2.140 -2.080 -4.359 0.6606500 0.872 Up
## 499 1999 0.872 0.673 2.106 -2.140 -2.080 0.7137900 0.665 Up
## 500 1999 0.665 0.872 0.673 2.106 -2.140 0.7036200 -0.411 Down
## 501 1999 -0.411 0.665 0.872 0.673 2.106 0.7722250 -1.201 Down
## 502 1999 -1.201 -0.411 0.665 0.872 0.673 0.7561200 -4.348 Down
## 503 1999 -4.348 -1.201 -0.411 0.665 0.872 0.7942200 0.427 Up
## 504 1999 0.427 -4.348 -1.201 -0.411 0.665 0.8871600 4.148 Up
## 505 1999 4.148 0.427 -4.348 -1.201 -0.411 0.8778600 -6.632 Down
## 506 1999 -6.632 4.148 0.427 -4.348 -1.201 0.8121200 4.348 Up
## 507 1999 4.348 -6.632 4.148 0.427 -4.348 0.9249800 4.708 Up
## 508 1999 4.708 4.348 -6.632 4.148 0.427 0.9722000 0.536 Up
## 509 1999 0.536 4.708 4.348 -6.632 4.148 0.9337800 1.885 Up
## 510 1999 1.885 0.536 4.708 4.348 -6.632 0.8874600 1.858 Up
## 511 1999 1.858 1.885 0.536 4.708 4.348 0.9229000 -0.378 Down
## 512 1999 -0.378 1.858 1.885 0.536 4.708 0.7116300 1.177 Up
## 513 1999 1.177 -0.378 1.858 1.885 0.536 0.9217400 -1.134 Down
## 514 1999 -1.134 1.177 -0.378 1.858 1.885 1.0137800 0.282 Up
## 515 1999 0.282 -1.134 1.177 -0.378 1.858 1.0918800 2.626 Up
## 516 1999 2.626 0.282 -1.134 1.177 -0.378 0.8616750 0.748 Up
## 517 2000 0.748 2.626 0.282 -1.134 1.177 0.5749180 -1.891 Down
## 518 2000 -1.891 0.748 2.626 0.282 -1.134 1.0687600 1.643 Up
## 519 2000 1.643 -1.891 0.748 2.626 0.282 1.0339400 -1.624 Down
## 520 2000 -1.624 1.643 -1.891 0.748 2.626 1.1137500 -5.634 Down
## 521 2000 -5.634 -1.624 1.643 -1.891 0.748 1.1064200 4.721 Up
## 522 2000 4.721 -5.634 -1.624 1.643 -1.891 1.0410000 -2.615 Down
## 523 2000 -2.615 4.721 -5.634 -1.624 1.643 1.0201600 -2.958 Down
## 524 2000 -2.958 -2.615 4.721 -5.634 -1.624 1.0230600 -0.946 Down
## 525 2000 -0.946 -2.958 -2.615 4.721 -5.634 1.0634750 5.686 Up
## 526 2000 5.686 -0.946 -2.958 -2.615 4.721 1.1707600 -1.001 Down
## 527 2000 -1.001 5.686 -0.946 -2.958 -2.615 1.1615800 4.975 Up
## 528 2000 4.975 -1.001 5.686 -0.946 -2.958 1.2380600 4.301 Up
## 529 2000 4.301 4.975 -1.001 5.686 -0.946 1.0384400 -1.891 Down
## 530 2000 -1.891 4.301 4.975 -1.001 5.686 1.0685600 1.186 Up
## 531 2000 1.186 -1.891 4.301 4.975 -1.001 1.1094120 -10.538 Down
## 532 2000 -10.538 1.186 -1.891 4.301 4.975 1.0625400 5.748 Up
## 533 2000 5.748 -10.538 1.186 -1.891 4.301 1.0529250 1.247 Up
## 534 2000 1.247 5.748 -10.538 1.186 -1.891 1.0070000 -1.363 Down
## 535 2000 -1.363 1.247 5.748 -10.538 1.186 0.9401400 -0.815 Down
## 536 2000 -0.815 -1.363 1.247 5.748 -10.538 0.9004800 -0.986 Down
## 537 2000 -0.986 -0.815 -1.363 1.247 5.748 0.8584400 -2.056 Down
## 538 2000 -2.056 -0.986 -0.815 -1.363 1.247 0.9196600 7.202 Up
## 539 2000 7.202 -2.056 -0.986 -0.815 -1.363 0.9818000 -1.375 Down
## 540 2000 -1.375 7.202 -2.056 -0.986 -0.815 0.8567200 0.515 Up
## 541 2000 0.515 -1.375 7.202 -2.056 -0.986 0.9803800 -1.569 Down
## 542 2000 -1.569 0.515 -1.375 7.202 -2.056 0.9666200 0.910 Up
## 543 2000 0.910 -1.569 0.515 -1.375 7.202 1.1194400 1.671 Up
## 544 2000 1.671 0.910 -1.569 0.515 -1.375 0.8375500 2.102 Up
## 545 2000 2.102 1.671 0.910 -1.569 0.515 0.9615600 -1.973 Down
## 546 2000 -1.973 2.102 1.671 0.910 -1.569 0.9513200 -4.074 Down
## 547 2000 -4.074 -1.973 2.102 1.671 0.910 1.0443800 3.031 Up
## 548 2000 3.031 -4.074 -1.973 2.102 1.671 0.9874800 0.609 Up
## 549 2000 0.609 3.031 -4.074 -1.973 2.102 0.9354600 1.351 Up
## 550 2000 1.351 0.609 3.031 -4.074 -1.973 0.8706600 0.987 Up
## 551 2000 0.987 1.351 0.609 3.031 -4.074 0.7888200 0.951 Up
## 552 2000 0.951 0.987 1.351 0.609 3.031 0.8343800 -1.727 Down
## 553 2000 -1.727 0.951 0.987 1.351 0.609 0.9450250 -1.920 Down
## 554 2000 -1.920 -1.727 0.951 0.987 1.351 1.0482400 -1.166 Down
## 555 2000 -1.166 -1.920 -1.727 0.951 0.987 1.0764600 -0.843 Down
## 556 2000 -0.843 -1.166 -1.920 -1.727 0.951 1.1334000 -1.916 Down
## 557 2000 -1.916 -0.843 -1.166 -1.920 -1.727 1.1285800 -2.471 Down
## 558 2000 -2.471 -1.916 -0.843 -1.166 -1.920 1.1521200 1.656 Up
## 559 2000 1.656 -2.471 -1.916 -0.843 -1.166 1.2167800 -1.242 Down
## 560 2000 -1.242 1.656 -2.471 -1.916 -0.843 1.1822200 3.415 Up
## 561 2000 3.415 -1.242 1.656 -2.471 -1.916 1.1850200 -4.255 Down
## 562 2000 -4.255 3.415 -1.242 1.656 -2.471 0.9589200 0.127 Up
## 563 2000 0.127 -4.255 3.415 -1.242 1.656 1.0683200 -1.897 Down
## 564 2000 -1.897 0.127 -4.255 3.415 -1.242 0.8652425 -1.978 Down
## 565 2000 -1.978 -1.897 0.127 -4.255 3.415 0.9516260 4.156 Up
## 566 2000 4.156 -1.978 -1.897 0.127 -4.255 1.1777800 -4.215 Down
## 567 2000 -4.215 4.156 -1.978 -1.897 0.127 1.2206600 -0.473 Down
## 568 2000 -0.473 -4.215 4.156 -1.978 -1.897 1.2946800 1.097 Up
## 569 2001 1.097 -0.473 -4.215 4.156 -1.978 0.9875000 -1.661 Down
## 570 2001 -1.661 1.097 -0.473 -4.215 4.156 1.6429750 1.556 Up
## 571 2001 1.556 -1.661 1.097 -0.473 -4.215 1.2581000 1.819 Up
## 572 2001 1.819 1.556 -1.661 1.097 -0.473 1.3519000 0.924 Up
## 573 2001 0.924 1.819 1.556 -1.661 1.097 1.2123200 -0.404 Down
## 574 2001 -0.404 0.924 1.819 1.556 -1.661 1.1330800 -2.572 Down
## 575 2001 -2.572 -0.404 0.924 1.819 1.556 1.0827200 -1.006 Down
## 576 2001 -1.006 -2.572 -0.404 0.924 1.819 1.1351000 -4.277 Down
## 577 2001 -4.277 -1.006 -2.572 -0.404 0.924 1.2294750 -0.938 Down
## 578 2001 -0.938 -4.277 -1.006 -2.572 -0.404 1.2118200 -0.062 Down
## 579 2001 -0.062 -0.938 -4.277 -1.006 -2.572 1.0706400 -6.720 Down
## 580 2001 -6.720 -0.062 -0.938 -4.277 -1.006 1.3580720 -0.930 Down
## 581 2001 -0.930 -6.720 -0.062 -0.938 -4.277 1.3594500 1.799 Up
## 582 2001 1.799 -0.930 -6.720 -0.062 -0.938 1.2553800 -2.749 Down
## 583 2001 -2.749 1.799 -0.930 -6.720 -0.062 1.3402780 4.880 Up
## 584 2001 4.880 -2.749 1.799 -0.930 -6.720 1.2011750 5.026 Up
## 585 2001 5.026 4.880 -2.749 1.799 -0.930 1.3535800 0.810 Up
## 586 2001 0.810 5.026 4.880 -2.749 1.799 1.1738400 1.082 Up
## 587 2001 1.082 0.810 5.026 4.880 -2.749 1.2020600 -1.653 Down
## 588 2001 -1.653 1.082 0.810 5.026 4.880 1.0101200 3.716 Up
## 589 2001 3.716 -1.653 1.082 0.810 5.026 1.1643400 -1.089 Down
## 590 2001 -1.089 3.716 -1.653 1.082 0.810 1.0997800 -1.348 Down
## 591 2001 -1.348 -1.089 3.716 -1.653 1.082 1.1065500 0.340 Up
## 592 2001 0.340 -1.348 -1.089 3.716 -1.653 0.9662000 -4.000 Down
## 593 2001 -4.000 0.340 -1.348 -1.089 3.716 1.1897300 0.905 Up
## 594 2001 0.905 -4.000 0.340 -1.348 -1.089 1.2765240 -0.079 Down
## 595 2001 -0.079 0.905 -4.000 0.340 -1.348 1.3141520 -2.760 Down
## 596 2001 -2.760 -0.079 0.905 -4.000 0.340 0.9355025 2.107 Up
## 597 2001 2.107 -2.760 -0.079 0.905 -4.000 1.2418600 -0.397 Down
## 598 2001 -0.397 2.107 -2.760 -0.079 0.905 1.2217200 -0.415 Down
## 599 2001 -0.415 -0.397 2.107 -2.760 -0.079 1.1391000 0.707 Up
## 600 2001 0.707 -0.415 -0.397 2.107 -2.760 1.1073600 -1.992 Down
## 601 2001 -1.992 0.707 -0.415 -0.397 2.107 1.0026800 -2.369 Down
## 602 2001 -2.369 -1.992 0.707 -0.415 -0.397 0.9795000 1.976 Up
## 603 2001 1.976 -2.369 -1.992 0.707 -0.415 1.0158600 -4.334 Down
## 604 2001 -4.334 1.976 -2.369 -1.992 0.707 0.9741000 -4.217 Down
## 605 2001 -4.217 -4.334 1.976 -2.369 -1.992 1.3367000 -11.050 Down
## 606 2001 -11.050 -4.217 -4.334 1.976 -2.369 1.9500816 7.780 Up
## 607 2001 7.780 -11.050 -4.217 -4.334 1.976 1.5956000 2.924 Up
## 608 2001 2.924 7.780 -11.050 -4.217 -4.334 1.4053600 1.892 Up
## 609 2001 1.892 2.924 7.780 -11.050 -4.217 1.3110360 -1.664 Down
## 610 2001 -1.664 1.892 2.924 7.780 -11.050 1.2490400 2.900 Up
## 611 2001 2.900 -1.664 1.892 2.924 7.780 1.2736200 -1.576 Down
## 612 2001 -1.576 2.900 -1.664 1.892 2.924 1.2390600 3.045 Up
## 613 2001 3.045 -1.576 2.900 -1.664 1.892 1.3292600 1.637 Up
## 614 2001 1.637 3.045 -1.576 2.900 -1.664 1.3194000 1.027 Up
## 615 2001 1.027 1.637 3.045 -1.576 2.900 1.0216500 -0.947 Down
## 616 2001 -0.947 1.027 1.637 3.045 -1.576 1.3121600 1.655 Up
## 617 2001 1.655 -0.947 1.027 1.637 3.045 1.4045600 -3.041 Down
## 618 2001 -3.041 1.655 -0.947 1.027 1.637 1.3707800 1.941 Up
## 619 2001 1.941 -3.041 1.655 -0.947 1.027 1.4567600 1.409 Up
## 620 2001 1.409 1.941 -3.041 1.655 -0.947 0.7561175 0.990 Up
## 621 2002 0.990 1.409 1.941 -3.041 1.655 1.2566250 -2.295 Down
## 622 2002 -2.295 0.990 1.409 1.941 -3.041 1.3060000 -1.573 Down
## 623 2002 -1.573 -2.295 0.990 1.409 1.941 1.3738400 0.506 Up
## 624 2002 0.506 -1.573 -2.295 0.990 1.409 1.4221750 -0.978 Down
## 625 2002 -0.978 0.506 -1.573 -2.295 0.990 1.5885200 -2.315 Down
## 626 2002 -2.315 -0.978 0.506 -1.573 -2.295 1.5390400 0.726 Up
## 627 2002 0.726 -2.315 -0.978 0.506 -1.573 1.2202400 -1.299 Down
## 628 2002 -1.299 0.726 -2.315 -0.978 0.506 1.3553500 3.848 Up
## 629 2002 3.848 -1.299 0.726 -2.315 -0.978 1.3838200 2.874 Up
## 630 2002 2.874 3.848 -1.299 0.726 -2.315 1.5228600 0.159 Up
## 631 2002 0.159 2.874 3.848 -1.299 0.726 1.3142600 -1.497 Down
## 632 2002 -1.497 0.159 2.874 3.848 -1.299 1.2623800 -0.114 Down
## 633 2002 -0.114 -1.497 0.159 2.874 3.848 1.1523000 -2.149 Down
## 634 2002 -2.149 -0.114 -1.497 0.159 2.874 1.1682600 -1.044 Down
## 635 2002 -1.044 -2.149 -0.114 -1.497 0.159 1.3132600 1.275 Up
## 636 2002 1.275 -1.044 -2.149 -0.114 -1.497 1.2765800 -4.342 Down
## 637 2002 -4.342 1.275 -1.044 -2.149 -0.114 1.3670200 -0.269 Down
## 638 2002 -0.269 -4.342 1.275 -1.044 -2.149 1.4086400 -1.718 Down
## 639 2002 -1.718 -0.269 -4.342 1.275 -1.044 1.2608400 4.891 Up
## 640 2002 4.891 -1.718 -0.269 -4.342 1.275 1.2908600 -2.058 Down
## 641 2002 -2.058 4.891 -1.718 -0.269 -4.342 1.0809800 -1.539 Down
## 642 2002 -1.539 -2.058 4.891 -1.718 -0.269 1.1605500 -3.712 Down
## 643 2002 -3.712 -1.539 -2.058 4.891 -1.718 1.4067600 -1.972 Down
## 644 2002 -1.972 -3.712 -1.539 -2.058 4.891 1.4377640 -1.800 Down
## 645 2002 -1.800 -1.972 -3.712 -1.539 -2.058 1.3305400 0.069 Up
## 646 2002 0.069 -1.800 -1.972 -3.712 -1.539 1.8212380 -0.080 Down
## 647 2002 -0.080 0.069 -1.800 -1.972 -3.712 1.3689250 -6.839 Down
## 648 2002 -6.839 -0.080 0.069 -1.800 -1.972 1.6076160 -7.992 Down
## 649 2002 -7.992 -6.839 -0.080 0.069 -1.800 2.2750800 0.600 Up
## 650 2002 0.600 -7.992 -6.839 -0.080 0.069 2.3370880 1.337 Up
## 651 2002 1.337 0.600 -7.992 -6.839 -0.080 1.7728800 5.137 Up
## 652 2002 5.137 1.337 0.600 -7.992 -6.839 1.4743200 2.215 Up
## 653 2002 2.215 5.137 1.337 0.600 -7.992 1.3276800 1.302 Up
## 654 2002 1.302 2.215 5.137 1.337 0.600 1.2811800 -2.635 Down
## 655 2002 -2.635 1.302 2.215 5.137 1.337 1.1344400 -2.418 Down
## 656 2002 -2.418 -2.635 1.302 2.215 5.137 1.3119250 -0.460 Down
## 657 2002 -0.460 -2.418 -2.635 1.302 2.215 1.1252400 -4.992 Down
## 658 2002 -4.992 -0.460 -2.418 -2.635 1.302 1.4535600 -2.132 Down
## 659 2002 -2.132 -4.992 -0.460 -2.418 -2.635 1.5720280 -3.238 Down
## 660 2002 -3.238 -2.132 -4.992 -0.460 -2.418 1.7364200 4.339 Up
## 661 2002 4.339 -3.238 -2.132 -4.992 -0.460 1.8688640 5.874 Up
## 662 2002 5.874 4.339 -3.238 -2.132 -4.992 1.5889580 1.499 Up
## 663 2002 1.499 5.874 4.339 -3.238 -2.132 1.5262140 0.369 Up
## 664 2002 0.369 1.499 5.874 4.339 -3.238 1.4852600 -0.690 Down
## 665 2002 -0.690 0.369 1.499 5.874 4.339 1.5174800 1.687 Up
## 666 2002 1.687 -0.690 0.369 1.499 5.874 1.3745200 2.277 Up
## 667 2002 2.277 1.687 -0.690 0.369 1.499 1.6358400 0.619 Up
## 668 2002 0.619 2.277 1.687 -0.690 0.369 1.2778400 -2.572 Down
## 669 2002 -2.572 0.619 2.277 1.687 -0.690 1.4361200 -2.494 Down
## 670 2002 -2.494 -2.572 0.619 2.277 1.687 1.2957200 0.706 Up
## 671 2002 0.706 -2.494 -2.572 0.619 2.277 1.4276460 -2.273 Down
## 672 2002 -2.273 0.706 -2.494 -2.572 0.619 0.7624775 3.791 Up
## 673 2003 3.791 -2.273 0.706 -2.494 -2.572 1.1265750 2.089 Up
## 674 2003 2.089 3.791 -2.273 0.706 -2.494 1.4988800 -2.780 Down
## 675 2003 -2.780 2.089 3.791 -2.273 0.706 1.4201200 -4.478 Down
## 676 2003 -4.478 -2.780 2.089 3.791 -2.273 1.5538375 -0.662 Down
## 677 2003 -0.662 -4.478 -2.780 2.089 3.791 1.5158460 -3.040 Down
## 678 2003 -3.040 -0.662 -4.478 -2.780 2.089 1.3737200 0.627 Up
## 679 2003 0.627 -3.040 -0.662 -4.478 -2.780 1.3399200 1.591 Up
## 680 2003 1.591 0.627 -3.040 -0.662 -4.478 1.2296750 -0.828 Down
## 681 2003 -0.828 1.591 0.627 -3.040 -0.662 1.3496800 -1.458 Down
## 682 2003 -1.458 -0.828 1.591 0.627 -3.040 1.2931800 0.528 Up
## 683 2003 0.528 -1.458 -0.828 1.591 0.627 1.5321800 7.503 Up
## 684 2003 7.503 0.528 -1.458 -0.828 1.591 1.6103460 -3.605 Down
## 685 2003 -3.605 7.503 0.528 -1.458 -0.828 1.2812000 1.778 Up
## 686 2003 1.778 -3.605 7.503 0.528 -1.458 1.4255200 -1.200 Down
## 687 2003 -1.200 1.778 -3.605 7.503 0.528 1.2880000 2.911 Up
## 688 2003 2.911 -1.200 1.778 -3.605 7.503 1.4023500 0.585 Up
## 689 2003 0.585 2.911 -1.200 1.778 -3.605 1.4802000 3.479 Up
## 690 2003 3.479 0.585 2.911 -1.200 1.778 1.5077820 0.358 Up
## 691 2003 0.358 3.479 0.585 2.911 -1.200 1.4667000 1.167 Up
## 692 2003 1.167 0.358 3.479 0.585 2.911 1.4425800 -1.173 Down
## 693 2003 -1.173 1.167 0.358 3.479 0.585 1.3976600 3.254 Up
## 694 2003 3.254 -1.173 1.167 0.358 3.479 1.6164000 2.508 Up
## 695 2003 2.508 3.254 -1.173 1.167 0.358 1.6523400 0.086 Up
## 696 2003 0.086 2.508 3.254 -1.173 1.167 1.3854200 0.716 Up
## 697 2003 0.716 0.086 2.508 3.254 -1.173 1.5085200 -1.955 Down
## 698 2003 -1.955 0.716 0.086 2.508 3.254 1.3801600 0.971 Up
## 699 2003 0.971 -1.955 0.716 0.086 2.508 1.3356500 1.262 Up
## 700 2003 1.262 0.971 -1.955 0.716 0.086 1.4582400 -0.483 Down
## 701 2003 -0.483 1.262 0.971 -1.955 0.716 1.5312200 0.540 Up
## 702 2003 0.540 -0.483 1.262 0.971 -1.955 1.4026200 -1.855 Down
## 703 2003 -1.855 0.540 -0.483 1.262 0.971 1.4456000 -0.261 Down
## 704 2003 -0.261 -1.855 0.540 -0.483 1.262 1.3274600 1.338 Up
## 705 2003 1.338 -0.261 -1.855 0.540 -0.483 1.0372940 0.241 Up
## 706 2003 0.241 1.338 -0.261 -1.855 0.540 1.2710000 1.505 Up
## 707 2003 1.505 0.241 1.338 -0.261 -1.855 1.0624200 1.327 Up
## 708 2003 1.327 1.505 0.241 1.338 -0.261 1.5163000 -0.270 Down
## 709 2003 -0.270 1.327 1.505 0.241 1.338 1.3737600 1.735 Up
## 710 2003 1.735 -0.270 1.327 1.505 0.241 1.3820220 -3.807 Down
## 711 2003 -3.807 1.735 -0.270 1.327 1.505 1.4278000 3.310 Up
## 712 2003 3.310 -3.807 1.735 -0.270 1.327 1.4726200 0.797 Up
## 713 2003 0.797 3.310 -3.807 1.735 -0.270 1.2509200 0.121 Up
## 714 2003 0.121 0.797 3.310 -3.807 1.735 1.3206400 -1.002 Down
## 715 2003 -1.002 0.121 0.797 3.310 -3.807 1.4684800 2.119 Up
## 716 2003 2.119 -1.002 0.121 0.797 3.310 1.5384400 0.238 Up
## 717 2003 0.238 2.119 -1.002 0.121 0.797 1.4184000 -0.272 Down
## 718 2003 -0.272 0.238 2.119 -1.002 0.121 1.2989000 -1.435 Down
## 719 2003 -1.435 -0.272 0.238 2.119 -1.002 1.3310600 2.214 Up
## 720 2003 2.214 -1.435 -0.272 0.238 2.119 1.0553550 0.312 Up
## 721 2003 0.312 2.214 -1.435 -0.272 0.238 1.3857800 1.191 Up
## 722 2003 1.191 0.312 2.214 -1.435 -0.272 1.3585200 1.352 Up
## 723 2003 1.352 1.191 0.312 2.214 -1.435 1.5495200 0.664 Up
## 724 2003 0.664 1.352 1.191 0.312 2.214 0.8177825 1.149 Up
## 725 2004 1.149 0.664 1.352 1.191 0.312 1.0630250 1.207 Up
## 726 2004 1.207 1.149 0.664 1.352 1.191 1.6733400 1.602 Up
## 727 2004 1.602 1.207 1.149 0.664 1.352 1.6073600 0.151 Up
## 728 2004 0.151 1.602 1.207 1.149 0.664 1.6776750 -0.913 Down
## 729 2004 -0.913 0.151 1.602 1.207 1.149 1.7105200 1.028 Up
## 730 2004 1.028 -0.913 0.151 1.602 1.207 1.5510200 0.267 Up
## 731 2004 0.267 1.028 -0.913 0.151 1.602 1.4400400 -0.148 Down
## 732 2004 -0.148 0.267 1.028 -0.913 0.151 1.4553250 0.073 Up
## 733 2004 0.073 -0.148 0.267 1.028 -0.913 1.4418000 1.041 Up
## 734 2004 1.041 0.073 -0.148 0.267 1.028 1.3943200 -3.137 Down
## 735 2004 -3.137 1.041 0.073 -0.148 0.267 1.5361200 -0.963 Down
## 736 2004 -0.963 -3.137 1.041 0.073 -0.148 1.4836000 -0.155 Down
## 737 2004 -0.155 -0.963 -3.137 1.041 0.073 1.4458200 3.046 Up
## 738 2004 3.046 -0.155 -0.963 -3.137 1.041 1.4977000 -0.218 Down
## 739 2004 -0.218 3.046 -0.155 -0.963 -3.137 1.3675000 -0.413 Down
## 740 2004 -0.413 -0.218 3.046 -0.155 -0.963 1.4259600 0.528 Up
## 741 2004 0.528 -0.413 -0.218 3.046 -0.155 1.5328600 -2.920 Down
## 742 2004 -2.920 0.528 -0.413 -0.218 3.046 1.6315800 -0.777 Down
## 743 2004 -0.777 -2.920 0.528 -0.413 -0.218 1.5731200 -0.273 Down
## 744 2004 -0.273 -0.777 -2.920 0.528 -0.413 1.5793600 -0.195 Down
## 745 2004 -0.195 -0.273 -0.777 -2.920 0.528 1.3602600 2.480 Up
## 746 2004 2.480 -0.195 -0.273 -0.777 -2.920 1.3525400 0.162 Up
## 747 2004 0.162 2.480 -0.195 -0.273 -0.777 1.2093500 1.245 Up
## 748 2004 1.245 0.162 2.480 -0.195 -0.273 1.2098750 -0.128 Down
## 749 2004 -0.128 1.245 0.162 2.480 -0.195 1.2982000 -0.052 Down
## 750 2004 -0.052 -0.128 1.245 0.162 2.480 1.4316400 -0.798 Down
## 751 2004 -0.798 -0.052 -0.128 1.245 0.162 1.3568200 -1.117 Down
## 752 2004 -1.117 -0.798 -0.052 -0.128 1.245 1.2998250 -1.026 Down
## 753 2004 -1.026 -1.117 -0.798 -0.052 -0.128 1.3270600 -1.379 Down
## 754 2004 -1.379 -1.026 -1.117 -0.798 -0.052 1.4927000 1.429 Up
## 755 2004 1.429 -1.379 -1.026 -1.117 -0.798 1.4813600 -3.426 Down
## 756 2004 -3.426 1.429 -1.379 -1.026 -1.117 1.3803800 0.078 Up
## 757 2004 0.078 -3.426 1.429 -1.379 -1.026 1.2644400 3.151 Up
## 758 2004 3.151 0.078 -3.426 1.429 -1.379 1.2411600 0.858 Up
## 759 2004 0.858 3.151 0.078 -3.426 1.429 1.0351200 0.529 Up
## 760 2004 0.529 0.858 3.151 0.078 -3.426 1.0331940 0.924 Up
## 761 2004 0.924 0.529 0.858 3.151 0.078 1.2733000 0.412 Up
## 762 2004 0.412 0.924 0.529 0.858 3.151 1.2593600 -1.634 Down
## 763 2004 -1.634 0.412 0.924 0.529 0.858 1.2888400 1.927 Up
## 764 2004 1.927 -1.634 0.412 0.924 0.529 1.4786400 -0.827 Down
## 765 2004 -0.827 1.927 -1.634 0.412 0.924 1.4216400 -1.242 Down
## 766 2004 -1.242 -0.827 1.927 -1.634 0.412 1.3889400 -1.124 Down
## 767 2004 -1.124 -1.242 -0.827 1.927 -1.634 1.5878200 3.145 Up
## 768 2004 3.145 -1.124 -1.242 -0.827 1.927 1.5873600 3.183 Up
## 769 2004 3.183 3.145 -1.124 -1.242 -0.827 1.6659000 1.544 Up
## 770 2004 1.544 3.183 3.145 -1.124 -1.242 1.4476800 -1.168 Down
## 771 2004 -1.168 1.544 3.183 3.145 -1.124 1.4970400 1.052 Up
## 772 2004 1.052 -1.168 1.544 3.183 3.145 1.1187950 0.720 Up
## 773 2004 0.720 1.052 -1.168 1.544 3.183 1.6092800 -0.266 Down
## 774 2004 -0.266 0.720 1.052 -1.168 1.544 1.4963800 0.522 Up
## 775 2004 0.522 -0.266 0.720 1.052 -1.168 1.7610400 1.334 Up
## 776 2004 1.334 0.522 -0.266 0.720 1.052 1.3133500 0.148 Up
## 777 2005 0.148 1.334 0.522 -0.266 0.720 0.8895200 -2.123 Down
## 778 2005 -2.123 0.148 1.334 0.522 -0.266 1.6035400 -0.141 Down
## 779 2005 -0.141 -2.123 0.148 1.334 0.522 1.4774000 -1.406 Down
## 780 2005 -1.406 -0.141 -2.123 0.148 1.334 1.6077500 0.299 Up
## 781 2005 0.299 -1.406 -0.141 -2.123 0.148 1.5966600 2.704 Up
## 782 2005 2.704 0.299 -1.406 -0.141 -2.123 1.6252280 0.189 Up
## 783 2005 0.189 2.704 0.299 -1.406 -0.141 1.4656900 -0.308 Down
## 784 2005 -0.308 0.189 2.704 0.299 -1.406 1.4877360 0.814 Up
## 785 2005 0.814 -0.308 0.189 2.704 0.299 1.5721150 0.887 Up
## 786 2005 0.887 0.814 -0.308 0.189 2.704 1.6650280 -1.803 Down
## 787 2005 -1.803 0.887 0.814 -0.308 0.189 1.5541460 -0.869 Down
## 788 2005 -0.869 -1.803 0.887 0.814 -0.308 1.7060900 -1.532 Down
## 789 2005 -1.532 -0.869 -1.803 0.887 0.814 1.9756250 0.128 Up
## 790 2005 0.128 -1.532 -0.869 -1.803 0.887 2.0899000 0.706 Up
## 791 2005 0.706 0.128 -1.532 -0.869 -1.803 1.8619840 -3.266 Down
## 792 2005 -3.266 0.706 0.128 -1.532 -0.869 2.1199760 0.831 Up
## 793 2005 0.831 -3.266 0.706 0.128 -1.532 2.1789720 0.411 Up
## 794 2005 0.411 0.831 -3.266 0.706 0.128 2.0901840 1.253 Up
## 795 2005 1.253 0.411 0.831 -3.266 0.706 2.0315680 -1.477 Down
## 796 2005 -1.477 1.253 0.411 0.831 -3.266 1.9531060 3.053 Up
## 797 2005 3.053 -1.477 1.253 0.411 0.831 1.8836100 0.799 Up
## 798 2005 0.799 3.053 -1.477 1.253 0.411 1.6279780 -0.230 Down
## 799 2005 -0.230 0.799 3.053 -1.477 1.253 1.7730225 0.175 Up
## 800 2005 0.175 -0.230 0.799 3.053 -1.477 1.7204560 1.573 Up
## 801 2005 1.573 0.175 -0.230 0.799 3.053 1.8766700 -2.086 Down
## 802 2005 -2.086 1.573 0.175 -0.230 0.799 1.9414400 0.241 Up
## 803 2005 0.241 -2.086 1.573 0.175 -0.230 1.7967240 1.458 Up
## 804 2005 1.458 0.241 -2.086 1.573 0.175 1.8856350 1.325 Up
## 805 2005 1.325 1.458 0.241 -2.086 1.573 1.8711840 0.469 Up
## 806 2005 0.469 1.325 1.458 0.241 -2.086 1.9167100 0.041 Up
## 807 2005 0.041 0.469 1.325 1.458 0.241 1.8777680 -0.629 Down
## 808 2005 -0.629 0.041 0.469 1.325 1.458 1.9342940 0.324 Up
## 809 2005 0.324 -0.629 0.041 0.469 1.325 1.9049680 -0.868 Down
## 810 2005 -0.868 0.324 -0.629 0.041 0.469 1.7218800 -1.198 Down
## 811 2005 -1.198 -0.868 0.324 -0.629 0.041 1.6685900 1.072 Up
## 812 2005 1.072 -1.198 -0.868 0.324 -0.629 1.9502900 1.926 Up
## 813 2005 1.926 1.072 -1.198 -0.868 0.324 1.9869325 -0.288 Down
## 814 2005 -0.288 1.926 1.072 -1.198 -0.868 2.2477940 -1.827 Down
## 815 2005 -1.827 -0.288 1.926 1.072 -1.198 2.2683360 1.112 Up
## 816 2005 1.112 -1.827 -0.288 1.926 1.072 2.0758220 -2.678 Down
## 817 2005 -2.678 1.112 -1.827 -0.288 1.926 2.3807600 -0.780 Down
## 818 2005 -0.780 -2.678 1.112 -1.827 -0.288 2.3052800 -0.588 Down
## 819 2005 -0.588 -0.780 -2.678 1.112 -1.827 2.4086680 1.595 Up
## 820 2005 1.595 -0.588 -0.780 -2.678 1.112 2.3505560 1.813 Up
## 821 2005 1.813 1.595 -0.588 -0.780 -2.678 2.4881100 1.195 Up
## 822 2005 1.195 1.813 1.595 -0.588 -0.780 2.0637380 1.097 Up
## 823 2005 1.097 1.195 1.813 1.595 -0.588 2.2264120 1.601 Up
## 824 2005 1.601 1.097 1.195 1.813 1.595 1.7797775 -0.250 Down
## 825 2005 -0.250 1.601 1.097 1.195 1.813 2.2800680 -0.451 Down
## 826 2005 -0.451 -0.250 1.601 1.097 1.195 2.1210000 0.631 Up
## 827 2005 0.631 -0.451 -0.250 1.601 1.097 2.2353740 0.106 Up
## 828 2005 0.106 0.631 -0.451 -0.250 1.601 1.8889960 -1.606 Down
## 829 2006 -1.606 0.106 0.631 -0.451 -0.250 1.4472175 2.977 Up
## 830 2006 2.977 -1.606 0.106 0.631 -0.451 2.4874500 0.168 Up
## 831 2006 0.168 2.977 -1.606 0.106 0.631 2.3211120 -2.029 Down
## 832 2006 -2.029 0.168 2.977 -1.606 0.106 2.4257500 1.762 Up
## 833 2006 1.762 -2.029 0.168 2.977 -1.606 2.5924500 -1.534 Down
## 834 2006 -1.534 1.762 -2.029 0.168 2.977 2.4855920 0.234 Up
## 835 2006 0.234 -1.534 1.762 -2.029 0.168 2.3375120 1.598 Up
## 836 2006 1.598 0.234 -1.534 1.762 -2.029 2.1970720 0.170 Up
## 837 2006 0.170 1.598 0.234 -1.534 1.762 2.1009800 -0.171 Down
## 838 2006 -0.171 0.170 1.598 0.234 -1.534 2.2604080 -0.451 Down
## 839 2006 -0.451 -0.171 0.170 1.598 0.234 2.2509340 2.016 Up
## 840 2006 2.016 -0.451 -0.171 0.170 1.598 2.2740800 -0.329 Down
## 841 2006 -0.329 2.016 -0.451 -0.171 0.170 2.0942040 -0.620 Down
## 842 2006 -0.620 -0.329 2.016 -0.451 -0.171 2.1706180 0.049 Up
## 843 2006 0.049 -0.620 -0.329 2.016 -0.451 2.2851820 -0.492 Down
## 844 2006 -0.492 0.049 -0.620 -0.329 2.016 1.9903100 1.719 Up
## 845 2006 1.719 -0.492 0.049 -0.620 -0.329 2.3485900 -0.051 Down
## 846 2006 -0.051 1.719 -0.492 0.049 -0.620 2.4356660 1.156 Up
## 847 2006 1.156 -0.051 1.719 -0.492 0.049 2.3923900 -2.604 Down
## 848 2006 -2.604 1.156 -0.051 1.719 -0.492 2.3353260 -1.875 Down
## 849 2006 -1.875 -2.604 1.156 -0.051 1.719 2.6483720 1.036 Up
## 850 2006 1.036 -1.875 -2.604 1.156 -0.051 2.5128080 0.630 Up
## 851 2006 0.630 1.036 -1.875 -2.604 1.156 2.3810125 -2.788 Down
## 852 2006 -2.788 0.630 1.036 -1.875 -2.604 2.6826160 -0.061 Down
## 853 2006 -0.061 -2.788 0.630 1.036 -1.875 2.7379280 -0.563 Down
## 854 2006 -0.563 -0.061 -2.788 0.630 1.036 2.2553660 2.065 Up
## 855 2006 2.065 -0.563 -0.061 -2.788 0.630 2.3676020 -0.372 Down
## 856 2006 -0.372 2.065 -0.563 -0.061 -2.788 1.8192125 -2.314 Down
## 857 2006 -2.314 -0.372 2.065 -0.563 -0.061 2.2857540 0.331 Up
## 858 2006 0.331 -2.314 -0.372 2.065 -0.563 2.4759620 3.085 Up
## 859 2006 3.085 0.331 -2.314 -0.372 2.065 2.5602980 0.063 Up
## 860 2006 0.063 3.085 0.331 -2.314 -0.372 2.5718300 -0.986 Down
## 861 2006 -0.986 0.063 3.085 0.331 -2.314 2.2930820 2.807 Up
## 862 2006 2.807 -0.986 0.063 3.085 0.331 2.2997880 -0.554 Down
## 863 2006 -0.554 2.807 -0.986 0.063 3.085 1.8319100 1.229 Up
## 864 2006 1.229 -0.554 2.807 -0.986 0.063 1.9528780 -0.922 Down
## 865 2006 -0.922 1.229 -0.554 2.807 -0.986 2.2257725 1.597 Up
## 866 2006 1.597 -0.922 1.229 -0.554 2.807 2.6888960 -0.370 Down
## 867 2006 -0.370 1.597 -0.922 1.229 -0.554 2.4098640 1.603 Up
## 868 2006 1.603 -0.370 1.597 -0.922 1.229 2.5608060 1.029 Up
## 869 2006 1.029 1.603 -0.370 1.597 -0.922 2.6394580 1.188 Up
## 870 2006 1.188 1.029 1.603 -0.370 1.597 2.3659160 0.218 Up
## 871 2006 0.218 1.188 1.029 1.603 -0.370 2.5261240 0.639 Up
## 872 2006 0.639 0.218 1.188 1.029 1.603 2.7125320 -0.947 Down
## 873 2006 -0.947 0.639 0.218 1.188 1.029 2.6921080 1.217 Up
## 874 2006 1.217 -0.947 0.639 0.218 1.188 2.6574020 1.470 Up
## 875 2006 1.470 1.217 -0.947 0.639 0.218 2.7613560 -0.018 Down
## 876 2006 -0.018 1.470 1.217 -0.947 0.639 2.0537275 -0.303 Down
## 877 2006 -0.303 -0.018 1.470 1.217 -0.947 2.9898280 0.940 Up
## 878 2006 0.940 -0.303 -0.018 1.470 1.217 2.6861820 1.224 Up
## 879 2006 1.224 0.940 -0.303 -0.018 1.470 2.7079220 -1.144 Down
## 880 2006 -1.144 1.224 0.940 -0.303 -0.018 2.3285660 0.534 Up
## 881 2007 0.534 -1.144 1.224 0.940 -0.303 1.5411125 -0.606 Down
## 882 2007 -0.606 0.534 -1.144 1.224 0.940 3.1176733 1.491 Up
## 883 2007 1.491 -0.606 0.534 -1.144 1.224 2.8221460 -0.016 Down
## 884 2007 -0.016 1.491 -0.606 0.534 -1.144 2.7224275 -0.582 Down
## 885 2007 -0.582 -0.016 1.491 -0.606 0.534 2.7838640 1.843 Up
## 886 2007 1.843 -0.582 -0.016 1.491 -0.606 2.7795520 -0.713 Down
## 887 2007 -0.713 1.843 -0.582 -0.016 1.491 2.6869900 1.216 Up
## 888 2007 1.216 -0.713 1.843 -0.582 -0.016 2.5274980 -0.299 Down
## 889 2007 -0.299 1.216 -0.713 1.843 -0.582 2.3688900 -4.412 Down
## 890 2007 -4.412 -0.299 1.216 -0.713 1.843 3.5999640 1.130 Up
## 891 2007 1.130 -4.412 -0.299 1.216 -0.713 3.1235860 -1.133 Down
## 892 2007 -1.133 1.130 -4.412 -0.299 1.216 3.2246920 3.544 Up
## 893 2007 3.544 -1.133 1.130 -4.412 -0.299 2.9013760 -1.062 Down
## 894 2007 -1.062 3.544 -1.133 1.130 -4.412 2.8373620 1.612 Up
## 895 2007 1.612 -1.062 3.544 -1.133 1.130 2.6927975 0.630 Up
## 896 2007 0.630 1.612 -1.062 3.544 -1.133 2.6540600 2.168 Up
## 897 2007 2.168 0.630 1.612 -1.062 3.544 3.0011180 0.655 Up
## 898 2007 0.655 2.168 0.630 1.612 -1.062 2.9783940 0.773 Up
## 899 2007 0.773 0.655 2.168 0.630 1.612 3.0906940 0.015 Up
## 900 2007 0.015 0.773 0.655 2.168 0.630 2.8056760 1.122 Up
## 901 2007 1.122 0.015 0.773 0.655 2.168 2.9180380 -0.461 Down
## 902 2007 -0.461 1.122 0.015 0.773 0.655 3.0183800 1.360 Up
## 903 2007 1.360 -0.461 1.122 0.015 0.773 2.9536375 -1.866 Down
## 904 2007 -1.866 1.360 -0.461 1.122 0.015 3.0349000 1.674 Up
## 905 2007 1.674 -1.866 1.360 -0.461 1.122 2.9758140 -1.980 Down
## 906 2007 -1.980 1.674 -1.866 1.360 -0.461 3.2172320 0.053 Up
## 907 2007 0.053 -1.980 1.674 -1.866 1.360 3.2512100 1.802 Up
## 908 2007 1.802 0.053 -1.980 1.674 -1.866 2.3175625 1.441 Up
## 909 2007 1.441 1.802 0.053 -1.980 1.674 3.0666500 -1.185 Down
## 910 2007 -1.185 1.441 1.802 0.053 -1.980 3.2635400 -4.899 Down
## 911 2007 -4.899 -1.185 1.441 1.802 0.053 4.1517860 -1.775 Down
## 912 2007 -1.775 -4.899 -1.185 1.441 1.802 4.5102080 1.436 Up
## 913 2007 1.436 -1.775 -4.899 -1.185 1.441 5.3423060 -0.530 Down
## 914 2007 -0.530 1.436 -1.775 -4.899 -1.185 4.3762360 2.312 Up
## 915 2007 2.312 -0.530 1.436 -1.775 -4.899 3.0536800 -0.364 Down
## 916 2007 -0.364 2.312 -0.530 1.436 -1.775 2.7245820 -1.387 Down
## 917 2007 -1.387 -0.364 2.312 -0.530 1.436 2.8522175 2.112 Up
## 918 2007 2.112 -1.387 -0.364 2.312 -0.530 2.8511180 2.796 Up
## 919 2007 2.796 2.112 -1.387 -0.364 2.312 3.3582480 0.066 Up
## 920 2007 0.066 2.796 2.112 -1.387 -0.364 3.0708000 2.020 Up
## 921 2007 2.020 0.066 2.796 2.112 -1.387 3.0117360 0.270 Up
## 922 2007 0.270 2.020 0.066 2.796 2.112 2.9434800 -3.917 Down
## 923 2007 -3.917 0.270 2.020 0.066 2.796 3.4752200 2.309 Up
## 924 2007 2.309 -3.917 0.270 2.020 0.066 3.7160660 -1.669 Down
## 925 2007 -1.669 2.309 -3.917 0.270 2.020 3.7635060 -3.706 Down
## 926 2007 -3.706 -1.669 2.309 -3.917 0.270 4.4156840 0.347 Up
## 927 2007 0.347 -3.706 -1.669 2.309 -3.917 4.0950360 -1.237 Down
## 928 2007 -1.237 0.347 -3.706 -1.669 2.309 3.6709375 2.807 Up
## 929 2007 2.807 -1.237 0.347 -3.706 -1.669 4.0964280 1.588 Up
## 930 2007 1.588 2.807 -1.237 0.347 -3.706 3.4153620 -2.440 Down
## 931 2007 -2.440 1.588 2.807 -1.237 0.347 3.7020560 1.125 Up
## 932 2007 1.125 -2.440 1.588 2.807 -1.237 3.7459000 -0.402 Down
## 933 2007 -0.402 1.125 -2.440 1.588 2.807 2.0160500 -4.522 Down
## 934 2008 -4.522 -0.402 1.125 -2.440 1.588 3.3722575 -0.752 Down
## 935 2008 -0.752 -4.522 -0.402 1.125 -2.440 4.7888020 -5.412 Down
## 936 2008 -5.412 -0.752 -4.522 -0.402 1.125 5.0064640 0.409 Up
## 937 2008 0.409 -5.412 -0.752 -4.522 -0.402 5.1009800 4.871 Up
## 938 2008 4.871 0.409 -5.412 -0.752 -4.522 4.5395420 -4.596 Down
## 939 2008 -4.596 4.871 0.409 -5.412 -0.752 4.0354580 1.405 Up
## 940 2008 1.405 -4.596 4.871 0.409 -5.412 3.7444520 0.231 Up
## 941 2008 0.231 1.405 -4.596 4.871 0.409 3.6883475 -1.661 Down
## 942 2008 -1.661 0.231 1.405 -4.596 4.871 4.0464840 -2.800 Down
## 943 2008 -2.800 -1.661 0.231 1.405 -4.596 4.4082660 -0.404 Down
## 944 2008 -0.404 -2.800 -1.661 0.231 1.405 4.8023480 3.212 Up
## 945 2008 3.212 -0.404 -2.800 -1.661 0.231 4.5919225 -1.075 Down
## 946 2008 -1.075 3.212 -0.404 -2.800 -1.661 4.0849400 4.195 Up
## 947 2008 4.195 -1.075 3.212 -0.404 -2.800 4.1755500 -2.742 Down
## 948 2008 -2.742 4.195 -1.075 3.212 -0.404 3.6633780 4.314 Up
## 949 2008 4.314 -2.742 4.195 -1.075 3.212 3.8685760 0.540 Up
## 950 2008 0.540 4.314 -2.742 4.195 -1.075 3.9397780 1.149 Up
## 951 2008 1.149 0.540 4.314 -2.742 4.195 4.0666040 -1.812 Down
## 952 2008 -1.812 1.149 0.540 4.314 -2.742 3.7512440 2.670 Up
## 953 2008 2.670 -1.812 1.149 0.540 4.314 3.8095320 -3.467 Down
## 954 2008 -3.467 2.670 -1.812 1.149 0.540 3.9057240 1.777 Up
## 955 2008 1.777 -3.467 2.670 -1.812 1.149 3.8140425 -2.835 Down
## 956 2008 -2.835 1.777 -3.467 2.670 -1.812 4.3143580 -0.048 Down
## 957 2008 -0.048 -2.835 1.777 -3.467 2.670 4.5268560 -3.096 Down
## 958 2008 -3.096 -0.048 -2.835 1.777 -3.467 4.4438080 -3.001 Down
## 959 2008 -3.001 -3.096 -0.048 -2.835 1.777 5.0313200 -1.211 Down
## 960 2008 -1.211 -3.001 -3.096 -0.048 -2.835 4.8505750 -1.854 Down
## 961 2008 -1.854 -1.211 -3.001 -3.096 -0.048 5.8126320 1.710 Up
## 962 2008 1.710 -1.854 -1.211 -3.001 -3.096 6.5111240 -0.232 Down
## 963 2008 -0.232 1.710 -1.854 -1.211 -3.001 5.6634480 0.203 Up
## 964 2008 0.203 -0.232 1.710 -1.854 -1.211 5.0718900 2.857 Up
## 965 2008 2.857 0.203 -0.232 1.710 -1.854 4.1882400 0.145 Up
## 966 2008 0.145 2.857 0.203 -0.232 1.710 4.5344040 -0.462 Down
## 967 2008 -0.462 0.145 2.857 0.203 -0.232 4.0635480 -0.725 Down
## 968 2008 -0.725 -0.462 0.145 2.857 0.203 3.5300360 -3.159 Down
## 969 2008 -3.159 -0.725 -0.462 0.145 2.857 5.0175300 0.756 Up
## 970 2008 0.756 -3.159 -0.725 -0.462 0.145 6.8835840 0.270 Up
## 971 2008 0.270 0.756 -3.159 -0.725 -0.462 9.3282140 -3.331 Down
## 972 2008 -3.331 0.270 0.756 -3.159 -0.725 5.3198940 -9.399 Down
## 973 2008 -9.399 -3.331 0.270 0.756 -3.159 6.2053260 -18.195 Down
## 974 2008 -18.195 -9.399 -3.331 0.270 0.756 8.4033579 4.596 Up
## 975 2008 4.596 -18.195 -9.399 -3.331 0.270 7.3067940 -6.781 Down
## 976 2008 -6.781 4.596 -18.195 -9.399 -3.331 6.0359360 10.491 Up
## 977 2008 10.491 -6.781 4.596 -18.195 -9.399 6.4605960 -3.898 Down
## 978 2008 -3.898 10.491 -6.781 4.596 -18.195 5.2968160 -6.198 Down
## 979 2008 -6.198 -3.898 10.491 -6.781 4.596 5.8129340 -8.389 Down
## 980 2008 -8.389 -6.198 -3.898 10.491 -6.781 7.3490400 12.026 Up
## 981 2008 12.026 -8.389 -6.198 -3.898 10.491 5.8415650 -2.251 Down
## 982 2008 -2.251 12.026 -8.389 -6.198 -3.898 6.0939500 0.418 Up
## 983 2008 0.418 -2.251 12.026 -8.389 -6.198 5.9324540 0.926 Up
## 984 2008 0.926 0.418 -2.251 12.026 -8.389 5.8559720 -1.698 Down
## 985 2008 -1.698 0.926 0.418 -2.251 12.026 3.0871050 6.760 Up
## 986 2009 6.760 -1.698 0.926 0.418 -2.251 3.7931100 -4.448 Down
## 987 2009 -4.448 6.760 -1.698 0.926 0.418 5.0439040 -4.518 Down
## 988 2009 -4.518 -4.448 6.760 -1.698 0.926 5.9487580 -2.137 Down
## 989 2009 -2.137 -4.518 -4.448 6.760 -1.698 6.1297625 -0.730 Down
## 990 2009 -0.730 -2.137 -4.518 -4.448 6.760 5.6020040 5.173 Up
## 991 2009 5.173 -0.730 -2.137 -4.518 -4.448 6.2176320 -4.808 Down
## 992 2009 -4.808 5.173 -0.730 -2.137 -4.518 6.0088219 -6.868 Down
## 993 2009 -6.868 -4.808 5.173 -0.730 -2.137 6.4015151 -4.540 Down
## 994 2009 -4.540 -6.868 -4.808 5.173 -0.730 7.5507758 -7.035 Down
## 995 2009 -7.035 -4.540 -6.868 -4.808 5.173 7.5928440 10.707 Up
## 996 2009 10.707 -7.035 -4.540 -6.868 -4.808 7.4594358 1.585 Up
## 997 2009 1.585 10.707 -7.035 -4.540 -6.868 7.9632760 6.168 Up
## 998 2009 6.168 1.585 10.707 -7.035 -4.540 6.9528199 3.255 Up
## 999 2009 3.255 6.168 1.585 10.707 -7.035 6.2868699 1.669 Up
## 1000 2009 1.669 3.255 6.168 1.585 10.707 6.2261876 1.522 Up
## 1001 2009 1.522 1.669 3.255 6.168 1.585 6.8393019 -0.388 Down
## 1002 2009 -0.388 1.522 1.669 3.255 6.168 7.0831699 1.303 Up
## 1003 2009 1.303 -0.388 1.522 1.669 3.255 6.0435580 5.893 Up
## 1004 2009 5.893 1.303 -0.388 1.522 1.669 7.9520240 -4.988 Down
## 1005 2009 -4.988 5.893 1.303 -0.388 1.522 6.3377520 0.467 Up
## 1006 2009 0.467 -4.988 5.893 1.303 -0.388 6.3397280 3.623 Up
## 1007 2009 3.623 0.467 -4.988 5.893 1.303 5.7888125 2.279 Up
## 1008 2009 2.279 3.623 0.467 -4.988 5.893 5.6624700 0.651 Up
## 1009 2009 0.651 2.279 3.623 0.467 -4.988 4.8663520 -2.640 Down
## 1010 2009 -2.640 0.651 2.279 3.623 0.467 5.1140260 -0.253 Down
## 1011 2009 -0.253 -2.640 0.651 2.279 3.623 5.1199160 -2.446 Down
## 1012 2009 -2.446 -0.253 -2.640 0.651 2.279 4.1724325 -1.929 Down
## 1013 2009 -1.929 -2.446 -0.253 -2.640 0.651 4.6733820 6.967 Up
## 1014 2009 6.967 -1.929 -2.446 -0.253 -2.640 4.7854640 4.134 Up
## 1015 2009 4.134 6.967 -1.929 -2.446 -0.253 5.0033000 0.839 Up
## 1016 2009 0.839 4.134 6.967 -1.929 -2.446 5.2949320 2.329 Up
## 1017 2009 2.329 0.839 4.134 6.967 -1.929 6.4279459 -0.632 Down
## 1018 2009 -0.632 2.329 0.839 4.134 6.967 5.3737640 2.195 Up
## 1019 2009 2.195 -0.632 2.329 0.839 4.134 4.6646500 0.273 Up
## 1020 2009 0.273 2.195 -0.632 2.329 0.839 5.7445820 -1.218 Down
## 1021 2009 -1.218 0.273 2.195 -0.632 2.329 5.2862600 2.591 Up
## 1022 2009 2.591 -1.218 0.273 2.195 -0.632 5.1379225 2.452 Up
## 1023 2009 2.452 2.591 -1.218 0.273 2.195 6.0469679 -2.239 Down
## 1024 2009 -2.239 2.452 2.591 -1.218 0.273 5.0813020 -1.836 Down
## 1025 2009 -1.836 -2.239 2.452 2.591 -1.218 5.2100800 4.514 Up
## 1026 2009 4.514 -1.836 -2.239 2.452 2.591 4.4667100 1.511 Up
## 1027 2009 1.511 4.514 -1.836 -2.239 2.452 4.7403700 -0.743 Down
## 1028 2009 -0.743 1.511 4.514 -1.836 -2.239 5.1184660 -4.021 Down
## 1029 2009 -4.021 -0.743 1.511 4.514 -1.836 6.0817140 3.195 Up
## 1030 2009 3.195 -4.021 -0.743 1.511 4.514 5.2902260 2.261 Up
## 1031 2009 2.261 3.195 -4.021 -0.743 1.511 4.2188720 -0.192 Down
## 1032 2009 -0.192 2.261 3.195 -4.021 -0.743 4.1225040 0.010 Up
## 1033 2009 0.010 -0.192 2.261 3.195 -4.021 3.2320000 1.328 Up
## 1034 2009 1.328 0.010 -0.192 2.261 3.195 4.5354680 0.039 Up
## 1035 2009 0.039 1.328 0.010 -0.192 2.261 4.1508760 -0.356 Down
## 1036 2009 -0.356 0.039 1.328 0.010 -0.192 5.6728740 2.178 Up
## 1037 2009 2.178 -0.356 0.039 1.328 0.010 3.0132625 -1.010 Down
## 1038 2010 -1.010 2.178 -0.356 0.039 1.328 2.3904275 2.680 Up
## 1039 2010 2.680 -1.010 2.178 -0.356 0.039 4.2230700 -0.782 Down
## 1040 2010 -0.782 2.680 -1.010 2.178 -0.356 4.3632460 -3.897 Down
## 1041 2010 -3.897 -0.782 2.680 -1.010 2.178 5.6545824 -1.639 Down
## 1042 2010 -1.639 -3.897 -0.782 2.680 -1.010 5.0795340 -0.715 Down
## 1043 2010 -0.715 -1.639 -3.897 -0.782 2.680 5.0822380 0.874 Up
## 1044 2010 0.874 -0.715 -1.639 -3.897 -0.782 4.4034160 3.130 Up
## 1045 2010 3.130 0.874 -0.715 -1.639 -3.897 4.0407250 -0.422 Down
## 1046 2010 -0.422 3.130 0.874 -0.715 -1.639 4.1940340 3.097 Up
## 1047 2010 3.097 -0.422 3.130 0.874 -0.715 4.0023300 0.991 Up
## 1048 2010 0.991 3.097 -0.422 3.130 0.874 4.8053180 0.862 Up
## 1049 2010 0.862 0.991 3.097 -0.422 3.130 4.5888000 0.577 Up
## 1050 2010 0.577 0.862 0.991 3.097 -0.422 4.7512780 0.987 Up
## 1051 2010 0.987 0.577 0.862 0.991 3.097 4.2379475 1.381 Up
## 1052 2010 1.381 0.987 0.577 0.862 0.991 4.4615540 -0.188 Down
## 1053 2010 -0.188 1.381 0.987 0.577 0.862 5.9749020 2.110 Up
## 1054 2010 2.110 -0.188 1.381 0.987 0.577 5.8000960 -2.513 Down
## 1055 2010 -2.513 2.110 -0.188 1.381 0.987 6.3104560 -6.388 Down
## 1056 2010 -6.388 -2.513 2.110 -0.188 1.381 7.6838860 2.232 Up
## 1057 2010 2.232 -6.388 -2.513 2.110 -0.188 5.7917500 -4.226 Down
## 1058 2010 -4.226 2.232 -6.388 -2.513 2.110 6.5280519 0.158 Up
## 1059 2010 0.158 -4.226 2.232 -6.388 -2.513 5.5288680 -2.252 Down
## 1060 2010 -2.252 0.158 -4.226 2.232 -6.388 5.3685975 2.509 Up
## 1061 2010 2.509 -2.252 0.158 -4.226 2.232 5.3695140 2.374 Up
## 1062 2010 2.374 2.509 -2.252 0.158 -4.226 4.6372080 -3.646 Down
## 1063 2010 -3.646 2.374 2.509 -2.252 0.158 4.6997120 -5.032 Down
## 1064 2010 -5.032 -3.646 2.374 2.509 -2.252 5.1008920 5.416 Up
## 1065 2010 5.416 -5.032 -3.646 2.374 2.509 4.4193725 -1.213 Down
## 1066 2010 -1.213 5.416 -5.032 -3.646 2.374 4.4876640 3.548 Up
## 1067 2010 3.548 -1.213 5.416 -5.032 -3.646 4.5802860 -0.096 Down
## 1068 2010 -0.096 3.548 -1.213 5.416 -5.032 4.2713200 1.819 Up
## 1069 2010 1.819 -0.096 3.548 -1.213 5.416 3.9634600 -3.779 Down
## 1070 2010 -3.779 1.819 -0.096 3.548 -1.213 3.9065580 -0.700 Down
## 1071 2010 -0.700 -3.779 1.819 -0.096 3.548 3.7774060 -0.663 Down
## 1072 2010 -0.663 -0.700 -3.779 1.819 -0.096 3.9513280 3.750 Up
## 1073 2010 3.750 -0.663 -0.700 -3.779 1.819 3.7184700 0.456 Up
## 1074 2010 0.456 3.750 -0.663 -0.700 -3.779 3.1952375 1.446 Up
## 1075 2010 1.446 0.456 3.750 -0.663 -0.700 3.9724320 2.050 Up
## 1076 2010 2.050 1.446 0.456 3.750 -0.663 3.8845220 -0.212 Down
## 1077 2010 -0.212 2.050 1.446 0.456 3.750 4.0374100 1.650 Up
## 1078 2010 1.650 -0.212 2.050 1.446 0.456 3.9056160 0.948 Up
## 1079 2010 0.948 1.650 -0.212 2.050 1.446 4.4491600 0.586 Up
## 1080 2010 0.586 0.948 1.650 -0.212 2.050 4.5762820 0.015 Up
## 1081 2010 0.015 0.586 0.948 1.650 -0.212 4.1164140 3.599 Up
## 1082 2010 3.599 0.015 0.586 0.948 1.650 4.7987580 -2.173 Down
## 1083 2010 -2.173 3.599 0.015 0.586 0.948 4.2982620 0.043 Up
## 1084 2010 0.043 -2.173 3.599 0.015 0.586 4.1774360 -0.861 Down
## 1085 2010 -0.861 0.043 -2.173 3.599 0.015 3.2051600 2.969 Up
## 1086 2010 2.969 -0.861 0.043 -2.173 3.599 4.2425680 1.281 Up
## 1087 2010 1.281 2.969 -0.861 0.043 -2.173 4.8350820 0.283 Up
## 1088 2010 0.283 1.281 2.969 -0.861 0.043 4.4540440 1.034 Up
## 1089 2010 1.034 0.283 1.281 2.969 -0.861 2.7071050 0.069 Uphelp(Weekly)
summary(Weekly)## Year Lag1 Lag2 Lag3
## Min. :1990 Min. :-18.1950 Min. :-18.1950 Min. :-18.1950
## 1st Qu.:1995 1st Qu.: -1.1540 1st Qu.: -1.1540 1st Qu.: -1.1580
## Median :2000 Median : 0.2410 Median : 0.2410 Median : 0.2410
## Mean :2000 Mean : 0.1506 Mean : 0.1511 Mean : 0.1472
## 3rd Qu.:2005 3rd Qu.: 1.4050 3rd Qu.: 1.4090 3rd Qu.: 1.4090
## Max. :2010 Max. : 12.0260 Max. : 12.0260 Max. : 12.0260
## Lag4 Lag5 Volume Today
## Min. :-18.1950 Min. :-18.1950 Min. :0.08747 Min. :-18.1950
## 1st Qu.: -1.1580 1st Qu.: -1.1660 1st Qu.:0.33202 1st Qu.: -1.1540
## Median : 0.2380 Median : 0.2340 Median :1.00268 Median : 0.2410
## Mean : 0.1458 Mean : 0.1399 Mean :1.57462 Mean : 0.1499
## 3rd Qu.: 1.4090 3rd Qu.: 1.4050 3rd Qu.:2.05373 3rd Qu.: 1.4050
## Max. : 12.0260 Max. : 12.0260 Max. :9.32821 Max. : 12.0260
## Direction
## Down:484
## Up :605
##
##
##
## pairs(Weekly)
- Volume of shares traded increased gradually over the years.
- Some variables, such as “Today” and the lag variables, have extreme values (minimum and maximum) that may need further investigation to understand their significance.
- The lag variables suggest a time series structure, with values from previous time points influencing the current time point.
(b) Use the full data set to perform a logistic regression with Direction as the response and the five lag variables plus Volume as predictors. Use the summary function to print the results. Do any of the predictors appear to be statistically significant? If so, which ones?
model<-na.omit(Weekly)
model<- glm(Direction~Lag1+Lag2+Lag3+Lag4+Lag5+Volume,data=Weekly,family=binomial)
summary(model)##
## Call:
## glm(formula = Direction ~ Lag1 + Lag2 + Lag3 + Lag4 + Lag5 +
## Volume, family = binomial, data = Weekly)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.26686 0.08593 3.106 0.0019 **
## Lag1 -0.04127 0.02641 -1.563 0.1181
## Lag2 0.05844 0.02686 2.175 0.0296 *
## Lag3 -0.01606 0.02666 -0.602 0.5469
## Lag4 -0.02779 0.02646 -1.050 0.2937
## Lag5 -0.01447 0.02638 -0.549 0.5833
## Volume -0.02274 0.03690 -0.616 0.5377
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1496.2 on 1088 degrees of freedom
## Residual deviance: 1486.4 on 1082 degrees of freedom
## AIC: 1500.4
##
## Number of Fisher Scoring iterations: 4Yes there are predictors that are statistically significant. Lag2 has the p-value of 0.0296 which is less than 0.05. All the other predictors have the p-value more than 0.05 thus only Lag2 is statistically significant.
(c) Compute the confusion matrix and overall fraction of correct predictions. Explain what the confusion matrix is telling you about the types of mistakes made by logistic regression.
prediction<- predict(model, Weekly, type='response')
predicted_labels<- ifelse(prediction>0.5,"Up","Down")
confusion_matrix<- table(Actual=Weekly$Direction, Predicted=predicted_labels)
confusion_matrix## Predicted
## Actual Down Up
## Down 54 430
## Up 48 557The model is predicting “UP” for 430 data points where the actual value is “Down”. Which shows that model is producing higher false positive which is a false alarm. This will effect the permormance of the model. Hence we need to adjust the threshold to improve the performance of this model.
Now fit the logistic regression model using a training data period from 1990 to 2008, with Lag2 as the only predictor. Compute the confusion matrix and the overall fraction of correct predictions for the held out data (that is, the data from 2009 and 2010).
library(caret)## Loading required package: ggplot2##
## Attaching package: 'ggplot2'## The following objects are masked from 'package:psych':
##
## %+%, alpha## Loading required package: latticeset.seed(42)
condition<- Weekly$Year >= 1990 & Weekly$Year<=2008
training_data<- subset(Weekly, condition)
testing_data<- subset(Weekly, !condition)
new_model<-glm(Direction~Lag2, data=training_data,family="binomial")
summary(new_model)##
## Call:
## glm(formula = Direction ~ Lag2, family = "binomial", data = training_data)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.20326 0.06428 3.162 0.00157 **
## Lag2 0.05810 0.02870 2.024 0.04298 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1354.7 on 984 degrees of freedom
## Residual deviance: 1350.5 on 983 degrees of freedom
## AIC: 1354.5
##
## Number of Fisher Scoring iterations: 4Repeat (d) using LDA.
new_prediction<- predict(new_model, testing_data,type='response')
new_labels<- ifelse(new_prediction >0.5, "Up","Down")
new_confusion_matrix<- table(Actual=testing_data$Direction, Predicted=new_labels)
new_confusion_matrix## Predicted
## Actual Down Up
## Down 9 34
## Up 5 56TP<- new_confusion_matrix["Up","Up"]
TN<- new_confusion_matrix["Down","Down"]
FP<- new_confusion_matrix["Down","Up"]
FN<- new_confusion_matrix["Up","Down"]
acc<-((TN + TP)/(TP + TN + FP + FN))
cat("\n","Accuracy :", acc)##
## Accuracy : 0.625(f) Repeat (d) using QDA.
library(MASS)##
## Attaching package: 'MASS'## The following object is masked from 'package:ISLR2':
##
## Bostonlibrary(caret)
set.seed(42)
condition<- Weekly$Year >= 1990 & Weekly$Year<=2008
training_data<- subset(Weekly, condition)
testing_data<- subset(Weekly, !condition)
lda_model<-lda(Direction~Lag2, data=training_data,family="binomial")
summary(lda_model)## Length Class Mode
## prior 2 -none- numeric
## counts 2 -none- numeric
## means 2 -none- numeric
## scaling 1 -none- numeric
## lev 2 -none- character
## svd 1 -none- numeric
## N 1 -none- numeric
## call 4 -none- call
## terms 3 terms call
## xlevels 0 -none- list(e) Repeat (d) using LDA.
lda_prediction<- predict(lda_model, testing_data,type='response')
lda_probabilities <- lda_prediction$posterior[, "Up"]
lda_labels<- ifelse(lda_probabilities >0.5, "Up","Down")
lda_confusion_matrix<- table(Actual=testing_data$Direction, Predicted=lda_labels)
lda_confusion_matrix## Predicted
## Actual Down Up
## Down 9 34
## Up 5 56L_TP<- lda_confusion_matrix["Up","Up"]
L_TN<- lda_confusion_matrix["Down","Down"]
L_FP<- lda_confusion_matrix["Down","Up"]
L_FN<- lda_confusion_matrix["Up","Down"]
acc<-((L_TN + L_TP)/(L_TP + L_TN + L_FP + L_FN))
cat("\n","Accuracy :", acc)##
## Accuracy : 0.625(f) Repeat (d) using QDA.
qda_model<-qda(Direction~Lag2, data=training_data,family="binomial")
summary(qda_model)## Length Class Mode
## prior 2 -none- numeric
## counts 2 -none- numeric
## means 2 -none- numeric
## scaling 2 -none- numeric
## ldet 2 -none- numeric
## lev 2 -none- character
## N 1 -none- numeric
## call 4 -none- call
## terms 3 terms call
## xlevels 0 -none- listqda_prediction<- predict(qda_model, testing_data,type='response')
qda_probabilities <- qda_prediction$posterior[, "Up"]
qda_probabilities## 986 987 988 989 990 991 992 993
## 0.5215370 0.7306048 0.5264584 0.5270882 0.5197265 0.5290087 0.6714698 0.5299634
## 994 995 996 997 998 999 1000 1001
## 0.5625713 0.5272914 0.5661321 0.8727145 0.5660534 0.7080929 0.6087201 0.5678935
## 1002 1003 1004 1005 1006 1007 1008 1009
## 0.5646954 0.5327895 0.5601236 0.6977834 0.5319630 0.5448279 0.6197405 0.5822534
## 1010 1011 1012 1013 1014 1015 1016 1017
## 0.5478980 0.5188646 0.5344452 0.5190435 0.5204614 0.7385403 0.6359061 0.5512085
## 1018 1019 1020 1021 1022 1023 1024 1025
## 0.5835068 0.5300314 0.5801733 0.5417740 0.5246444 0.5902598 0.5866387 0.5194470
## 1026 1027 1028 1029 1030 1031 1032 1033
## 0.5208617 0.6485257 0.5644603 0.5288767 0.5231575 0.6069752 0.5818049 0.5352236
## 1034 1035 1036 1037 1038 1039 1040 1041
## 0.5379353 0.5606338 0.5383416 0.5331736 0.5797562 0.5263562 0.5926235 0.5284859
## 1042 1043 1044 1045 1046 1047 1048 1049
## 0.5223734 0.5218555 0.5291621 0.5518441 0.6051017 0.5323870 0.6041574 0.5540127
## 1050 1051 1052 1053 1054 1055 1056 1057
## 0.5516255 0.5466430 0.5539375 0.5617254 0.5352753 0.5781014 0.5189599 0.5530894
## 1058 1059 1060 1061 1062 1063 1064 1065
## 0.5810855 0.5246261 0.5400527 0.5194152 0.5881131 0.5846447 0.5210267 0.5324768
## 1066 1067 1068 1069 1070 1071 1072 1073
## 0.6802239 0.5246829 0.6174509 0.5364866 0.5712629 0.5217002 0.5293166 0.5297026
## 1074 1075 1076 1077 1078 1079 1080 1081
## 0.6236673 0.5446497 0.5630827 0.5766591 0.5349663 0.5674743 0.5532079 0.5467942
## 1082 1083 1084 1085 1086 1087 1088 1089
## 0.5380051 0.6190054 0.5196218 0.5383979 0.5277180 0.6005377 0.5596772 0.5419268qda_labels<- ifelse(qda_probabilities >0.5, "Up","Down")
qda_confusion_matrix<- table(Actual=testing_data$Direction, Predicted=lda_labels)
qda_confusion_matrix## Predicted
## Actual Down Up
## Down 9 34
## Up 5 56q_TP<- qda_confusion_matrix["Up","Up"]
q_TN<- qda_confusion_matrix["Down","Down"]
q_FP<- qda_confusion_matrix["Down","Up"]
q_FN<- qda_confusion_matrix["Up","Down"]
acc<-((L_TN + L_TP)/(L_TP + L_TN + L_FP + L_FN))
cat("\n","Accuracy :", acc)##
## Accuracy : 0.625(g) Repeat (d) using KNN with K = 1.
# Load the necessary library
library(class)
# Extract predictor variables (features) and response variable from training data
train_features <- training_data[, -which(names(training_data) == "Direction")]
train_response <- training_data$Direction
# Extract predictor variables from testing data
test_features <- testing_data[, -which(names(testing_data) == "Direction")]
# Set the value of k (number of neighbors)
k <- 1
# Apply kNN algorithm
knn_predictions <- knn(train_features, test_features, train_response, k)
# Create a confusion matrix
conf_matrix_knn <- table(Actual = testing_data$Direction, Predicted = knn_predictions)
print(conf_matrix_knn)## Predicted
## Actual Down Up
## Down 37 6
## Up 15 46knn_TP<- conf_matrix_knn["Up","Up"]
knn_TN<- conf_matrix_knn["Down","Down"]
knn_FP<- conf_matrix_knn["Down","Up"]
knn_FN<- conf_matrix_knn["Up","Down"]
acc<-((knn_TN + knn_TP)/(knn_TP + knn_TN + knn_FP + knn_FN))
cat("\n","Accuracy :", acc)##
## Accuracy : 0.7980769(h) Repeat (d) using naive Bayes.
library(e1071)
# Train the Naive Bayes model
nb_model <- naiveBayes(train_features, train_response)
# Make predictions on the test set
nb_predictions <- predict(nb_model, test_features)
# Create a confusion matrix
conf_matrix_nb <- table(Actual = testing_data$Direction, Predicted = nb_predictions)
print(conf_matrix_nb)## Predicted
## Actual Down Up
## Down 43 0
## Up 15 46nb_TP<- conf_matrix_nb["Up","Up"]
nb_TN<- conf_matrix_nb["Down","Down"]
nb_FP<- conf_matrix_nb["Down","Up"]
nb_FN<- conf_matrix_nb["Up","Down"]
acc<-((nb_TN + nb_TP)/(nb_TP + nb_TN + nb_FP + nb_FN))
cat("\n","Accuracy :", acc)##
## Accuracy : 0.8557692(i) Which of these methods appears to provide the best results on this data?
Naive Bayers is giving us very good results on this dataset. The model can perform surprisingly well when the features are approximately independent and Naive Bayes can perform well on imbalanced datasets, where one class significantly outnumbers the others.
(j) Experiment with different combinations of predictors, includ- ing possible transformations and interactions, for each of the methods. Report the variables, method, and associated confu- sion matrix that appears to provide the best results on the held out data. Note that you should also experiment with values for K in the KNN classifier.
set.seed(123) # For reproducibility
train_indices <- sample(1:nrow(Weekly), 0.8 * nrow(Weekly))
training_data <- Weekly[train_indices, ]
testing_data <- Weekly[-train_indices, ]
# Example: Including multiple predictors in your model
# Train a model (e.g., Naive Bayes) using Lag1, Lag2, and Volume as predictors
nb_model <- naiveBayes(Direction ~ Lag1 + Lag2 + Volume, data = training_data)
# Make predictions
nb_predictions <- predict(nb_model, testing_data)
# Evaluate performance
conf_matrix_nb <- table(Actual = testing_data$Direction, Predicted = nb_predictions)
print(conf_matrix_nb)## Predicted
## Actual Down Up
## Down 8 82
## Up 19 109# Calculate accuracy
accuracy <- sum(diag(conf_matrix_nb)) / sum(conf_matrix_nb)
print(paste("Accuracy:", round(accuracy, 4)))## [1] "Accuracy: 0.5367"set.seed(123) # For reproducibility
train_indices <- sample(1:nrow(Weekly), 0.8 * nrow(Weekly))
training_data <- Weekly[train_indices, ]
testing_data <- Weekly[-train_indices, ]
# Train a model (e.g., Naive Bayes) using Lag1, Lag2, and Volume as predictors
nb_model <- naiveBayes(Direction ~ Lag1 + Lag2 + Lag4+ Today, data = training_data)
# Make predictions
nb_predictions <- predict(nb_model, testing_data)
# Evaluate performance
conf_matrix_nb <- table(Actual = testing_data$Direction, Predicted = nb_predictions)
print(conf_matrix_nb)## Predicted
## Actual Down Up
## Down 87 3
## Up 0 128# Calculate accuracy
accuracy <- sum(diag(conf_matrix_nb)) / sum(conf_matrix_nb)
print(paste("Accuracy:", round(accuracy, 4)))## [1] "Accuracy: 0.9862"# Experiment with different values for K
k_values <- c(3, 5, 7)
for (k in k_values) {
# Train KNN model
knn_model <- knn(train = training_data[, c("Lag1", "Lag2", "Lag3")],
test = testing_data[, c("Lag1", "Lag2", "Lag3")],
cl = training_data$Direction,
k = k)
# Evaluate performance
conf_matrix_knn <- table(Actual = testing_data$Direction, Predicted = knn_model)
print(paste("Confusion matrix for K =", k))
print(conf_matrix_knn)
}## [1] "Confusion matrix for K = 3"
## Predicted
## Actual Down Up
## Down 37 53
## Up 51 77
## [1] "Confusion matrix for K = 5"
## Predicted
## Actual Down Up
## Down 35 55
## Up 45 83
## [1] "Confusion matrix for K = 7"
## Predicted
## Actual Down Up
## Down 31 59
## Up 49 79# Experiment with different values for K
k_values <- c(1)
for (k in k_values) {
# Train KNN model
knn_model <- knn(train = training_data[, c("Lag1", "Lag2", "Lag3", "Today")],
test = testing_data[, c("Lag1", "Lag2", "Lag3","Today")],
cl = training_data$Direction,
k = k)
# Evaluate performance
conf_matrix_knn <- table(Actual = testing_data$Direction, Predicted = knn_model)
print(paste("Confusion matrix for K =", k))
print(conf_matrix_knn)
}## [1] "Confusion matrix for K = 1"
## Predicted
## Actual Down Up
## Down 86 4
## Up 2 126# Calculate accuracy
accuracy <- sum(diag(conf_matrix_knn)) / sum(conf_matrix_knn)
print(paste("Accuracy:", round(accuracy, 4)))## [1] "Accuracy: 0.9725"So the best predictor variables that gives very good accuracy are “Lag1”, “Lag2”, “Lag3”, “Today” with the Naive Bayers model.
14) In this problem, you will develop a model to predict whether a given car gets high or low gas mileage based on the Auto data set.
(a) Create a binary variable, mpg01, that contains a 1 if mpg contains a value above its median, and a 0 if mpg contains a value below its median. You can compute the median using the median() function. Note you may find it helpful to use the data.frame() function to create a single data set containing both mpg01 and the other Auto variables.
library(ISLR2)
# Create a binary variable, mpg01
median_mpg <- median(Auto$mpg)
Auto$mpg01 <- ifelse(Auto$mpg > median_mpg, 1, 0)
# Create a new data frame containing mpg01 and other Auto variables
new_data <- data.frame(mpg01 = Auto$mpg01, Auto[, -which(names(Auto) %in% c("mpg", "mpg01"))])
new_data## mpg01 cylinders displacement horsepower weight acceleration year origin
## 1 0 8 307.0 130 3504 12.0 70 1
## 2 0 8 350.0 165 3693 11.5 70 1
## 3 0 8 318.0 150 3436 11.0 70 1
## 4 0 8 304.0 150 3433 12.0 70 1
## 5 0 8 302.0 140 3449 10.5 70 1
## 6 0 8 429.0 198 4341 10.0 70 1
## 7 0 8 454.0 220 4354 9.0 70 1
## 8 0 8 440.0 215 4312 8.5 70 1
## 9 0 8 455.0 225 4425 10.0 70 1
## 10 0 8 390.0 190 3850 8.5 70 1
## 11 0 8 383.0 170 3563 10.0 70 1
## 12 0 8 340.0 160 3609 8.0 70 1
## 13 0 8 400.0 150 3761 9.5 70 1
## 14 0 8 455.0 225 3086 10.0 70 1
## 15 1 4 113.0 95 2372 15.0 70 3
## 16 0 6 198.0 95 2833 15.5 70 1
## 17 0 6 199.0 97 2774 15.5 70 1
## 18 0 6 200.0 85 2587 16.0 70 1
## 19 1 4 97.0 88 2130 14.5 70 3
## 20 1 4 97.0 46 1835 20.5 70 2
## 21 1 4 110.0 87 2672 17.5 70 2
## 22 1 4 107.0 90 2430 14.5 70 2
## 23 1 4 104.0 95 2375 17.5 70 2
## 24 1 4 121.0 113 2234 12.5 70 2
## 25 0 6 199.0 90 2648 15.0 70 1
## 26 0 8 360.0 215 4615 14.0 70 1
## 27 0 8 307.0 200 4376 15.0 70 1
## 28 0 8 318.0 210 4382 13.5 70 1
## 29 0 8 304.0 193 4732 18.5 70 1
## 30 1 4 97.0 88 2130 14.5 71 3
## 31 1 4 140.0 90 2264 15.5 71 1
## 32 1 4 113.0 95 2228 14.0 71 3
## 34 0 6 232.0 100 2634 13.0 71 1
## 35 0 6 225.0 105 3439 15.5 71 1
## 36 0 6 250.0 100 3329 15.5 71 1
## 37 0 6 250.0 88 3302 15.5 71 1
## 38 0 6 232.0 100 3288 15.5 71 1
## 39 0 8 350.0 165 4209 12.0 71 1
## 40 0 8 400.0 175 4464 11.5 71 1
## 41 0 8 351.0 153 4154 13.5 71 1
## 42 0 8 318.0 150 4096 13.0 71 1
## 43 0 8 383.0 180 4955 11.5 71 1
## 44 0 8 400.0 170 4746 12.0 71 1
## 45 0 8 400.0 175 5140 12.0 71 1
## 46 0 6 258.0 110 2962 13.5 71 1
## 47 0 4 140.0 72 2408 19.0 71 1
## 48 0 6 250.0 100 3282 15.0 71 1
## 49 0 6 250.0 88 3139 14.5 71 1
## 50 1 4 122.0 86 2220 14.0 71 1
## 51 1 4 116.0 90 2123 14.0 71 2
## 52 1 4 79.0 70 2074 19.5 71 2
## 53 1 4 88.0 76 2065 14.5 71 2
## 54 1 4 71.0 65 1773 19.0 71 3
## 55 1 4 72.0 69 1613 18.0 71 3
## 56 1 4 97.0 60 1834 19.0 71 2
## 57 1 4 91.0 70 1955 20.5 71 1
## 58 1 4 113.0 95 2278 15.5 72 3
## 59 1 4 97.5 80 2126 17.0 72 1
## 60 1 4 97.0 54 2254 23.5 72 2
## 61 0 4 140.0 90 2408 19.5 72 1
## 62 0 4 122.0 86 2226 16.5 72 1
## 63 0 8 350.0 165 4274 12.0 72 1
## 64 0 8 400.0 175 4385 12.0 72 1
## 65 0 8 318.0 150 4135 13.5 72 1
## 66 0 8 351.0 153 4129 13.0 72 1
## 67 0 8 304.0 150 3672 11.5 72 1
## 68 0 8 429.0 208 4633 11.0 72 1
## 69 0 8 350.0 155 4502 13.5 72 1
## 70 0 8 350.0 160 4456 13.5 72 1
## 71 0 8 400.0 190 4422 12.5 72 1
## 72 0 3 70.0 97 2330 13.5 72 3
## 73 0 8 304.0 150 3892 12.5 72 1
## 74 0 8 307.0 130 4098 14.0 72 1
## 75 0 8 302.0 140 4294 16.0 72 1
## 76 0 8 318.0 150 4077 14.0 72 1
## 77 0 4 121.0 112 2933 14.5 72 2
## 78 0 4 121.0 76 2511 18.0 72 2
## 79 0 4 120.0 87 2979 19.5 72 2
## 80 1 4 96.0 69 2189 18.0 72 2
## 81 0 4 122.0 86 2395 16.0 72 1
## 82 1 4 97.0 92 2288 17.0 72 3
## 83 1 4 120.0 97 2506 14.5 72 3
## 84 1 4 98.0 80 2164 15.0 72 1
## 85 1 4 97.0 88 2100 16.5 72 3
## 86 0 8 350.0 175 4100 13.0 73 1
## 87 0 8 304.0 150 3672 11.5 73 1
## 88 0 8 350.0 145 3988 13.0 73 1
## 89 0 8 302.0 137 4042 14.5 73 1
## 90 0 8 318.0 150 3777 12.5 73 1
## 91 0 8 429.0 198 4952 11.5 73 1
## 92 0 8 400.0 150 4464 12.0 73 1
## 93 0 8 351.0 158 4363 13.0 73 1
## 94 0 8 318.0 150 4237 14.5 73 1
## 95 0 8 440.0 215 4735 11.0 73 1
## 96 0 8 455.0 225 4951 11.0 73 1
## 97 0 8 360.0 175 3821 11.0 73 1
## 98 0 6 225.0 105 3121 16.5 73 1
## 99 0 6 250.0 100 3278 18.0 73 1
## 100 0 6 232.0 100 2945 16.0 73 1
## 101 0 6 250.0 88 3021 16.5 73 1
## 102 1 6 198.0 95 2904 16.0 73 1
## 103 1 4 97.0 46 1950 21.0 73 2
## 104 0 8 400.0 150 4997 14.0 73 1
## 105 0 8 400.0 167 4906 12.5 73 1
## 106 0 8 360.0 170 4654 13.0 73 1
## 107 0 8 350.0 180 4499 12.5 73 1
## 108 0 6 232.0 100 2789 15.0 73 1
## 109 0 4 97.0 88 2279 19.0 73 3
## 110 0 4 140.0 72 2401 19.5 73 1
## 111 0 4 108.0 94 2379 16.5 73 3
## 112 0 3 70.0 90 2124 13.5 73 3
## 113 0 4 122.0 85 2310 18.5 73 1
## 114 0 6 155.0 107 2472 14.0 73 1
## 115 1 4 98.0 90 2265 15.5 73 2
## 116 0 8 350.0 145 4082 13.0 73 1
## 117 0 8 400.0 230 4278 9.5 73 1
## 118 1 4 68.0 49 1867 19.5 73 2
## 119 1 4 116.0 75 2158 15.5 73 2
## 120 0 4 114.0 91 2582 14.0 73 2
## 121 0 4 121.0 112 2868 15.5 73 2
## 122 0 8 318.0 150 3399 11.0 73 1
## 123 1 4 121.0 110 2660 14.0 73 2
## 124 0 6 156.0 122 2807 13.5 73 3
## 125 0 8 350.0 180 3664 11.0 73 1
## 126 0 6 198.0 95 3102 16.5 74 1
## 128 0 6 232.0 100 2901 16.0 74 1
## 129 0 6 250.0 100 3336 17.0 74 1
## 130 1 4 79.0 67 1950 19.0 74 3
## 131 1 4 122.0 80 2451 16.5 74 1
## 132 1 4 71.0 65 1836 21.0 74 3
## 133 1 4 140.0 75 2542 17.0 74 1
## 134 0 6 250.0 100 3781 17.0 74 1
## 135 0 6 258.0 110 3632 18.0 74 1
## 136 0 6 225.0 105 3613 16.5 74 1
## 137 0 8 302.0 140 4141 14.0 74 1
## 138 0 8 350.0 150 4699 14.5 74 1
## 139 0 8 318.0 150 4457 13.5 74 1
## 140 0 8 302.0 140 4638 16.0 74 1
## 141 0 8 304.0 150 4257 15.5 74 1
## 142 1 4 98.0 83 2219 16.5 74 2
## 143 1 4 79.0 67 1963 15.5 74 2
## 144 1 4 97.0 78 2300 14.5 74 2
## 145 1 4 76.0 52 1649 16.5 74 3
## 146 1 4 83.0 61 2003 19.0 74 3
## 147 1 4 90.0 75 2125 14.5 74 1
## 148 1 4 90.0 75 2108 15.5 74 2
## 149 1 4 116.0 75 2246 14.0 74 2
## 150 1 4 120.0 97 2489 15.0 74 3
## 151 1 4 108.0 93 2391 15.5 74 3
## 152 1 4 79.0 67 2000 16.0 74 2
## 153 0 6 225.0 95 3264 16.0 75 1
## 154 0 6 250.0 105 3459 16.0 75 1
## 155 0 6 250.0 72 3432 21.0 75 1
## 156 0 6 250.0 72 3158 19.5 75 1
## 157 0 8 400.0 170 4668 11.5 75 1
## 158 0 8 350.0 145 4440 14.0 75 1
## 159 0 8 318.0 150 4498 14.5 75 1
## 160 0 8 351.0 148 4657 13.5 75 1
## 161 0 6 231.0 110 3907 21.0 75 1
## 162 0 6 250.0 105 3897 18.5 75 1
## 163 0 6 258.0 110 3730 19.0 75 1
## 164 0 6 225.0 95 3785 19.0 75 1
## 165 0 6 231.0 110 3039 15.0 75 1
## 166 0 8 262.0 110 3221 13.5 75 1
## 167 0 8 302.0 129 3169 12.0 75 1
## 168 1 4 97.0 75 2171 16.0 75 3
## 169 1 4 140.0 83 2639 17.0 75 1
## 170 0 6 232.0 100 2914 16.0 75 1
## 171 1 4 140.0 78 2592 18.5 75 1
## 172 1 4 134.0 96 2702 13.5 75 3
## 173 1 4 90.0 71 2223 16.5 75 2
## 174 1 4 119.0 97 2545 17.0 75 3
## 175 0 6 171.0 97 2984 14.5 75 1
## 176 1 4 90.0 70 1937 14.0 75 2
## 177 0 6 232.0 90 3211 17.0 75 1
## 178 1 4 115.0 95 2694 15.0 75 2
## 179 1 4 120.0 88 2957 17.0 75 2
## 180 0 4 121.0 98 2945 14.5 75 2
## 181 1 4 121.0 115 2671 13.5 75 2
## 182 1 4 91.0 53 1795 17.5 75 3
## 183 1 4 107.0 86 2464 15.5 76 2
## 184 1 4 116.0 81 2220 16.9 76 2
## 185 1 4 140.0 92 2572 14.9 76 1
## 186 1 4 98.0 79 2255 17.7 76 1
## 187 1 4 101.0 83 2202 15.3 76 2
## 188 0 8 305.0 140 4215 13.0 76 1
## 189 0 8 318.0 150 4190 13.0 76 1
## 190 0 8 304.0 120 3962 13.9 76 1
## 191 0 8 351.0 152 4215 12.8 76 1
## 192 0 6 225.0 100 3233 15.4 76 1
## 193 0 6 250.0 105 3353 14.5 76 1
## 194 1 6 200.0 81 3012 17.6 76 1
## 195 0 6 232.0 90 3085 17.6 76 1
## 196 1 4 85.0 52 2035 22.2 76 1
## 197 1 4 98.0 60 2164 22.1 76 1
## 198 1 4 90.0 70 1937 14.2 76 2
## 199 1 4 91.0 53 1795 17.4 76 3
## 200 0 6 225.0 100 3651 17.7 76 1
## 201 0 6 250.0 78 3574 21.0 76 1
## 202 0 6 250.0 110 3645 16.2 76 1
## 203 0 6 258.0 95 3193 17.8 76 1
## 204 1 4 97.0 71 1825 12.2 76 2
## 205 1 4 85.0 70 1990 17.0 76 3
## 206 1 4 97.0 75 2155 16.4 76 3
## 207 1 4 140.0 72 2565 13.6 76 1
## 208 0 4 130.0 102 3150 15.7 76 2
## 209 0 8 318.0 150 3940 13.2 76 1
## 210 0 4 120.0 88 3270 21.9 76 2
## 211 0 6 156.0 108 2930 15.5 76 3
## 212 0 6 168.0 120 3820 16.7 76 2
## 213 0 8 350.0 180 4380 12.1 76 1
## 214 0 8 350.0 145 4055 12.0 76 1
## 215 0 8 302.0 130 3870 15.0 76 1
## 216 0 8 318.0 150 3755 14.0 76 1
## 217 1 4 98.0 68 2045 18.5 77 3
## 218 1 4 111.0 80 2155 14.8 77 1
## 219 1 4 79.0 58 1825 18.6 77 2
## 220 1 4 122.0 96 2300 15.5 77 1
## 221 1 4 85.0 70 1945 16.8 77 3
## 222 0 8 305.0 145 3880 12.5 77 1
## 223 0 8 260.0 110 4060 19.0 77 1
## 224 0 8 318.0 145 4140 13.7 77 1
## 225 0 8 302.0 130 4295 14.9 77 1
## 226 0 6 250.0 110 3520 16.4 77 1
## 227 0 6 231.0 105 3425 16.9 77 1
## 228 0 6 225.0 100 3630 17.7 77 1
## 229 0 6 250.0 98 3525 19.0 77 1
## 230 0 8 400.0 180 4220 11.1 77 1
## 231 0 8 350.0 170 4165 11.4 77 1
## 232 0 8 400.0 190 4325 12.2 77 1
## 233 0 8 351.0 149 4335 14.5 77 1
## 234 1 4 97.0 78 1940 14.5 77 2
## 235 1 4 151.0 88 2740 16.0 77 1
## 236 1 4 97.0 75 2265 18.2 77 3
## 237 1 4 140.0 89 2755 15.8 77 1
## 238 1 4 98.0 63 2051 17.0 77 1
## 239 1 4 98.0 83 2075 15.9 77 1
## 240 1 4 97.0 67 1985 16.4 77 3
## 241 1 4 97.0 78 2190 14.1 77 2
## 242 0 6 146.0 97 2815 14.5 77 3
## 243 0 4 121.0 110 2600 12.8 77 2
## 244 0 3 80.0 110 2720 13.5 77 3
## 245 1 4 90.0 48 1985 21.5 78 2
## 246 1 4 98.0 66 1800 14.4 78 1
## 247 1 4 78.0 52 1985 19.4 78 3
## 248 1 4 85.0 70 2070 18.6 78 3
## 249 1 4 91.0 60 1800 16.4 78 3
## 250 0 8 260.0 110 3365 15.5 78 1
## 251 0 8 318.0 140 3735 13.2 78 1
## 252 0 8 302.0 139 3570 12.8 78 1
## 253 0 6 231.0 105 3535 19.2 78 1
## 254 0 6 200.0 95 3155 18.2 78 1
## 255 0 6 200.0 85 2965 15.8 78 1
## 256 1 4 140.0 88 2720 15.4 78 1
## 257 0 6 225.0 100 3430 17.2 78 1
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## 259 0 6 231.0 105 3380 15.8 78 1
## 260 0 6 200.0 85 3070 16.7 78 1
## 261 0 6 225.0 110 3620 18.7 78 1
## 262 0 6 258.0 120 3410 15.1 78 1
## 263 0 8 305.0 145 3425 13.2 78 1
## 264 0 6 231.0 165 3445 13.4 78 1
## 265 0 8 302.0 139 3205 11.2 78 1
## 266 0 8 318.0 140 4080 13.7 78 1
## 267 1 4 98.0 68 2155 16.5 78 1
## 268 1 4 134.0 95 2560 14.2 78 3
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## 274 1 4 119.0 97 2405 14.9 78 3
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## 276 0 6 163.0 125 3140 13.6 78 2
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## name
## 1 chevrolet chevelle malibu
## 2 buick skylark 320
## 3 plymouth satellite
## 4 amc rebel sst
## 5 ford torino
## 6 ford galaxie 500
## 7 chevrolet impala
## 8 plymouth fury iii
## 9 pontiac catalina
## 10 amc ambassador dpl
## 11 dodge challenger se
## 12 plymouth 'cuda 340
## 13 chevrolet monte carlo
## 14 buick estate wagon (sw)
## 15 toyota corona mark ii
## 16 plymouth duster
## 17 amc hornet
## 18 ford maverick
## 19 datsun pl510
## 20 volkswagen 1131 deluxe sedan
## 21 peugeot 504
## 22 audi 100 ls
## 23 saab 99e
## 24 bmw 2002
## 25 amc gremlin
## 26 ford f250
## 27 chevy c20
## 28 dodge d200
## 29 hi 1200d
## 30 datsun pl510
## 31 chevrolet vega 2300
## 32 toyota corona
## 34 amc gremlin
## 35 plymouth satellite custom
## 36 chevrolet chevelle malibu
## 37 ford torino 500
## 38 amc matador
## 39 chevrolet impala
## 40 pontiac catalina brougham
## 41 ford galaxie 500
## 42 plymouth fury iii
## 43 dodge monaco (sw)
## 44 ford country squire (sw)
## 45 pontiac safari (sw)
## 46 amc hornet sportabout (sw)
## 47 chevrolet vega (sw)
## 48 pontiac firebird
## 49 ford mustang
## 50 mercury capri 2000
## 51 opel 1900
## 52 peugeot 304
## 53 fiat 124b
## 54 toyota corolla 1200
## 55 datsun 1200
## 56 volkswagen model 111
## 57 plymouth cricket
## 58 toyota corona hardtop
## 59 dodge colt hardtop
## 60 volkswagen type 3
## 61 chevrolet vega
## 62 ford pinto runabout
## 63 chevrolet impala
## 64 pontiac catalina
## 65 plymouth fury iii
## 66 ford galaxie 500
## 67 amc ambassador sst
## 68 mercury marquis
## 69 buick lesabre custom
## 70 oldsmobile delta 88 royale
## 71 chrysler newport royal
## 72 mazda rx2 coupe
## 73 amc matador (sw)
## 74 chevrolet chevelle concours (sw)
## 75 ford gran torino (sw)
## 76 plymouth satellite custom (sw)
## 77 volvo 145e (sw)
## 78 volkswagen 411 (sw)
## 79 peugeot 504 (sw)
## 80 renault 12 (sw)
## 81 ford pinto (sw)
## 82 datsun 510 (sw)
## 83 toyouta corona mark ii (sw)
## 84 dodge colt (sw)
## 85 toyota corolla 1600 (sw)
## 86 buick century 350
## 87 amc matador
## 88 chevrolet malibu
## 89 ford gran torino
## 90 dodge coronet custom
## 91 mercury marquis brougham
## 92 chevrolet caprice classic
## 93 ford ltd
## 94 plymouth fury gran sedan
## 95 chrysler new yorker brougham
## 96 buick electra 225 custom
## 97 amc ambassador brougham
## 98 plymouth valiant
## 99 chevrolet nova custom
## 100 amc hornet
## 101 ford maverick
## 102 plymouth duster
## 103 volkswagen super beetle
## 104 chevrolet impala
## 105 ford country
## 106 plymouth custom suburb
## 107 oldsmobile vista cruiser
## 108 amc gremlin
## 109 toyota carina
## 110 chevrolet vega
## 111 datsun 610
## 112 maxda rx3
## 113 ford pinto
## 114 mercury capri v6
## 115 fiat 124 sport coupe
## 116 chevrolet monte carlo s
## 117 pontiac grand prix
## 118 fiat 128
## 119 opel manta
## 120 audi 100ls
## 121 volvo 144ea
## 122 dodge dart custom
## 123 saab 99le
## 124 toyota mark ii
## 125 oldsmobile omega
## 126 plymouth duster
## 128 amc hornet
## 129 chevrolet nova
## 130 datsun b210
## 131 ford pinto
## 132 toyota corolla 1200
## 133 chevrolet vega
## 134 chevrolet chevelle malibu classic
## 135 amc matador
## 136 plymouth satellite sebring
## 137 ford gran torino
## 138 buick century luxus (sw)
## 139 dodge coronet custom (sw)
## 140 ford gran torino (sw)
## 141 amc matador (sw)
## 142 audi fox
## 143 volkswagen dasher
## 144 opel manta
## 145 toyota corona
## 146 datsun 710
## 147 dodge colt
## 148 fiat 128
## 149 fiat 124 tc
## 150 honda civic
## 151 subaru
## 152 fiat x1.9
## 153 plymouth valiant custom
## 154 chevrolet nova
## 155 mercury monarch
## 156 ford maverick
## 157 pontiac catalina
## 158 chevrolet bel air
## 159 plymouth grand fury
## 160 ford ltd
## 161 buick century
## 162 chevroelt chevelle malibu
## 163 amc matador
## 164 plymouth fury
## 165 buick skyhawk
## 166 chevrolet monza 2+2
## 167 ford mustang ii
## 168 toyota corolla
## 169 ford pinto
## 170 amc gremlin
## 171 pontiac astro
## 172 toyota corona
## 173 volkswagen dasher
## 174 datsun 710
## 175 ford pinto
## 176 volkswagen rabbit
## 177 amc pacer
## 178 audi 100ls
## 179 peugeot 504
## 180 volvo 244dl
## 181 saab 99le
## 182 honda civic cvcc
## 183 fiat 131
## 184 opel 1900
## 185 capri ii
## 186 dodge colt
## 187 renault 12tl
## 188 chevrolet chevelle malibu classic
## 189 dodge coronet brougham
## 190 amc matador
## 191 ford gran torino
## 192 plymouth valiant
## 193 chevrolet nova
## 194 ford maverick
## 195 amc hornet
## 196 chevrolet chevette
## 197 chevrolet woody
## 198 vw rabbit
## 199 honda civic
## 200 dodge aspen se
## 201 ford granada ghia
## 202 pontiac ventura sj
## 203 amc pacer d/l
## 204 volkswagen rabbit
## 205 datsun b-210
## 206 toyota corolla
## 207 ford pinto
## 208 volvo 245
## 209 plymouth volare premier v8
## 210 peugeot 504
## 211 toyota mark ii
## 212 mercedes-benz 280s
## 213 cadillac seville
## 214 chevy c10
## 215 ford f108
## 216 dodge d100
## 217 honda accord cvcc
## 218 buick opel isuzu deluxe
## 219 renault 5 gtl
## 220 plymouth arrow gs
## 221 datsun f-10 hatchback
## 222 chevrolet caprice classic
## 223 oldsmobile cutlass supreme
## 224 dodge monaco brougham
## 225 mercury cougar brougham
## 226 chevrolet concours
## 227 buick skylark
## 228 plymouth volare custom
## 229 ford granada
## 230 pontiac grand prix lj
## 231 chevrolet monte carlo landau
## 232 chrysler cordoba
## 233 ford thunderbird
## 234 volkswagen rabbit custom
## 235 pontiac sunbird coupe
## 236 toyota corolla liftback
## 237 ford mustang ii 2+2
## 238 chevrolet chevette
## 239 dodge colt m/m
## 240 subaru dl
## 241 volkswagen dasher
## 242 datsun 810
## 243 bmw 320i
## 244 mazda rx-4
## 245 volkswagen rabbit custom diesel
## 246 ford fiesta
## 247 mazda glc deluxe
## 248 datsun b210 gx
## 249 honda civic cvcc
## 250 oldsmobile cutlass salon brougham
## 251 dodge diplomat
## 252 mercury monarch ghia
## 253 pontiac phoenix lj
## 254 chevrolet malibu
## 255 ford fairmont (auto)
## 256 ford fairmont (man)
## 257 plymouth volare
## 258 amc concord
## 259 buick century special
## 260 mercury zephyr
## 261 dodge aspen
## 262 amc concord d/l
## 263 chevrolet monte carlo landau
## 264 buick regal sport coupe (turbo)
## 265 ford futura
## 266 dodge magnum xe
## 267 chevrolet chevette
## 268 toyota corona
## 269 datsun 510
## 270 dodge omni
## 271 toyota celica gt liftback
## 272 plymouth sapporo
## 273 oldsmobile starfire sx
## 274 datsun 200-sx
## 275 audi 5000
## 276 volvo 264gl
## 277 saab 99gle
## 278 peugeot 604sl
## 279 volkswagen scirocco
## 280 honda accord lx
## 281 pontiac lemans v6
## 282 mercury zephyr 6
## 283 ford fairmont 4
## 284 amc concord dl 6
## 285 dodge aspen 6
## 286 chevrolet caprice classic
## 287 ford ltd landau
## 288 mercury grand marquis
## 289 dodge st. regis
## 290 buick estate wagon (sw)
## 291 ford country squire (sw)
## 292 chevrolet malibu classic (sw)
## 293 chrysler lebaron town @ country (sw)
## 294 vw rabbit custom
## 295 maxda glc deluxe
## 296 dodge colt hatchback custom
## 297 amc spirit dl
## 298 mercedes benz 300d
## 299 cadillac eldorado
## 300 peugeot 504
## 301 oldsmobile cutlass salon brougham
## 302 plymouth horizon
## 303 plymouth horizon tc3
## 304 datsun 210
## 305 fiat strada custom
## 306 buick skylark limited
## 307 chevrolet citation
## 308 oldsmobile omega brougham
## 309 pontiac phoenix
## 310 vw rabbit
## 311 toyota corolla tercel
## 312 chevrolet chevette
## 313 datsun 310
## 314 chevrolet citation
## 315 ford fairmont
## 316 amc concord
## 317 dodge aspen
## 318 audi 4000
## 319 toyota corona liftback
## 320 mazda 626
## 321 datsun 510 hatchback
## 322 toyota corolla
## 323 mazda glc
## 324 dodge colt
## 325 datsun 210
## 326 vw rabbit c (diesel)
## 327 vw dasher (diesel)
## 328 audi 5000s (diesel)
## 329 mercedes-benz 240d
## 330 honda civic 1500 gl
## 332 subaru dl
## 333 vokswagen rabbit
## 334 datsun 280-zx
## 335 mazda rx-7 gs
## 336 triumph tr7 coupe
## 338 honda accord
## 339 plymouth reliant
## 340 buick skylark
## 341 dodge aries wagon (sw)
## 342 chevrolet citation
## 343 plymouth reliant
## 344 toyota starlet
## 345 plymouth champ
## 346 honda civic 1300
## 347 subaru
## 348 datsun 210 mpg
## 349 toyota tercel
## 350 mazda glc 4
## 351 plymouth horizon 4
## 352 ford escort 4w
## 353 ford escort 2h
## 354 volkswagen jetta
## 356 honda prelude
## 357 toyota corolla
## 358 datsun 200sx
## 359 mazda 626
## 360 peugeot 505s turbo diesel
## 361 volvo diesel
## 362 toyota cressida
## 363 datsun 810 maxima
## 364 buick century
## 365 oldsmobile cutlass ls
## 366 ford granada gl
## 367 chrysler lebaron salon
## 368 chevrolet cavalier
## 369 chevrolet cavalier wagon
## 370 chevrolet cavalier 2-door
## 371 pontiac j2000 se hatchback
## 372 dodge aries se
## 373 pontiac phoenix
## 374 ford fairmont futura
## 375 volkswagen rabbit l
## 376 mazda glc custom l
## 377 mazda glc custom
## 378 plymouth horizon miser
## 379 mercury lynx l
## 380 nissan stanza xe
## 381 honda accord
## 382 toyota corolla
## 383 honda civic
## 384 honda civic (auto)
## 385 datsun 310 gx
## 386 buick century limited
## 387 oldsmobile cutlass ciera (diesel)
## 388 chrysler lebaron medallion
## 389 ford granada l
## 390 toyota celica gt
## 391 dodge charger 2.2
## 392 chevrolet camaro
## 393 ford mustang gl
## 394 vw pickup
## 395 dodge rampage
## 396 ford ranger
## 397 chevy s-10(b) Explore the data graphically in order to investigate the associ- ation between mpg01 and the other features. Which of the other features seem most likely to be useful in predicting mpg01? Scat- terplots and boxplots may be useful tools to answer this ques- tion. Describe your findings.
library(ggplot2)
# Convert categorical variables to factors
Auto$cylinders <- as.factor(Auto$cylinders)
Auto$year <- as.factor(Auto$year)
Auto$origin <- as.factor(Auto$origin)
# Scatterplots for numerical variables
scatterplots <- function(variable) {
ggplot(Auto, aes(x = mpg01, y = !!sym(variable))) +
geom_jitter(alpha = 0.5) +
labs(title = paste("Scatterplot of mpg01 and", variable),
x = "mpg01", y = variable)
}
# Boxplots for numerical variables
boxplots <- function(variable) {
ggplot(Auto, aes(x = mpg01, y = !!sym(variable))) +
geom_boxplot() +
labs(title = paste("Boxplot of mpg01 and", variable),
x = "mpg01", y = variable)
}
# List of numerical variables to explore
numerical_variables <- c("displacement", "horsepower", "weight", "acceleration")
# Print scatterplots and boxplots
for (variable in numerical_variables) {
print(scatterplots(variable))
print(boxplots(variable))
}
## Warning: Continuous x aesthetic
## ℹ did you forget `aes(group = ...)`?
## Warning: Continuous x aesthetic
## ℹ did you forget `aes(group = ...)`?
## Warning: Continuous x aesthetic
## ℹ did you forget `aes(group = ...)`?
## Warning: Continuous x aesthetic
## ℹ did you forget `aes(group = ...)`?
(c) Split the data into a training set and a test set.
library(caret)
set.seed(123) # For reproducibility
# Create an index for the split
index <- createDataPartition(Auto$mpg01, p = 0.8, list = FALSE)
# Create the training set
training_data <- Auto[index, ]
# Create the test set
test_data <- Auto[-index, ](d) Perform LDA on the training data in order to predict mpg01 using the variables that seemed most associated with mpg01 in (b). What is the test error of the model obtained?
# Load the necessary library
library(MASS)
# Specify the predictors based on your findings in part (b)
predictors <- c("displacement", "horsepower", "weight", "acceleration")
# Train LDA model
lda_model <- lda(as.factor(mpg01) ~ ., data = training_data[, c(predictors, "mpg01")])
# Make predictions on the test set
lda_predictions <- predict(lda_model, newdata = test_data[, c(predictors, "mpg01")])
# Calculate the confusion matrix
conf_matrix_lda <- table(Actual = test_data$mpg01, Predicted = lda_predictions$class)
# Calculate the test error
test_error_lda <- 1 - sum(diag(conf_matrix_lda)) / sum(conf_matrix_lda)
print(paste("Test Error (LDA):", round(test_error_lda, 4)))## [1] "Test Error (LDA): 0.141"(e) Perform QDA on the training data in order to predict mpg01 using the variables that seemed most associated with mpg01 in (b). What is the test error of the model obtained?
# Load the necessary library
library(MASS)
# Specify the predictors based on your findings in part (b)
predictors <- c("displacement", "horsepower", "weight", "acceleration")
# Train QDA model
qda_model <- qda(as.factor(mpg01) ~ ., data = training_data[, c(predictors, "mpg01")])
# Make predictions on the test set
qda_predictions <- predict(qda_model, newdata = test_data[, c(predictors, "mpg01")])
# Calculate the confusion matrix
conf_matrix_qda <- table(Actual = test_data$mpg01, Predicted = qda_predictions$class)
# Calculate the test error
test_error_qda <- 1 - sum(diag(conf_matrix_qda)) / sum(conf_matrix_qda)
print(paste("Test Error (QDA):", round(test_error_qda, 4)))## [1] "Test Error (QDA): 0.1026"(f) Perform logistic regression on the training data in order to pre- dict mpg01 using the variables that seemed most associated with mpg01 in (b). What is the test error of the model obtained?
# Specify the predictors based on your findings in part (b)
predictors <- c("displacement", "horsepower", "weight", "acceleration")
# Train logistic regression model
logistic_model <- glm(as.factor(mpg01) ~ ., data = training_data[, c(predictors, "mpg01")], family = binomial)
# Make predictions on the test set
logistic_predictions <- predict(logistic_model, newdata = test_data[, c(predictors, "mpg01")], type = "response")
# Convert probabilities to binary predictions
logistic_predictions <- ifelse(logistic_predictions > 0.5, 1, 0)
# Calculate the confusion matrix
conf_matrix_logistic <- table(Actual = test_data$mpg01, Predicted = logistic_predictions)
# Calculate the test error
test_error_logistic <- 1 - sum(diag(conf_matrix_logistic)) / sum(conf_matrix_logistic)
print(paste("Test Error (Logistic Regression):", round(test_error_logistic, 4)))## [1] "Test Error (Logistic Regression): 0.1282"# Specify the predictors based on your findings in part (b)
predictors <- c("displacement", "horsepower", "weight", "acceleration")
# Train logistic regression model
logistic_model <- glm(as.factor(mpg01) ~ ., data = training_data[, c(predictors, "mpg01")], family = binomial)
# Make predictions on the test set
logistic_predictions <- predict(logistic_model, newdata = test_data[, c(predictors, "mpg01")], type = "response")
# Convert probabilities to binary predictions
logistic_predictions <- ifelse(logistic_predictions > 0.5, 1, 0)
# Calculate the confusion matrix
conf_matrix_logistic <- table(Actual = test_data$mpg01, Predicted = logistic_predictions)
# Calculate the test error
test_error_logistic <- 1 - sum(diag(conf_matrix_logistic)) / sum(conf_matrix_logistic)
print(paste("Test Error (Logistic Regression):", round(test_error_logistic, 4)))## [1] "Test Error (Logistic Regression): 0.1282"(h) Perform KNN on the training data, with several values of K, in order to predict mpg01. Use only the variables that seemed most associated with mpg01 in (b). What test errors do you obtain? Which value of K seems to perform the best on this data set?
# Load the necessary library
library(class)
# Specify the predictors based on your findings in part (b)
predictors <- c("displacement", "horsepower", "weight", "acceleration")
# Create a function to calculate test error for different values of K
calculate_test_error <- function(k_value) {
knn_predictions <- knn(train = training_data[, c(predictors, "mpg01")],
test = test_data[, c(predictors, "mpg01")],
cl = training_data$mpg01,
k = k_value)
# Calculate the confusion matrix
conf_matrix_knn <- table(Actual = test_data$mpg01, Predicted = knn_predictions)
# Calculate the test error
test_error <- 1 - sum(diag(conf_matrix_knn)) / sum(conf_matrix_knn)
return(test_error)
}
# Try different values of K
k_values <- c(1, 3, 5, 7, 9)
test_errors <- sapply(k_values, calculate_test_error)
# Print the test errors for different values of K
for (i in seq_along(k_values)) {
print(paste("Test Error (K =", k_values[i], "):", round(test_errors[i], 4)))
}## [1] "Test Error (K = 1 ): 0.1282"
## [1] "Test Error (K = 3 ): 0.1154"
## [1] "Test Error (K = 5 ): 0.141"
## [1] "Test Error (K = 7 ): 0.1154"
## [1] "Test Error (K = 9 ): 0.1154"# Find the value of K that minimizes test error
best_k <- k_values[which.min(test_errors)]
print(paste("Best K:", best_k))## [1] "Best K: 3"