#Part 1: Association Analysis
1. Load the bob_ross csv file into R. This data contains information about various paintings done by Bob Ross. Bob Ross was an American artist know for his TV show called The Joy of Painting. This dataset lists possible elements of each painting, such as a barn or tree, and whether they were present or absent.

library(class)
bob <- read.csv("/Users/jusimioni/Desktop/MSDA 2021-23/Spring 2023/Big Data/Data/bob_ross.csv")
bob
##     EPISODE                         TITLE APPLE_FRAME AURORA_BOREALIS BARN
## 1    S01E01         "A WALK IN THE WOODS"           0               0    0
## 2    S01E02                "MT. MCKINLEY"           0               0    0
## 3    S01E03                "EBONY SUNSET"           0               0    0
## 4    S01E04                 "WINTER MIST"           0               0    0
## 5    S01E05                "QUIET STREAM"           0               0    0
## 6    S01E06                 "WINTER MOON"           0               0    0
## 7    S01E07            "AUTUMN MOUNTAINS"           0               0    0
## 8    S01E08             "PEACEFUL VALLEY"           0               0    0
## 9    S01E09                    "SEASCAPE"           0               0    0
## 10   S01E10               "MOUNTAIN LAKE"           0               0    0
## 11   S01E11                 "WINTER GLOW"           0               0    0
## 12   S01E12                    "SNOWFALL"           0               0    0
## 13   S01E13           "FINAL REFLECTIONS"           0               0    0
## 14   S02E01                 "MEADOW LAKE"           0               0    0
## 15   S02E02                  "WINTER SUN"           0               0    0
## 16   S02E03                   "EBONY SEA"           0               0    0
## 17   S02E04              "SHADES OF GREY"           0               0    0
## 18   S02E05             "AUTUMN SPLENDOR"           0               0    0
## 19   S02E06                 "BLACK RIVER"           0               0    0
## 20   S02E07              "BROWN MOUNTAIN"           0               0    0
## 21   S02E08                 "REFLECTIONS"           0               0    0
## 22   S02E09      "BLACK & WHITE SEASCAPE"           0               0    0
## 23   S02E10                  "LAZY RIVER"           0               0    0
## 24   S02E11             "BLACK WATERFALL"           0               0    0
## 25   S02E12          "MOUNTAIN WATERFALL"           0               0    0
## 26   S02E13                 "FINAL GRACE"           0               0    0
## 27   S03E01            "MOUNTAIN RETREAT"           0               0    0
## 28   S03E02                   "BLUE MOON"           0               0    0
## 29   S03E03             "BUBBLING STREAM"           0               0    0
## 30   S03E04                "WINTER NIGHT"           0               0    0
## 31   S03E05               "DISTANT HILLS"           0               0    0
## 32   S03E06              "COVERED BRIDGE"           0               0    0
## 33   S03E07                 "QUIET INLET"           0               0    0
## 34   S03E08                 "NIGHT LIGHT"           0               0    0
## 35   S03E09                "THE OLD MILL"           0               0    0
## 36   S03E10                    "CAMPFIRE"           0               0    0
## 37   S03E11                 "RUSTIC BARN"           0               0    1
## 38   S03E12                 "HIDDEN LAKE"           0               0    0
## 39   S03E13             "PEACEFUL WATERS"           0               0    0
## 40   S04E01             "PURPLE SPLENDOR"           0               0    0
## 41   S04E02             "TRANQUIL VALLEY"           0               0    0
## 42   S04E03          "MAJESTIC MOUNTAINS"           0               0    0
## 43   S04E04             "WINTER SAWSCAPE"           0               0    0
## 44   S04E05            "EVENING SEASCAPE"           0               0    0
## 45   S04E06             "WARM SUMMER DAY"           0               0    0
## 46   S04E07          "CABIN IN THE WOODS"           0               0    0
## 47   S04E08                    "WETLANDS"           0               0    0
## 48   S04E09                 "COOL WATERS"           0               0    0
## 49   S04E10                 "QUIET WOODS"           0               0    0
## 50   S04E11           "NORTHWEST MAJESTY"           0               0    0
## 51   S04E12                 "AUTUMN DAYS"           0               0    0
## 52   S04E13          "MOUNTAIN CHALLENGE"           0               0    0
## 53   S05E01          "MOUNTAIN WATERFALL"           0               0    0
## 54   S05E02             "TWILIGHT MEADOW"           0               0    0
## 55   S05E03           "MOUNTAIN BLOSSOMS"           0               0    0
## 56   S05E04            "WINTER STILLNESS"           0               0    0
## 57   S05E05                  "QUIET POND"           0               0    0
## 58   S05E06               "OCEAN SUNRISE"           0               0    0
## 59   S05E07              "BUBBLING BROOK"           0               0    0
## 60   S05E08            "ARIZONA SPLENDOR"           0               0    0
## 61   S05E09           "ANATOMY OF A WAVE"           0               0    0
## 62   S05E10                "THE WINDMILL"           0               0    1
## 63   S05E11                "AUTUMN GLORY"           0               0    0
## 64   S05E12                 "INDIAN GIRL"           0               0    0
## 65   S05E13               "MEADOW STREAM"           0               0    1
## 66   S06E01                  "BLUE RIVER"           0               0    0
## 67   S06E02               "NATURE'S EDGE"           0               0    0
## 68   S06E03                "MORNING MIST"           0               0    0
## 69   S06E04           "WHISPERING STREAM"           0               0    0
## 70   S06E05             "SECLUDED FOREST"           0               0    0
## 71   S06E06                  "SNOW TRAIL"           0               0    0
## 72   S06E07               "ARCTIC BEAUTY"           0               0    0
## 73   S06E08               "HORIZONS WEST"           0               0    0
## 74   S06E09                "HIGH CHATEAU"           0               0    0
## 75   S06E10                "COUNTRY LIFE"           0               0    1
## 76   S06E11             "WESTERN EXPANSE"           0               0    0
## 77   S06E12                  "MARSHLANDS"           0               0    0
## 78   S06E13              "BLAZE OF COLOR"           0               0    0
## 79   S07E01                "WINTER CABIN"           0               0    0
## 80   S07E02               "SECLUDED LAKE"           0               0    0
## 81   S07E03        "EVERGREENS AT SUNSET"           0               0    0
## 82   S07E04              "MOUNTAIN CABIN"           0               0    0
## 83   S07E05           "PORTRAIT OF SALLY"           0               0    0
## 84   S07E06             "MISTY WATERFALL"           0               0    0
## 85   S07E07              "BARN AT SUNSET"           0               0    1
## 86   S07E08           "MOUNTAIN SPLENDOR"           0               0    0
## 87   S07E09            "LAKE BY MOUNTAIN"           0               0    0
## 88   S07E10              "MOUNTAIN GLORY"           0               0    0
## 89   S07E11                 "GREY WINTER"           0               0    0
## 90   S07E12                  "DOCK SCENE"           0               0    0
## 91   S07E13              "DARK WATERFALL"           0               0    0
## 92   S08E01         "MISTY ROLLING HILLS"           0               0    0
## 93   S08E02              "LAKESIDE CABIN"           0               0    0
## 94   S08E03             "WARM WINTER DAY"           0               0    0
## 95   S08E04               "WATERSIDE WAY"           0               0    0
## 96   S08E05              "HUNTER'S HAVEN"           0               0    0
## 97   S08E06     "BUBBLING MOUNTAIN BROOK"           0               0    0
## 98   S08E07             "WINTER HIDEAWAY"           0               0    0
## 99   S08E08        "FOOT OF THE MOUNTAIN"           0               0    0
## 100  S08E09               "MAJESTIC PINE"           0               0    0
## 101  S08E10            "CACTUS AT SUNSET"           0               0    0
## 102  S08E11              "MOUNTAIN RANGE"           0               0    0
## 103  S08E12              "LONELY RETREAT"           0               0    0
## 104  S08E13             "NORTHERN LIGHTS"           0               1    0
## 105  S09E01           "WINTER EVERGREENS"           0               0    0
## 106  S09E02                   "SURF'S UP"           0               0    0
## 107  S09E03                  "RED SUNSET"           0               0    0
## 108  S09E04                 "MEADOW ROAD"           0               0    0
## 109  S09E05                 "WINTER OVAL"           0               0    0
## 110  S09E06              "SECLUDED BEACH"           0               0    0
## 111  S09E07                "FOREST HILLS"           0               0    0
## 112  S09E08    "LITTLE HOUSE BY-THE-ROAD"           0               0    0
## 113  S09E09               "MOUNTAIN PATH"           0               0    0
## 114  S09E10               "COUNTRY CHARM"           0               0    0
## 115  S09E11           "NATURE'S PARADISE"           0               0    0
## 116  S09E12         "MOUNTAIN-BY-THE-SEA"           0               0    0
## 117  S09E13          "MOUNTAIN HIDE-AWAY"           0               0    0
## 118  S10E01              "TOWERING PEAKS"           0               0    0
## 119  S10E02             "CABIN AT SUNSET"           0               0    0
## 120  S10E03                  "TWIN FALLS"           0               0    0
## 121  S10E04             "SECLUDED BRIDGE"           0               0    0
## 122  S10E05                "OCEAN BREEZE"           0               0    0
## 123  S10E06                "AUTUMN WOODS"           0               0    0
## 124  S10E07             "WINTER SOLITUDE"           0               0    0
## 125  S10E08               "GOLDEN SUNSET"           0               0    0
## 126  S10E09               "MOUNTAIN OVAL"           0               0    0
## 127  S10E10                "OCEAN SUNSET"           0               0    0
## 128  S10E11                 "TRIPLE VIEW"           0               0    0
## 129  S10E12                "WINTER FROST"           0               0    0
## 130  S10E13              "LAKESIDE CABIN"           0               0    0
## 131  S11E01             "MOUNTAIN STREAM"           0               0    0
## 132  S11E02               "COUNTRY CABIN"           0               0    0
## 133  S11E03               "DAISY DELIGHT"           0               0    0
## 134  S11E04               "HIDDEN STREAM"           0               0    0
## 135  S11E05            "TOWERING GLACIER"           0               0    0
## 136  S11E06                   "OVAL BARN"           0               0    1
## 137  S11E07               "LAKESIDE PATH"           0               0    0
## 138  S11E08                 "SUNSET OVAL"           0               0    0
## 139  S11E09                 "WINTER BARN"           0               0    1
## 140  S11E10       "SUNSET OVER THE WAVES"           0               0    0
## 141  S11E11                 "GOLDEN GLOW"           0               0    0
## 142  S11E12               "ROADSIDE BARN"           0               0    1
## 143  S11E13              "HAPPY ACCIDENT"           0               0    0
## 144  S12E01                "GOLDEN KNOLL"           0               0    0
## 145  S12E02        "MOUNTAIN REFLECTIONS"           0               0    0
## 146  S12E03           "SECLUDED MOUNTAIN"           0               0    0
## 147  S12E04         "BRIGHT AUTUMN TREES"           0               0    0
## 148  S12E05              "BLACK SEASCAPE"           0               0    0
## 149  S12E06             "STEEP MOUNTAINS"           0               0    0
## 150  S12E07        "QUIET MOUNTAIN RIVER"           0               0    0
## 151  S12E08           "EVENING WATERFALL"           0               0    0
## 152  S12E09           "TROPICAL SEASCAPE"           0               0    0
## 153  S12E10          "MOUNTAIN AT SUNSET"           0               0    0
## 154  S12E11          "SOFT MOUNTAIN GLOW"           0               0    0
## 155  S12E12         "MOUNTAIN IN AN OVAL"           0               0    0
## 156  S12E13             "WINTER MOUNTAIN"           0               0    0
## 157  S13E01               "ROLLING HILLS"           0               0    0
## 158  S13E02             "FROZEN SOLITUDE"           0               0    0
## 159  S13E03                "MEADOW BROOK"           0               0    0
## 160  S13E04           "EVENING AT SUNSET"           0               0    0
## 161  S13E05               "MOUNTAIN VIEW"           0               0    0
## 162  S13E06                "HIDDEN CREEK"           0               0    0
## 163  S13E07              "PEACEFUL HAVEN"           0               0    0
## 164  S13E08         "MOUNTAIN EXHIBITION"           0               0    0
## 165  S13E09              "EMERALD WATERS"           0               0    0
## 166  S13E10             "MOUNTAIN SUMMIT"           0               0    0
## 167  S13E11              "CABIN HIDEAWAY"           0               0    0
## 168  S13E12                "OVAL ESSENCE"           0               0    0
## 169  S13E13                   "LOST LAKE"           0               0    0
## 170  S14E01           "DISTANT MOUNTAINS"           0               0    0
## 171  S14E02       "MEADOW BROOK SURPRISE"           0               0    0
## 172  S14E03     "MOUNTAIN MOONLIGHT OVAL"           0               0    0
## 173  S14E04              "SNOWY SOLITUDE"           0               0    0
## 174  S14E05              "MOUNTAIN RIVER"           0               0    0
## 175  S14E06          "GRACEFUL MOUNTAINS"           0               0    0
## 176  S14E07                 "WINDY WAVES"           0               0    0
## 177  S14E08              "ON A CLEAR DAY"           0               0    0
## 178  S14E09       "RIVERSIDE ESCAPE OVAL"           0               0    0
## 179  S14E10            "SURPRISING FALLS"           0               0    0
## 180  S14E11                 "SHADOW POND"           0               0    0
## 181  S14E12           "MISTY FOREST OVAL"           0               0    0
## 182  S14E13              "NATURAL WONDER"           0               0    0
## 183  S15E01          "SPLENDOR OF WINTER"           0               0    0
## 184  S15E02            "COLORS OF NATURE"           0               0    0
## 185  S15E03              "GRANDPA'S BARN"           0               0    1
## 186  S15E04        "PEACEFUL REFLECTIONS"           0               0    0
## 187  S15E05     "HIDDEN WINTER MOON OVAL"           0               0    0
## 188  S15E06             "WAVES OF WONDER"           0               0    0
## 189  S15E07           "CABIN BY THE POND"           0               0    0
## 190  S15E08                 "FALL STREAM"           0               0    0
## 191  S15E09          "CHRISTMAS EVE SNOW"           0               0    0
## 192  S15E10            "FOREST DAWN OVAL"           0               0    0
## 193  S15E11           "PATHWAY TO AUTUMN"           0               0    0
## 194  S15E12            "DEEP FOREST LAKE"           0               0    0
## 195  S15E13            "PEAKS OF MAJESTY"           0               0    0
## 196  S16E01                 "TWO SEASONS"           0               0    0
## 197  S16E02               "NESTLED CABIN"           0               0    0
## 198  S16E03        "WINTERTIME DISCOVERY"           0               0    0
## 199  S16E04             "MOUNTAIN MIRAGE"           0               0    0
## 200  S16E05         "DOUBLE OVAL FANTASY"           0               0    0
## 201  S16E06          "CONTEMPLATIVE LADY"           0               0    0
## 202  S16E07                  "DEEP WOODS"           0               0    0
## 203  S16E08                   "HIGH TIDE"           0               0    0
## 204  S16E09           "BARN IN SNOW OVAL"           0               0    1
## 205  S16E10           "THAT TIME OF YEAR"           0               0    0
## 206  S16E11            "WATERFALL WONDER"           0               0    0
## 207  S16E12        "MIGHTY MOUNTAIN LAKE"           0               0    0
## 208  S16E13          "WOODED STREAM OVAL"           0               0    0
## 209  S17E01            "GOLDEN MIST OVAL"           0               0    0
## 210  S17E02          "THE OLD HOME PLACE"           0               0    0
## 211  S17E03              "SOOTHING VISTA"           0               0    0
## 212  S17E04                 "STORMY SEAS"           0               0    0
## 213  S17E05                "COUNTRY TIME"           0               0    0
## 214  S17E06         "A MILD WINTER'S DAY"           0               0    0
## 215  S17E07       "SPECTACULAR WATERFALL"           0               0    0
## 216  S17E08          "VIEW FROM THE PARK"           1               0    0
## 217  S17E09                   "LAKE VIEW"           0               0    0
## 218  S17E10            "OLD COUNTRY MILL"           0               0    0
## 219  S17E11                "MORNING WALK"           0               0    0
## 220  S17E12           "NATURE'S SPLENDOR"           0               0    0
## 221  S17E13             "MOUNTAIN BEAUTY"           0               0    0
## 222  S18E01          "HALF-OVAL VIGNETTE"           0               0    0
## 223  S18E02           "ABSOLUTELY AUTUMN"           0               0    0
## 224  S18E03          "MOUNTAIN SECLUSION"           0               0    0
## 225  S18E04                "CRIMSON OVAL"           0               0    0
## 226  S18E05           "AUTUMN EXHIBITION"           0               0    0
## 227  S18E06              "MAJESTIC PEAKS"           0               0    0
## 228  S18E07         "GOLDEN MORNING MIST"           0               0    0
## 229  S18E08                 "WINTER LACE"           0               0    0
## 230  S18E09            "SEASCAPE FANTASY"           0               0    0
## 231  S18E10          "DOUBLE OVAL STREAM"           0               0    0
## 232  S18E11            "ENCHANTED FOREST"           0               0    0
## 233  S18E12          "SOUTHWEST SERENITY"           0               0    0
## 234  S18E13             "RIPPLING WATERS"           0               0    0
## 235  S19E01              "SNOWFALL MAGIC"           0               0    0
## 236  S19E02         "QUIET MOUNTAIN LAKE"           0               0    0
## 237  S19E03    "FINAL EMBERS OF SUNLIGHT"           0               0    0
## 238  S19E04                  "SNOWY MORN"           0               0    0
## 239  S19E05              "CAMPER'S HAVEN"           0               0    0
## 240  S19E06      "WATERFALL IN THE WOODS"           0               0    0
## 241  S19E07         "COVERED BRIDGE OVAL"           0               0    0
## 242  S19E08            "SCENIC SECLUSION"           0               0    0
## 243  S19E09                    "EBB TIDE"           0               0    0
## 244  S19E10              "AFTER THE RAIN"           0               0    0
## 245  S19E11           "WINTER'S ELEGANCE"           0               0    0
## 246  S19E12             "EVENING'S PEACE"           0               0    1
## 247  S19E13       "VALLEY OF TRANQUILITY"           0               0    0
## 248  S20E01             "MYSTIC MOUNTAIN"           0               0    0
## 249  S20E02              "NEW DAY'S DAWN"           0               0    1
## 250  S20E03               "PASTEL WINTER"           0               0    0
## 251  S20E04                    "HAZY DAY"           0               0    0
## 252  S20E05             "DIVINE ELEGANCE"           0               0    0
## 253  S20E06                   "CLIFFSIDE"           0               0    0
## 254  S20E07              "AUTUMN FANTASY"           0               0    0
## 255  S20E08            "THE OLD OAK TREE"           0               0    0
## 256  S20E09           "WINTER'S PARADISE"           0               0    0
## 257  S20E10                "DAYS GONE BY"           0               0    0
## 258  S20E11           "CHANGE OF SEASONS"           0               0    0
## 259  S20E12              "HIDDEN DELIGHT"           0               0    0
## 260  S20E13                 "DOUBLE TAKE"           0               0    0
## 261  S21E01                 "VALLEY VIEW"           0               0    0
## 262  S21E02               "TRANQUIL DAWN"           0               0    0
## 263  S21E03               "ROYAL MAJESTY"           0               0    0
## 264  S21E04                    "SERENITY"           0               0    0
## 265  S21E05        "CABIN AT TRAIL'S END"           0               0    0
## 266  S21E06           "MOUNTAIN RHAPSODY"           0               0    0
## 267  S21E07            "WILDERNESS CABIN"           0               0    0
## 268  S21E08                  "BY THE SEA"           0               0    0
## 269  S21E09               "INDIAN SUMMER"           0               0    0
## 270  S21E10                 "BLUE WINTER"           0               0    0
## 271  S21E11                 "DESERT GLOW"           0               0    0
## 272  S21E12               "LONE MOUNTAIN"           0               0    0
## 273  S21E13             "FLORIDA'S GLORY"           0               0    0
## 274  S22E01               "AUTUMN IMAGES"           0               0    0
## 275  S22E02          "HINT OF SPRINGTIME"           0               0    0
## 276  S22E03             "AROUND THE BEND"           0               0    0
## 277  S22E04            "COUNTRYSIDE OVAL"           0               0    0
## 278  S22E05               "RUSSET WINTER"           0               0    1
## 279  S22E06                 "PURPLE HAZE"           0               0    0
## 280  S22E07                  "DIMENSIONS"           0               0    0
## 281  S22E08        "DEEP WILDERNESS HOME"           0               0    0
## 282  S22E09         "HAVEN IN THE VALLEY"           0               0    0
## 283  S22E10            "WINTERTIME BLUES"           0               0    0
## 284  S22E11             "PASTEL SEASCAPE"           0               0    0
## 285  S22E12               "COUNTRY CREEK"           0               0    0
## 286  S22E13               "SILENT FOREST"           0               0    0
## 287  S23E01          "FROSTY WINTER MORN"           0               0    0
## 288  S23E02                 "FOREST EDGE"           0               0    0
## 289  S23E03         "MOUNTAIN RIDGE LAKE"           0               0    0
## 290  S23E04         "REFLECTIONS OF GOLD"           0               0    0
## 291  S23E05                  "QUIET COVE"           0               0    0
## 292  S23E06               "RIVER'S PEACE"           0               0    0
## 293  S23E07             "AT DAWN'S LIGHT"           0               0    0
## 294  S23E08            "VALLEY WATERFALL"           0               0    0
## 295  S23E09            "TOWARD DAY'S END"           0               0    0
## 296  S23E10           "FALLS IN THE GLEN"           0               0    0
## 297  S23E11   "FROZEN BEAUTY IN VIGNETTE"           0               0    0
## 298  S23E12                "CRIMSON TIDE"           0               0    0
## 299  S23E13                "WINTER BLISS"           0               0    0
## 300  S24E01               "GRAY MOUNTAIN"           0               0    0
## 301  S24E02                "WAYSIDE POND"           0               0    0
## 302  S24E03                "TETON WINTER"           0               0    0
## 303  S24E04   "LITTLE HOME IN THE MEADOW"           0               0    0
## 304  S24E05         "A PRETTY AUTUMN DAY"           0               0    0
## 305  S24E06             "MIRRORED IMAGES"           0               0    0
## 306  S24E07                "BACK COUNTRY"           0               0    0
## 307  S24E08          "GRACEFUL WATERFALL"           0               0    0
## 308  S24E09                    "ICY LAKE"           0               0    0
## 309  S24E10        "ROWBOAT ON THE BEACH"           0               0    0
## 310  S24E11          "PORTRAIT OF WINTER"           0               0    0
## 311  S24E12              "THE FOOTBRIDGE"           0               0    0
## 312  S24E13             "SNOWBOUND CABIN"           0               0    0
## 313  S25E01             "HIDE-A-WAY COVE"           0               0    0
## 314  S25E02        "ENCHANTED FALLS OVAL"           0               0    0
## 315  S25E03            "NOT QUITE SPRING"           0               0    0
## 316  S25E04          "SPLASHES OF AUTUMN"           0               0    0
## 317  S25E05      "SUMMER IN THE MOUNTAIN"           0               0    0
## 318  S25E06              "ORIENTAL FALLS"           0               0    0
## 319  S25E07              "AUTUMN PALETTE"           0               0    0
## 320  S25E08               "CYPRESS SWAMP"           0               0    0
## 321  S25E09             "DOWNSTREAM VIEW"           0               0    0
## 322  S25E10       "JUST BEFORE THE STORM"           0               0    0
## 323  S25E11        "FISHERMAN'S PARADISE"           0               0    0
## 324  S25E12                 "DESERT HUES"           0               0    0
## 325  S25E13           "THE PROPERTY LINE"           0               0    0
## 326  S26E01 "IN THE STILLNESS OF MORNING"           0               0    0
## 327  S26E02      "DELIGHTFUL MEADOW HOME"           0               0    0
## 328  S26E03                  "FIRST SNOW"           0               0    0
## 329  S26E04          "LAKE IN THE VALLEY"           0               0    0
## 330  S26E05             "TRACE OF SPRING"           0               0    0
## 331  S26E06           "ARCTIC WINTER DAY"           0               0    0
## 332  S26E07                  "SNOW BIRCH"           0               0    0
## 333  S26E08                "EARLY AUTUMN"           0               0    0
## 334  S26E09      "TRANQUIL WOODED STREAM"           0               0    0
## 335  S26E10       "PURPLE MOUNTAIN RANGE"           0               0    0
## 336  S26E11            "STORM'S A COMIN'"           0               0    0
## 337  S26E12                "SUNSET AGLOW"           0               0    0
## 338  S26E13        "EVENING AT THE FALLS"           0               0    0
## 339  S27E01             "TWILIGHT BEAUTY"           0               0    0
## 340  S27E02              "ANGLER'S HAVEN"           0               0    0
## 341  S27E03         "RUSTIC WINTER WOODS"           0               0    0
## 342  S27E04            "WILDERNESS FALLS"           0               0    0
## 343  S27E05          "WINTER AT THE FARM"           0               0    0
## 344  S27E06             "DAISIES AT DAWN"           0               0    0
## 345  S27E07            "SPECTACULAR VIEW"           0               0    0
## 346  S27E08                    "DAYBREAK"           0               0    0
## 347  S27E09             "ISLAND PARADISE"           0               0    0
## 348  S27E10     "SUNLIGHT IN THE SHADOWS"           0               0    0
## 349  S27E11   "SPLENDOR OF A SNOWY WHITE"           0               0    0
## 350  S27E12                "FOREST RIVER"           0               0    0
## 351  S27E13      "GOLDEN GLOW OF MORNING"           0               0    0
## 352  S28E01           "FISHERMAN'S TRAIL"           0               0    0
## 353  S28E02            "TO A WARM WINTER"           0               0    1
## 354  S28E03          "UNDER PASTEL SKIES"           0               0    0
## 355  S28E04     "GOLDEN RAYS OF SUNLIGHT"           0               0    0
## 356  S28E05               "MAGIC OF FALL"           0               0    0
## 357  S28E06                "GLACIER LAKE"           0               0    0
## 358  S28E07      "THE OLD WEATHERED BARN"           0               0    1
## 359  S28E08           "DEEP FOREST FALLS"           0               0    0
## 360  S28E09              "WINTER'S GRACE"           0               0    0
## 361  S28E10          "SPLENDOR OF AUTUMN"           0               0    0
## 362  S28E11               "TRANQUIL SEAS"           0               0    0
## 363  S28E12           "MOUNTAIN SERENITY"           0               0    0
## 364  S28E13       "HOME BEFORE NIGHTFALL"           0               0    0
## 365  S29E01    "ISLAND IN THE WILDERNESS"           0               0    0
## 366  S29E02                 "AUTUMN OVAL"           0               0    0
## 367  S29E03        "SEASONAL PROGRESSION"           0               0    0
## 368  S29E04         "LIGHT AT THE SUMMIT"           0               0    0
## 369  S29E05            "COUNTRYSIDE BARN"           0               0    1
## 370  S29E06         "MOUNTAIN LAKE FALLS"           0               0    0
## 371  S29E07               "CYPRESS CREEK"           0               0    0
## 372  S29E08             "TRAPPER'S CABIN"           0               0    0
## 373  S29E09        "STORM ON THE HORIZON"           0               0    0
## 374  S29E10               "POT 'O POSIES"           0               0    0
## 375  S29E11        "PERFECT WINTER'S DAY"           0               0    0
## 376  S29E12              "AURORA'S DANCE"           0               1    0
## 377  S29E13       "THE WOODMAN'S RETREAT"           0               0    0
## 378  S30E01              "BABBLING BROOK"           0               0    0
## 379  S30E02              "WOODGRAIN VIEW"           0               0    0
## 380  S30E03              "WINTER'S PEACE"           0               0    0
## 381  S30E04            "WILDERNESS TRAIL"           0               0    0
## 382  S30E05               "COPPER WINTER"           0               0    0
## 383  S30E06             "MISTY FOOTHILLS"           0               0    0
## 384  S30E07          "THROUGH THE WINDOW"           0               0    0
## 385  S30E08          "HOME IN THE VALLEY"           0               0    0
## 386  S30E09          "MOUNTAINS OF GRACE"           0               0    0
## 387  S30E10             "SEASIDE HARMONY"           0               0    0
## 388  S30E11             "COLD SPRING DAY"           0               0    0
## 389  S30E12              "EVENING'S GLOW"           0               0    0
## 390  S30E13            "BLUE RIDGE FALLS"           0               0    0
## 391  S31E01         "REFLECTIONS OF CALM"           0               0    0
## 392  S31E02         "BEFORE THE SNOWFALL"           0               0    0
## 393  S31E03              "WINDING STREAM"           0               0    0
## 394  S31E04            "TRANQUILITY COVE"           0               0    0
## 395  S31E05         "CABIN IN THE HOLLOW"           0               0    0
## 396  S31E06       "VIEW FROM CLEAR CREEK"           0               0    0
## 397  S31E07            "BRIDGE TO AUTUMN"           0               0    0
## 398  S31E08                 "TRAIL'S END"           0               0    0
## 399  S31E09            "EVERGREEN VALLEY"           0               0    0
## 400  S31E10                 "BALMY BEACH"           0               0    0
## 401  S31E11           "LAKE AT THE RIDGE"           0               0    0
## 402  S31E12      "IN THE MIDST OF WINTER"           0               0    1
## 403  S31E13              "WILDERNESS DAY"           0               0    0
##     BEACH BOAT BRIDGE BUILDING BUSHES CABIN CACTUS CIRCLE_FRAME CIRRUS CLIFF
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##     CLOUDS CONIFER CUMULUS DECIDUOUS DIANE_ANDRE DOCK DOUBLE_OVAL_FRAME FARM
## 1        0       0       0         1           0    0                 0    0
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## 382      0       1       0         1           0    0                 0    0
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## 385      1       1       1         0           0    0                 0    0
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##     FENCE FIRE FLORIDA_FRAME FLOWERS FOG FRAMED GRASS GUEST HALF_CIRCLE_FRAME
## 1       0    0             0       0   0      0     1     0                 0
## 2       0    0             0       0   0      0     0     0                 0
## 3       1    0             0       0   0      0     0     0                 0
## 4       0    0             0       0   0      0     0     0                 0
## 5       0    0             0       0   0      0     0     0                 0
## 6       0    0             0       0   0      0     0     0                 0
## 7       0    0             0       0   0      0     0     0                 0
## 8       0    0             0       0   0      0     0     0                 0
## 9       1    0             0       0   0      0     0     0                 0
## 10      0    0             0       0   0      0     0     0                 0
## 11      0    0             0       0   0      0     0     0                 0
## 12      0    0             0       0   0      0     0     0                 0
## 13      0    0             0       0   0      0     1     0                 0
## 14      0    0             0       0   0      0     1     0                 0
## 15      0    0             0       0   0      0     0     0                 0
## 16      0    0             0       0   0      0     0     0                 0
## 17      0    0             0       0   0      0     0     0                 0
## 18      0    0             0       0   0      0     1     0                 0
## 19      0    0             0       0   0      0     1     0                 0
## 20      0    0             0       0   0      0     1     0                 0
## 21      0    0             0       0   0      0     0     0                 0
## 22      0    0             0       0   0      0     0     0                 0
## 23      0    0             0       0   0      0     1     0                 0
## 24      0    0             0       0   0      0     1     0                 0
## 25      0    0             0       0   0      0     1     0                 0
## 26      0    0             0       0   0      0     0     0                 0
## 27      0    0             0       0   0      0     0     0                 0
## 28      0    0             0       0   0      0     0     0                 0
## 29      0    0             0       0   0      0     1     0                 0
## 30      0    0             0       0   0      0     0     0                 0
## 31      0    0             0       0   0      0     0     0                 0
## 32      0    0             0       0   0      0     0     0                 0
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## 36      0    1             0       0   0      0     0     0                 0
## 37      1    0             0       0   0      0     0     0                 0
## 38      0    0             0       0   0      0     0     0                 0
## 39      0    0             0       0   0      0     0     1                 0
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## 41      0    0             0       0   0      0     1     0                 0
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##     HALF_OVAL_FRAME HILLS LAKE LAKES LIGHTHOUSE MILL MOON MOUNTAIN MOUNTAINS
## 1                 0     0    0     0          0    0    0        0         0
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##     NIGHT OCEAN OVAL_FRAME PALM_TREES PATH PERSON PORTRAIT RECTANGLE_3D_FRAME
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##     SPLIT_FRAME STEVE_ROSS STRUCTURE SUN TOMB_FRAME TREE TREES TRIPLE_FRAME
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  1. To perform association analysis on this dataset, we need to first remove all non-binary columns from the dataset, and then convert the dataset into a matrix of transactions.
#Removing the columns that are not needed
bob <- bob[,-(1:2)]
bob
##     APPLE_FRAME AURORA_BOREALIS BARN BEACH BOAT BRIDGE BUILDING BUSHES CABIN
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##     PATH PERSON PORTRAIT RECTANGLE_3D_FRAME RECTANGULAR_FRAME RIVER ROCKS
## 1      0      0        0                  0                 0     1     0
## 2      0      0        0                  0                 0     0     0
## 3      0      0        0                  0                 0     0     0
## 4      0      0        0                  0                 0     0     0
## 5      0      0        0                  0                 0     1     1
## 6      0      0        0                  0                 0     0     0
## 7      0      0        0                  0                 0     0     0
## 8      0      0        0                  0                 0     0     0
## 9      0      0        0                  0                 0     0     0
## 10     0      0        0                  0                 0     0     0
## 11     0      0        0                  0                 0     0     0
## 12     0      0        0                  0                 0     0     0
## 13     0      0        0                  0                 0     0     0
## 14     0      0        0                  0                 0     0     0
## 15     0      0        0                  0                 0     0     0
## 16     0      0        0                  0                 0     0     0
## 17     0      0        0                  0                 0     0     0
## 18     0      0        0                  0                 0     0     0
## 19     0      0        0                  0                 0     1     0
## 20     0      0        0                  0                 0     0     0
## 21     0      0        0                  0                 0     0     0
## 22     0      0        0                  0                 0     0     1
## 23     0      0        0                  0                 0     1     0
## 24     0      0        0                  0                 0     1     1
## 25     0      0        0                  0                 0     0     0
## 26     0      0        0                  0                 0     0     0
## 27     0      0        0                  0                 0     0     0
## 28     0      0        0                  0                 0     0     0
## 29     0      0        0                  0                 0     1     1
## 30     0      0        0                  0                 0     0     0
## 31     0      0        0                  0                 0     0     0
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## 33     0      0        0                  0                 0     0     0
## 34     0      0        0                  0                 0     0     0
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## 37     0      0        0                  0                 0     0     0
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## 47     0      0        0                  0                 0     0     0
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## 50     0      0        0                  0                 0     0     0
## 51     0      0        0                  0                 0     0     0
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## 53     0      0        0                  0                 0     0     0
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## 65     0      0        0                  0                 0     1     1
## 66     0      0        0                  0                 0     1     0
## 67     0      0        0                  0                 0     0     0
## 68     0      0        0                  0                 0     0     0
## 69     0      0        0                  0                 0     1     1
## 70     0      0        0                  0                 0     1     0
## 71     0      0        0                  0                 0     0     0
## 72     0      0        0                  0                 0     1     0
## 73     0      0        0                  0                 0     0     0
## 74     0      0        0                  0                 0     0     1
## 75     0      0        0                  0                 0     0     0
## 76     0      0        0                  0                 0     1     0
## 77     0      0        0                  0                 0     0     0
## 78     0      0        0                  0                 0     1     0
## 79     0      0        0                  0                 0     0     0
## 80     0      0        0                  0                 0     0     1
## 81     0      0        0                  0                 0     1     0
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## 86     0      0        0                  0                 0     1     0
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## 93     0      0        0                  0                 0     0     0
## 94     0      0        0                  0                 0     0     0
## 95     1      0        0                  0                 0     0     1
## 96     1      0        0                  0                 0     1     1
## 97     0      0        0                  0                 0     1     0
## 98     0      0        0                  0                 0     0     0
## 99     0      0        0                  0                 0     1     0
## 100    0      0        0                  0                 1     0     0
## 101    1      0        0                  0                 0     0     1
## 102    0      0        0                  0                 0     0     0
## 103    0      0        0                  0                 0     0     0
## 104    0      0        0                  0                 0     0     0
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## 106    0      0        0                  0                 0     0     1
## 107    0      0        0                  0                 0     0     0
## 108    1      0        0                  0                 0     0     0
## 109    0      0        0                  0                 0     1     0
## 110    0      0        0                  0                 0     0     1
## 111    0      0        0                  0                 0     1     1
## 112    1      0        0                  0                 0     0     0
## 113    0      0        0                  0                 0     1     0
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## 115    0      0        0                  0                 0     1     0
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## 140    0      0        0                  0                 0     0     1
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## 142    1      0        0                  0                 0     0     0
## 143    0      0        0                  0                 0     1     1
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## 147    1      0        0                  0                 0     1     0
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## 150    0      0        0                  0                 0     1     0
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## 155    0      0        0                  0                 0     1     0
## 156    0      0        0                  0                 0     1     0
## 157    0      0        0                  0                 0     0     0
## 158    0      0        0                  0                 0     0     0
## 159    0      0        0                  0                 0     1     0
## 160    0      0        0                  0                 0     1     1
## 161    0      0        0                  0                 0     1     1
## 162    0      0        0                  0                 0     1     0
## 163    1      0        0                  0                 0     1     0
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## 168    0      0        0                  0                 0     0     1
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## 170    1      0        0                  0                 0     0     0
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## 202    0      0        0                  0                 0     1     1
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## 205    0      0        0                  0                 0     0     0
## 206    0      0        0                  0                 0     1     1
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## 243    0      0        0                  0                 0     0     1
## 244    1      0        0                  0                 0     0     0
## 245    0      0        0                  0                 0     0     1
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##     WINTER WOOD_FRAMED
## 1        0           0
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#Package for Association
library(arules)
## Loading required package: Matrix
## 
## Attaching package: 'arules'
## The following objects are masked from 'package:base':
## 
##     abbreviate, write
#Transforming into a Matrix of Transaction
bobM <- as(as.matrix(bob), "transactions")
  1. Perform association analysis to determine rules with a support of at least 30% and confidence of at least 90%. Bob Ross included trees in a large number of his drawings. Display all of the rules that you find in your output, and using these rules, describe some of the types of landscapes in which Bob Ross tended to draw tree(s).
bob_rules <- apriori(bobM, parameter = list(sup = 0.3, conf = 0.9, target = "rules"))
## Apriori
## 
## Parameter specification:
##  confidence minval smax arem  aval originalSupport maxtime support minlen
##         0.9    0.1    1 none FALSE            TRUE       5     0.3      1
##  maxlen target  ext
##      10  rules TRUE
## 
## Algorithmic control:
##  filter tree heap memopt load sort verbose
##     0.1 TRUE TRUE  FALSE TRUE    2    TRUE
## 
## Absolute minimum support count: 120 
## 
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[66 item(s), 403 transaction(s)] done [0.00s].
## sorting and recoding items ... [9 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 4 done [0.00s].
## writing ... [31 rule(s)] done [0.00s].
## creating S4 object  ... done [0.00s].
inspect(bob_rules)
##      lhs                           rhs     support   confidence coverage 
## [1]  {RIVER}                    => {TREES} 0.3002481 0.9603175  0.3126551
## [2]  {RIVER}                    => {TREE}  0.3126551 1.0000000  0.3126551
## [3]  {GRASS}                    => {TREE}  0.3374690 0.9577465  0.3523573
## [4]  {LAKE}                     => {TREES} 0.3325062 0.9370629  0.3548387
## [5]  {LAKE}                     => {TREE}  0.3523573 0.9930070  0.3548387
## [6]  {MOUNTAIN}                 => {TREES} 0.3672457 0.9250000  0.3970223
## [7]  {MOUNTAIN}                 => {TREE}  0.3870968 0.9750000  0.3970223
## [8]  {DECIDUOUS}                => {TREES} 0.5136476 0.9118943  0.5632754
## [9]  {DECIDUOUS}                => {TREE}  0.5632754 1.0000000  0.5632754
## [10] {CONIFER}                  => {TREES} 0.5161290 0.9811321  0.5260546
## [11] {CONIFER}                  => {TREE}  0.5260546 1.0000000  0.5260546
## [12] {TREES}                    => {TREE}  0.8362283 1.0000000  0.8362283
## [13] {TREE}                     => {TREES} 0.8362283 0.9335180  0.8957816
## [14] {RIVER, TREES}             => {TREE}  0.3002481 1.0000000  0.3002481
## [15] {RIVER, TREE}              => {TREES} 0.3002481 0.9603175  0.3126551
## [16] {GRASS, TREES}             => {TREE}  0.3126551 1.0000000  0.3126551
## [17] {GRASS, TREE}              => {TREES} 0.3126551 0.9264706  0.3374690
## [18] {LAKE, TREES}              => {TREE}  0.3325062 1.0000000  0.3325062
## [19] {LAKE, TREE}               => {TREES} 0.3325062 0.9436620  0.3523573
## [20] {CONIFER, MOUNTAIN}        => {TREES} 0.3126551 0.9767442  0.3200993
## [21] {CONIFER, MOUNTAIN}        => {TREE}  0.3200993 1.0000000  0.3200993
## [22] {MOUNTAIN, TREES}          => {TREE}  0.3672457 1.0000000  0.3672457
## [23] {MOUNTAIN, TREE}           => {TREES} 0.3672457 0.9487179  0.3870968
## [24] {CLOUDS, TREES}            => {TREE}  0.3424318 1.0000000  0.3424318
## [25] {CLOUDS, TREE}             => {TREES} 0.3424318 0.9387755  0.3647643
## [26] {DECIDUOUS, TREES}         => {TREE}  0.5136476 1.0000000  0.5136476
## [27] {DECIDUOUS, TREE}          => {TREES} 0.5136476 0.9118943  0.5632754
## [28] {CONIFER, TREES}           => {TREE}  0.5161290 1.0000000  0.5161290
## [29] {CONIFER, TREE}            => {TREES} 0.5161290 0.9811321  0.5260546
## [30] {CONIFER, MOUNTAIN, TREES} => {TREE}  0.3126551 1.0000000  0.3126551
## [31] {CONIFER, MOUNTAIN, TREE}  => {TREES} 0.3126551 0.9767442  0.3200993
##      lift     count
## [1]  1.148392 121  
## [2]  1.116343 126  
## [3]  1.069174 136  
## [4]  1.120583 134  
## [5]  1.108537 142  
## [6]  1.106157 148  
## [7]  1.088435 156  
## [8]  1.090485 207  
## [9]  1.116343 227  
## [10] 1.173283 208  
## [11] 1.116343 212  
## [12] 1.116343 337  
## [13] 1.116343 337  
## [14] 1.116343 121  
## [15] 1.148392 121  
## [16] 1.116343 126  
## [17] 1.107916 126  
## [18] 1.116343 134  
## [19] 1.128474 134  
## [20] 1.168035 126  
## [21] 1.116343 129  
## [22] 1.116343 148  
## [23] 1.134520 148  
## [24] 1.116343 138  
## [25] 1.122631 138  
## [26] 1.116343 207  
## [27] 1.090485 207  
## [28] 1.116343 208  
## [29] 1.173283 208  
## [30] 1.116343 126  
## [31] 1.168035 126

All the rules have shown tree or trees as a strong factor.
#Part 2: Predicting a Numeric Column of Data
1. Load the nhanes_train csv file into R. This data contains information about the weight, age, height, and pulse of various individuals. Use this data in completing the next question.

library(class)
nhanes_train <- read.csv("/Users/jusimioni/Desktop/MSDA 2021-23/Spring 2023/Big Data/Data/nhanes_train.csv")
nhanes_train
##      Age Weight Height Pulse
## 1     80   97.6  175.8    58
## 2     48  120.7  185.9    56
## 3     20   46.8  163.6    78
## 4     18  100.2  176.9    84
## 5     46  112.2  180.5    90
## 6     63   79.3  182.8    66
## 7     42   89.9  173.7   100
## 8     43   91.2  177.9   100
## 9     46   77.3  184.9    54
## 10    50   78.5  169.2    74
## 11    20   53.0  169.7    80
## 12    22   73.4  170.2    72
## 13    36   74.6  183.2    58
## 14    25  147.2  167.7    86
## 15    80  106.3  181.6    58
## 16    39  102.8  173.3    74
## 17    16   69.4  161.0    88
## 18    31   63.6  174.5    64
## 19    45   55.4  173.0    60
## 20    80   50.1  164.9    84
## 21    41   90.7  170.6    68
## 22    45   63.6  164.4    84
## 23    73   66.5  155.6    62
## 24    25  107.2  169.7    90
## 25    56   80.1  157.7    82
## 26    79   94.5  182.3    68
## 27    80   47.9  156.9    84
## 28    50  110.5  187.5    68
## 29    23   69.7  161.5    66
## 30    46   71.5  171.5    70
## 31    33   82.4  171.3    58
## 32    58   78.2  174.5    64
## 33    20   63.1  175.5    68
## 34    18  122.9  176.4    50
## 35    18   63.9  175.4   110
## 36    49   74.6  177.1    68
## 37    78   62.4  168.6    74
## 38    80   68.7  154.9   100
## 39    22   84.5  166.9    82
## 40    27   97.0  157.4    70
## 41    44   79.5  175.4    54
## 42    70   72.3  182.9    82
## 43    59   80.0  159.6    72
## 44    35   90.2  159.6    86
## 45    47   79.9  164.8    70
## 46    79   59.8  163.2    76
## 47    25   70.6  177.4    78
## 48    79   82.8  164.4    52
## 49    49   78.0  180.9    78
## 50    58   73.0  164.4    60
## 51    59   85.6  157.3    78
## 52    54   67.3  161.7    88
## 53    21   62.9  172.7    80
## 54    50  138.1  167.1   104
## 55    39   52.7  160.8    56
## 56    49   65.0  167.7    72
## 57    53  113.6  176.6    82
## 58    59   64.6  171.2    58
## 59    80   50.2  161.0    66
## 60    62   88.7  176.6    62
## 61    49   82.6  170.3    70
## 62    30   72.7  159.0    60
## 63    55   58.3  179.4   106
## 64    16   47.7  162.7    74
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## 1058  44   81.1  153.8    68
## 1059  31   97.0  174.9    92
## 1060  29   82.7  173.3    62
## 1061  20  101.5  176.1    52
## 1062  16   63.8  171.4    58
## 1063  45   75.7  166.7    62
## 1064  46   71.3  162.6    60
## 1065  80   60.6  171.3    62
## 1066  77   75.2  156.5    60
## 1067  28   56.3  162.8    62
## 1068  20   57.2  156.1    78
## 1069  46   43.7  148.1    88
## 1070  50   77.3  151.2    80
## 1071  50   89.9  155.8    94
## 1072  31   77.6  161.6    76
## 1073  29   72.1  173.2    62
## 1074  52   95.8  181.1    56
## 1075  73  106.8  182.3    66
## 1076  80   61.7  164.0    78
## 1077  25   87.5  186.1    82
## 1078  60  166.5  175.5    66
## 1079  59   80.9  175.2    72
## 1080  48   63.3  168.7    66
## 1081  67   61.0  155.9    74
## 1082  37  125.7  169.8    98
## 1083  55  114.4  170.2    84
## 1084  18   80.6  159.6    82
## 1085  28   79.9  168.9    74
## 1086  29  115.6  175.1    78
## 1087  73   70.2  160.6    76
## 1088  36   74.2  163.5    68
## 1089  30   70.9  171.0    74
## 1090  16   72.3  173.3    76
## 1091  39   58.8  147.8    78
## 1092  59   82.9  165.6    80
## 1093  52   66.0  163.6    70
## 1094  38  110.1  176.1    78
## 1095  39  110.8  179.5    80
## 1096  57   91.2  178.1    58
## 1097  43   55.0  169.2    64
## 1098  55   86.6  179.2    80
## 1099  44   91.0  175.0    84
## 1100  39   65.5  168.2    76
## 1101  29   95.6  170.6    88
## 1102  64   93.5  162.4    62
## 1103  16  100.4  179.5    80
## 1104  68   65.4  158.8    76
## 1105  51   61.5  156.7    72
## 1106  32   82.3  168.5    70
## 1107  19   75.7  158.1    86
## 1108  53  140.1  184.9   100
## 1109  33   97.7  187.5    80
## 1110  28   80.9  177.1    58
## 1111  29   86.6  169.7    70
## 1112  16   76.7  166.4    82
## 1113  61   91.8  180.4    68
## 1114  45   78.1  167.3    64
## 1115  51  110.7  199.2    80
## 1116  71   44.5  148.5    84
## 1117  64   98.0  176.0    66
## 1118  31  129.3  162.6    80
## 1119  32   71.4  175.3    82
## 1120  79   59.8  163.2    76
## 1121  39  110.9  175.3    66
## 1122  40  143.6  184.3    86
## 1123  59  106.7  178.3    82
## 1124  48   79.7  168.2    64
## 1125  36   82.7  161.4    78
## 1126  66   78.8  164.3    74
## 1127  41   71.8  164.0    78
## 1128  38   94.9  170.4    78
## 1129  38   94.9  158.4    84
## 1130  54   73.5  167.0    68
## 1131  62   69.5  161.5    86
## 1132  27   97.0  157.4    70
## 1133  21   74.5  168.6    66
## 1134  33   89.9  163.0    78
## 1135  35   76.3  163.3    80
## 1136  39   68.9  168.0    66
## 1137  50   98.3  166.4    72
## 1138  51   67.3  175.1    76
## 1139  80  111.0  178.6    70
## 1140  46   59.2  168.7    76
## 1141  44  118.0  174.3    88
## 1142  34  103.0  167.2    72
## 1143  49   84.3  170.9    72
## 1144  27   71.5  159.4    68
## 1145  72   90.7  153.0    54
## 1146  23   78.1  170.9    74
## 1147  42   79.6  176.9    48
## 1148  60   78.4  168.8    76
## 1149  26   80.4  158.4    92
## 1150  64   60.1  158.6    60
## 1151  56   74.2  179.3    90
## 1152  58   73.8  168.1    84
## 1153  30   69.4  177.3    96
## 1154  39   55.3  168.7    70
## 1155  31   77.9  154.5    58
## 1156  49   72.4  165.0    60
## 1157  48   72.3  166.6    72
## 1158  22   78.0  177.6    66
## 1159  26   82.6  160.0    78
## 1160  74  111.4  177.4    84
## 1161  55   60.7  162.4    72
## 1162  17   78.9  154.5    82
## 1163  32   69.2  161.4   114
## 1164  18   95.8  179.3    58
## 1165  17   61.5  169.8    54
## 1166  65  128.5  176.2    60
## 1167  71   99.9  183.4    66
## 1168  23   76.1  166.7    70
## 1169  67   88.7  169.8    60
## 1170  22   84.7  161.7    86
## 1171  39   70.7  182.9    68
## 1172  37  223.0  186.8   104
## 1173  64  113.3  187.5    76
## 1174  53   80.7  174.0    68
## 1175  71   67.3  173.0    58
## 1176  31  145.3  167.9   100
## 1177  30   87.4  175.3    86
## 1178  29  168.1  186.5   100
## 1179  74   49.4  161.5    70
## 1180  37   70.7  168.0    82
## 1181  32  107.3  175.9    84
## 1182  22   70.7  176.0    76
## 1183  41   69.4  162.7    80
## 1184  80   75.0  176.4    74
## 1185  80   47.9  156.9    84
## 1186  16   49.2  161.0   102
## 1187  65   72.0  161.8    68
## 1188  20   93.4  166.0    92
## 1189  57  121.4  185.1    72
## 1190  25  129.9  172.8    68
## 1191  43   82.2  164.7    90
## 1192  63   86.4  178.2    70
## 1193  41  100.2  181.4    72
## 1194  56   91.8  180.7    54
## 1195  35  141.4  176.7    82
## 1196  70  111.6  175.8    74
## 1197  50   65.1  169.2    80
## 1198  47   95.3  168.8    80
## 1199  31   77.4  180.7    62
## 1200  80   71.5  175.4    54
## 1201  23   78.8  174.7    66
## 1202  80   77.3  153.7    50
## 1203  62   85.8  182.5    66
## 1204  29   73.8  165.7    86
## 1205  28   75.6  174.3    70
## 1206  20   54.7  157.6    84
## 1207  43   79.7  179.5    54
## 1208  69   62.8  163.4    82
## 1209  37   51.8  164.0    82
## 1210  21   66.1  166.7    84
## 1211  36  114.3  178.3   106
## 1212  30   97.5  178.8    88
## 1213  52  101.0  156.5    64
## 1214  48   98.7  171.7    88
## 1215  47   87.6  174.7    64
## 1216  77   85.8  166.0    66
## 1217  21   82.8  174.1    54
## 1218  52   72.1  184.3    70
## 1219  48   64.6  174.8    62
## 1220  31  138.2  184.1    80
## 1221  28   88.8  174.0    88
## 1222  53   95.2  167.1    64
## 1223  24   92.1  189.5    62
## 1224  17   67.0  156.5    78
## 1225  51   55.9  168.2    70
## 1226  55   71.7  166.1    72
## 1227  25   63.7  162.5    70
## 1228  59   89.7  171.5    72
## 1229  56   47.0  160.6   102
## 1230  48   65.9  168.5    74
## 1231  67   87.8  170.5    64
## 1232  62   99.0  166.1   118
## 1233  45   67.6  163.2    64
## 1234  29   52.0  159.9    50
## 1235  49  107.8  162.2    80
## 1236  52   68.5  163.7    64
## 1237  20   65.9  164.0    66
## 1238  33  132.7  166.5    66
## 1239  36   91.6  189.3    80
## 1240  41   86.6  165.8    74
## 1241  41   88.7  178.2    60
## 1242  80   42.5  146.5    66
## 1243  51   61.5  156.7    72
## 1244  18   75.2  183.0    92
## 1245  54  104.4  178.1    80
## 1246  46  102.5  161.9    72
## 1247  19   71.6  169.1    68
## 1248  48  107.3  171.1    70
## 1249  69   62.8  163.4    82
## 1250  58   80.1  170.1    76
## 1251  24   50.7  168.8    68
## 1252  23   61.1  179.7    76
## 1253  26   80.2  160.1    90
## 1254  56   63.8  159.4    72
## 1255  63   85.0  169.6    70
## 1256  29   56.2  149.2    62
## 1257  48  120.7  185.9    56
## 1258  71  110.7  180.0    72
## 1259  75  107.0  173.1    84
## 1260  63   74.0  167.9    72
## 1261  80   68.5  149.3    58
## 1262  65   91.9  182.4    62
## 1263  24   78.2  178.7    76
## 1264  59   86.1  183.7    72
## 1265  39   72.2  159.5    76
## 1266  42   62.8  169.5    62
## 1267  31   72.4  164.1    70
## 1268  80   59.6  160.3    64
## 1269  80   77.9  168.2    84
## 1270  32   80.4  176.9    78
## 1271  80   80.8  164.9    62
## 1272  45   86.4  171.2    52
## 1273  46   93.8  171.3    86
## 1274  26   75.8  162.3   116
## 1275  27   81.8  180.3    78
## 1276  30  107.3  163.5    64
## 1277  74   99.9  158.1    78
## 1278  26   99.3  178.6    70
## 1279  46  101.0  185.6    58
## 1280  54   62.5  149.9    60
## 1281  65   85.3  182.4    68
## 1282  61   67.0  157.2    66
## 1283  73   70.9  163.9    48
## 1284  80   65.8  158.5    78
## 1285  36   67.5  158.7    90
## 1286  43   99.5  183.0    78
## 1287  53   66.6  178.4    54
## 1288  49   86.7  168.4    86
## 1289  22   67.3  156.8    84
## 1290  28   65.5  171.1    76
## 1291  17   62.0  169.5    90
## 1292  45   66.9  154.1    74
## 1293  22   74.1  169.4    80
## 1294  26   68.3  175.1    58
## 1295  24   83.1  157.9    78
## 1296  46   49.7  148.2    60
## 1297  49  102.6  176.8    98
## 1298  54   93.8  156.3    92
## 1299  43   84.8  165.4    82
## 1300  37  107.4  185.7    58
## 1301  56   97.0  177.1    74
## 1302  50   99.4  173.2    84
## 1303  50   86.6  169.9    68
## 1304  70   46.2  148.6    62
## 1305  51   78.7  167.5    54
## 1306  57   75.8  164.7    60
## 1307  55   71.7  166.1    72
## 1308  36  104.6  163.4    80
## 1309  52   77.6  176.4    56
## 1310  54   58.5  159.8    76
## 1311  41  110.4  165.8    74
## 1312  20   51.0  157.9    78
## 1313  51  109.4  184.4    60
## 1314  41   79.1  165.5    62
## 1315  72   48.9  148.7    72
## 1316  27   90.7  177.4    78
## 1317  27  108.1  181.8    88
## 1318  33   74.8  158.4    82
## 1319  54   77.8  164.9    66
## 1320  55   82.1  164.5    86
## 1321  53  106.2  176.6    84
## 1322  38   91.1  169.1    86
## 1323  33   64.4  164.3    90
## 1324  40   75.6  161.5    60
## 1325  23   70.1  180.1    82
## 1326  68   79.0  153.6    72
## 1327  53   95.2  167.1    64
## 1328  79   51.3  156.6    56
## 1329  64   68.6  161.2    58
## 1330  50  104.9  183.9    58
## 1331  53  140.1  184.9   100
## 1332  22  111.6  182.1    86
## 1333  58   73.8  176.2    50
## 1334  52   70.7  165.9    64
## 1335  36   56.8  155.4    68
## 1336  49   81.3  183.4    58
## 1337  46  108.9  178.4    80
## 1338  70   90.5  165.4    80
## 1339  66   88.7  178.9    80
## 1340  45  107.7  186.9    80
## 1341  54   68.8  169.3    72
## 1342  70   57.5  159.5    54
## 1343  79   58.2  151.4    60
## 1344  54  117.3  171.9    58
## 1345  57   86.1  192.8    82
## 1346  22   99.7  153.2    90
## 1347  65   83.0  154.8    78
## 1348  40   71.1  165.8    68
## 1349  37  106.0  168.3    96
## 1350  35   60.5  156.8    84
## 1351  35   73.3  190.5    60
## 1352  24   61.5  153.3    84
## 1353  80   77.4  178.0    74
## 1354  56   79.4  182.9    62
## 1355  35   94.0  180.1    64
## 1356  50   69.3  163.5    58
## 1357  60  124.0  199.4    48
## 1358  44   77.6  173.2    68
## 1359  45   65.0  150.5    68
## 1360  32   97.3  183.8    78
## 1361  72   83.4  181.7    50
## 1362  52   44.9  153.1    60
## 1363  80   65.6  162.8    82
## 1364  61  119.7  168.8    66
## 1365  65   72.0  161.8    68
## 1366  17  103.8  181.5    64
## 1367  80   94.2  179.3    60
## 1368  28   77.4  171.4    92
## 1369  44   94.4  175.3    86
## 1370  22   99.9  176.8    80
## 1371  33   97.6  165.0    70
## 1372  62   69.3  182.9    64
## 1373  44   52.6  162.2    80
## 1374  63   79.3  182.8    66
## 1375  59   85.4  188.2    56
## 1376  28   98.5  182.0    64
## 1377  45   59.2  155.5    82
## 1378  58   73.8  168.1    84
## 1379  38   64.9  180.1    92
## 1380  56  112.0  163.7    64
## 1381  46   86.3  172.2    54
## 1382  31   52.3  154.5    68
## 1383  49   65.0  167.7    72
## 1384  76   83.1  159.0    80
## 1385  61   65.3  173.3    64
## 1386  52   64.5  160.9    68
## 1387  69   73.0  162.8    58
## 1388  43   68.8  164.2    86
## 1389  21   72.7  170.7    74
## 1390  52   66.0  163.6    70
## 1391  26  105.7  180.0    70
## 1392  59   54.3  145.1    84
## 1393  37  100.1  166.3    68
## 1394  29   83.3  182.2    76
## 1395  54  120.4  190.8    88
## 1396  32   63.4  155.0    68
## 1397  53   75.4  173.2    72
## 1398  24  107.6  174.5    76
## 1399  58   83.3  186.1    70
## 1400  57   61.5  160.7    92
## 1401  80   77.0  159.1    62
## 1402  29   93.9  153.7    74
## 1403  64   61.1  155.3    76
## 1404  20   79.9  163.9    70
## 1405  80  104.6  175.7    68
## 1406  29   71.0  169.6    84
## 1407  73   66.8  157.3    54
## 1408  32  135.1  189.0    72
## 1409  18   97.4  164.5    80
## 1410  64   79.4  175.7    78
## 1411  40  143.6  184.3    86
## 1412  50   92.1  179.5    68
## 1413  64   82.6  173.2    64
## 1414  43  110.2  179.8    56
## 1415  46   67.9  186.8    74
## 1416  35  125.9  187.0    74
## 1417  44   61.8  144.4    66
## 1418  34   80.6  181.9    86
## 1419  73   69.6  156.7    68
## 1420  49   59.3  166.2    68
## 1421  30   55.0  159.6    94
## 1422  74  111.3  177.6   100
## 1423  45  100.2  173.3    80
## 1424  68   64.0  159.6    86
## 1425  18  125.6  152.0    92
## 1426  53   93.7  179.2    62
## 1427  50   84.1  177.8    74
## 1428  55   73.2  173.1    90
## 1429  64   82.1  167.3    98
## 1430  56   82.1  160.8    98
## 1431  80   77.2  152.7    76
## 1432  33  188.9  165.9   102
## 1433  76   50.1  157.2    64
## 1434  60   96.5  187.8    74
## 1435  63  105.7  160.4    78
## 1436  30   75.0  174.2    76
## 1437  47   63.0  164.6    76
## 1438  48   74.6  171.3    76
## 1439  70   97.6  157.8    58
## 1440  80   75.1  155.7    74
## 1441  60   89.2  179.8    66
## 1442  41   55.6  155.6    82
## 1443  38   91.7  163.2    74
## 1444  39  103.7  180.3    76
## 1445  56   97.0  177.1    74
## 1446  20   69.1  171.2    58
## 1447  21   52.6  162.9    80
## 1448  65   69.4  169.8    58
## 1449  80   80.9  151.3    62
## 1450  80   85.2  162.1    62
## 1451  62  109.1  158.3    62
## 1452  62   85.5  176.8    66
## 1453  57   82.4  154.3    64
## 1454  28   48.3  159.8    74
## 1455  58  123.2  179.1    76
## 1456  25   90.8  184.1    76
## 1457  21   72.1  169.8    62
## 1458  30   75.0  174.2    76
## 1459  66   70.8  169.4    78
## 1460  49   92.9  175.8    74
## 1461  16   84.3  159.0    68
## 1462  46  101.0  185.6    58
## 1463  64   83.9  177.5    74
## 1464  19   66.7  167.5    74
## 1465  70  106.6  161.1    68
## 1466  22   63.8  162.0    62
## 1467  19   57.6  177.6    78
## 1468  45   87.2  160.8    72
## 1469  16   61.4  168.7    80
## 1470  39   75.0  154.7    90
## 1471  16   57.6  166.2    96
## 1472  32   76.5  155.4    88
## 1473  52  101.0  156.5    64
## 1474  49   77.8  161.6    80
## 1475  47  103.8  161.0   102
## 1476  44   79.3  165.8    74
## 1477  16   47.7  162.7    74
## 1478  22   80.7  163.1    70
## 1479  26   94.1  160.5    94
## 1480  70   79.5  159.4    56
## 1481  57   56.4  170.4    70
## 1482  57   57.6  163.8    72
## 1483  62  172.5  170.9    78
## 1484  57  109.1  180.5    76
## 1485  39   63.4  160.2    78
## 1486  63  114.9  159.1   104
## 1487  30   81.3  176.5    82
## 1488  52   45.6  160.0    48
## 1489  47   89.2  178.5    76
## 1490  36   46.6  160.5    76
## 1491  20   53.6  168.3    64
## 1492  78   88.0  161.6    70
## 1493  43  105.1  177.2    72
## 1494  31   85.4  167.6    72
## 1495  46   68.4  160.6    68
## 1496  38   51.5  156.0    82
## 1497  25   98.8  186.2    54
## 1498  53   77.5  153.4    84
## 1499  37  137.6  180.2    74
## 1500  22   64.3  186.2    60
## 1501  75   70.1  171.1    76
## 1502  54   79.8  170.8    76
## 1503  67  104.7  187.0    58
## 1504  50   84.5  165.1    68
## 1505  50   60.3  168.9    72
## 1506  80   72.4  158.8    74
## 1507  58   78.1  167.4    56
## 1508  61  101.3  176.1    86
## 1509  51   94.5  166.3    56
## 1510  35   65.3  170.8    84
## 1511  62   82.3  171.4    90
## 1512  26   54.6  168.5    78
## 1513  42   88.5  168.9    50
## 1514  36   87.8  180.7   108
## 1515  64   61.7  159.6    80
## 1516  43   63.3  163.6    88
## 1517  79   90.8  154.4    78
## 1518  56  106.3  185.5    62
## 1519  45   99.1  169.6    78
## 1520  70   90.6  164.3    56
## 1521  49   80.8  153.0    78
## 1522  25   70.6  177.4    78
## 1523  69   77.1  163.6    52
## 1524  26  145.5  180.1    90
## 1525  37  123.9  184.3    56
## 1526  80   81.0  173.0    64
## 1527  63   80.7  160.6    52
## 1528  55   74.6  176.7    68
## 1529  27   70.4  171.5    78
## 1530  47   63.9  162.3    62
## 1531  40  104.0  177.6    96
## 1532  31   97.2  171.5    82
## 1533  48   65.9  168.5    74
## 1534  48   78.5  161.7    94
## 1535  37   86.9  164.4    68
## 1536  43   87.4  185.9    74
## 1537  44   64.2  157.6    66
## 1538  61   56.9  154.4    50
## 1539  51   84.2  176.8    78
## 1540  22   99.7  153.2    90
## 1541  76   78.3  163.3    70
## 1542  29   95.4  173.1    82
## 1543  53  140.1  184.9   100
## 1544  19   59.6  181.3    84
## 1545  41   58.2  160.8    84
## 1546  45  104.8  174.8    56
## 1547  39   71.3  161.4    76
## 1548  50   59.8  157.5    58
## 1549  72   98.2  168.6    56
## 1550  37   93.5  176.7    90
## 1551  50   91.4  163.6    78
## 1552  39   73.4  175.7    70
## 1553  17   63.7  170.4    72
## 1554  42   80.6  170.5    56
## 1555  32  117.3  180.6    86
## 1556  80   62.3  158.4    70
## 1557  66   56.1  162.0    58
## 1558  22   69.4  172.0    88
## 1559  34   73.4  181.4    78
## 1560  74   63.4  164.5    64
## 1561  68  115.6  167.6    62
## 1562  50   70.5  172.9    50
## 1563  59   57.2  157.1    66
## 1564  55   71.7  166.1    72
## 1565  42   61.5  166.1    72
## 1566  21   56.6  174.5    78
## 1567  69   81.1  177.4    76
## 1568  54   64.8  160.9    64
## 1569  46   75.4  172.7    66
## 1570  41  105.1  182.5    70
## 1571  40   84.3  171.2    58
## 1572  27   69.2  159.8    86
## 1573  60  103.4  170.7    74
## 1574  36  109.4  179.1    70
## 1575  28   68.1  169.1    64
## 1576  29   78.8  168.6    54
## 1577  71   88.8  161.2    76
## 1578  45   90.8  178.2    54
## 1579  39   91.7  187.3    50
## 1580  36  104.9  186.8    96
## 1581  80   42.5  146.5    66
## 1582  36   62.5  173.4    92
## 1583  53  119.2  169.5    82
## 1584  44   86.5  165.9    80
## 1585  55   82.7  175.1    96
## 1586  24   71.7  171.7    56
## 1587  17  104.2  166.3    74
## 1588  65   75.5  165.8    80
## 1589  19   74.5  177.4    62
## 1590  46   73.7  170.5    74
## 1591  70  103.5  155.1    70
## 1592  66   77.5  157.8    62
## 1593  24  100.6  159.7    60
## 1594  37   70.7  177.7    64
## 1595  43   74.1  170.1    68
## 1596  30   77.8  158.6    82
## 1597  51   68.0  174.7    76
## 1598  29   68.5  168.9    60
## 1599  26  132.6  180.2    72
## 1600  38   76.2  177.2    70
## 1601  80   76.1  158.5    64
## 1602  40   77.9  175.1    60
## 1603  56   67.9  145.4    60
## 1604  70   86.9  150.2    70
## 1605  51   78.1  172.8    62
## 1606  45   86.1  171.8    74
## 1607  49   65.0  167.7    72
## 1608  76   98.8  157.3    72
## 1609  80   71.5  166.6    70
## 1610  50   96.7  173.8    50
## 1611  31   86.5  182.1    56
## 1612  49   87.9  165.8    76
## 1613  59  129.7  181.9    52
## 1614  53  106.2  176.6    84
## 1615  52   93.2  168.3    60
## 1616  70   83.7  177.6    62
## 1617  67  120.7  175.9    70
## 1618  65  100.0  175.2    70
## 1619  60   81.3  163.9    48
## 1620  55   88.1  182.1    92
## 1621  36   70.6  156.9    62
## 1622  22   95.8  180.5    96
## 1623  43   76.6  166.2    76
## 1624  62   71.7  164.0    58
## 1625  44   86.9  164.9    80
## 1626  47   83.8  158.2    88
## 1627  27  115.9  180.3    92
## 1628  63   91.1  171.9    60
## 1629  53   92.8  174.6    76
## 1630  71   88.8  161.2    76
## 1631  54   98.5  170.7    72
## 1632  64   77.0  165.3    64
## 1633  38   79.6  178.9    68
## 1634  16   59.0  157.5    58
## 1635  48   58.1  162.9   102
## 1636  30   64.7  182.0    50
## 1637  28   99.0  171.7    90
## 1638  50  104.4  175.4    74
## 1639  48   70.6  152.1    68
## 1640  22   62.7  176.2    70
## 1641  38   91.3  166.6    78
## 1642  27   90.5  149.4    76
## 1643  71   81.0  163.7    76
## 1644  33   63.9  172.0    62
## 1645  25  102.0  167.6    68
## 1646  46   76.2  171.7    68
## 1647  67   84.1  170.0    78
## 1648  61   72.9  163.9    80
## 1649  29   82.7  173.3    62
## 1650  61   65.3  173.3    64
## 1651  33   79.6  179.7    74
## 1652  37   58.3  171.1    64
## 1653  47   94.7  175.3    48
## 1654  68   69.6  172.3    66
## 1655  30  114.3  166.4    78
## 1656  18  108.5  177.2    80
## 1657  24   79.3  178.1    72
## 1658  17   71.1  173.8    92
## 1659  48   72.3  166.6    72
## 1660  38   91.7  193.9    54
## 1661  42   86.4  176.6    52
## 1662  80   90.4  170.0    68
## 1663  56   98.5  180.4    80
## 1664  77   53.1  166.5    76
## 1665  48   93.4  180.8    70
## 1666  80   80.4  173.5    50
## 1667  80   75.9  153.5    58
## 1668  40   77.9  192.9   102
## 1669  26   67.9  162.0    60
## 1670  30   94.3  167.9    72
## 1671  70  105.1  170.6    58
## 1672  22   51.8  165.9    80
## 1673  21   74.5  168.6    66
## 1674  34   68.0  174.8    76
## 1675  39  110.9  175.3    66
## 1676  76   71.2  166.3    62
## 1677  39   80.6  168.4    58
## 1678  22   51.8  165.9    80
## 1679  45  125.5  168.5    70
## 1680  53  106.2  176.6    84
## 1681  41   91.3  172.7    68
## 1682  16   74.3  156.0    78
## 1683  24   83.0  156.8    84
## 1684  30   93.9  158.7    86
## 1685  23   58.3  165.1    56
## 1686  49   86.5  167.6    72
## 1687  54   66.6  168.3    56
## 1688  78   95.5  189.0    64
## 1689  18   44.5  148.5    94
## 1690  31   82.5  177.9    72
## 1691  67  128.3  180.2    70
## 1692  57   76.7  152.2    60
## 1693  80   80.4  173.5    50
## 1694  69   66.9  163.4    58
## 1695  17   71.1  173.8    92
## 1696  70  102.8  179.5    82
## 1697  32  135.1  189.0    72
## 1698  30   65.7  170.8    74
## 1699  60  110.4  180.6    76
## 1700  30  129.4  181.5    56
## 1701  32   86.0  176.2    64
## 1702  38   85.8  173.8    70
## 1703  29  122.8  188.0    56
## 1704  39   59.1  162.5    78
## 1705  57   82.4  154.3    64
## 1706  65   75.7  154.8    78
## 1707  31   83.4  185.0    58
## 1708  57  105.0  176.9    78
## 1709  40   66.3  172.1    76
## 1710  45   52.1  160.8    64
## 1711  48   60.6  148.2    82
## 1712  24  107.9  177.9    68
## 1713  65  128.5  176.2    60
## 1714  80   58.0  154.3    80
## 1715  72   70.4  162.3    84
## 1716  69   94.6  172.0    82
## 1717  43  102.1  181.1    88
## 1718  71   64.1  164.9    84
## 1719  28  134.1  165.7    96
## 1720  39   79.4  178.4    68
## 1721  39   78.2  164.6    76
## 1722  77   98.5  168.6    82
## 1723  66  128.8  170.3    60
## 1724  57   60.3  158.7    68
## 1725  60  111.9  165.2    62
## 1726  44   62.7  161.2    70
## 1727  49   83.7  171.9    70
## 1728  33   89.9  163.0    78
## 1729  17   56.6  171.5    60
## 1730  30   98.8  169.0    68
## 1731  65   86.1  156.7    56
## 1732  19  112.7  174.3    68
## 1733  50   71.9  165.4    72
## 1734  23   72.3  160.0    72
## 1735  80   81.1  152.0    56
## 1736  17   77.7  161.8    74
## 1737  38   96.4  163.6    78
## 1738  21   75.6  174.7    92
## 1739  45  127.3  186.9    54
## 1740  20  106.6  181.5    80
## 1741  48  116.3  171.2    60
## 1742  46  102.1  185.5    64
## 1743  43   57.7  156.5    70
## 1744  40   49.3  164.5   102
## 1745  63   80.9  169.1    74
## 1746  48   74.8  183.2    76
## 1747  54   95.3  173.2    62
## 1748  56   82.1  174.9    76
## 1749  33   73.8  179.5    62
## 1750  44   95.6  163.5    70
## 1751  31   69.1  185.1    54
## 1752  58   76.0  152.9    82
## 1753  41  126.4  168.1    62
## 1754  77   58.9  155.8    54
## 1755  40   70.8  174.4    68
## 1756  36   86.1  171.0    94
## 1757  33   73.8  179.5    62
## 1758  49   97.2  176.7    58
## 1759  43   54.8  156.6    82
## 1760  66   78.4  171.5    60
## 1761  38   66.8  163.9    64
## 1762  64   57.8  161.7    70
## 1763  63   84.2  162.5    74
## 1764  23   63.1  162.1    66
## 1765  43  131.3  188.3    74
## 1766  30   89.6  186.6    86
## 1767  56  128.2  171.0    78
## 1768  41   77.2  173.7    64
## 1769  36   67.9  147.9    64
## 1770  27   76.4  169.0    74
## 1771  56   96.1  190.3    70
## 1772  77   61.5  155.9    50
## 1773  16   63.6  167.6    76
## 1774  16   66.5  168.3    94
## 1775  22   76.1  154.9    70
## 1776  35   75.8  158.2    84
## 1777  75   55.4  177.2    60
## 1778  28  131.1  180.2   108
## 1779  53   76.6  149.4    68
## 1780  41  105.1  182.5    70
## 1781  63   87.0  173.3    68
## 1782  35   78.3  174.8    66
## 1783  21   67.5  159.6    64
## 1784  33   75.2  172.7    68
## 1785  25   86.2  158.7    84
## 1786  75   72.8  159.3    60
## 1787  19   82.0  169.1    72
## 1788  22   65.8  170.1    62
## 1789  38   75.3  175.2    70
## 1790  61   70.3  166.7    62
## 1791  38   89.7  164.8    60
## 1792  54   74.4  167.6    70
## 1793  50   90.2  164.8    80
## 1794  34   82.1  177.5    68
## 1795  33  104.7  171.4    56
## 1796  43   63.1  164.4    76
## 1797  71  109.6  150.8    86
## 1798  43   57.5  167.9    80
## 1799  80   58.1  148.3    86
## 1800  36   89.8  183.0    66
## 1801  31   70.9  155.6    66
## 1802  51   55.9  168.2    70
## 1803  73   62.4  149.0    72
## 1804  76   65.9  158.4    70
## 1805  69   82.0  180.5    70
## 1806  27   73.4  173.2    92
## 1807  50   67.2  164.1    62
## 1808  46  108.8  183.7    66
## 1809  64   91.5  170.4    78
## 1810  80   66.5  162.1    90
## 1811  68   65.5  157.9    70
## 1812  53  119.2  169.5    82
## 1813  56   95.4  179.7    72
## 1814  57   52.6  150.2    66
## 1815  44   62.7  161.2    70
## 1816  36  104.0  167.8    80
## 1817  23   87.2  163.8    80
## 1818  22   62.7  176.2    70
## 1819  46   64.5  174.7    74
## 1820  54   90.5  182.0    78
## 1821  60   73.1  180.0    72
## 1822  26   67.9  162.0    60
## 1823  38   73.9  165.9    88
## 1824  80   81.1  158.7    60
## 1825  58  103.4  186.3    74
## 1826  80   77.9  158.8    62
## 1827  28   90.4  179.0    70
## 1828  69   62.8  163.4    82
## 1829  57   68.5  148.0    70
## 1830  52   64.5  160.9    68
## 1831  48   70.6  152.1    68
## 1832  79   77.4  169.6    74
## 1833  39   79.4  178.4    68
## 1834  53   75.4  173.2    72
## 1835  22   88.3  154.0    82
## 1836  53   61.7  167.5    98
## 1837  47   46.1  157.3   116
## 1838  53   63.6  169.5    56
## 1839  40   89.1  171.7    72
## 1840  57   60.7  176.2    86
## 1841  31  113.1  167.3    62
## 1842  50   85.7  171.3    94
## 1843  29  117.6  173.5    78
## 1844  41   76.6  168.9    72
## 1845  33   65.7  165.2    72
## 1846  47   84.7  148.2    74
## 1847  52   39.3  144.3    74
## 1848  35   62.0  173.4    96
## 1849  47   87.6  174.7    64
## 1850  34   68.0  174.8    76
## 1851  60  159.1  188.6    68
## 1852  22   89.2  168.5    74
## 1853  57   65.3  157.8    76
## 1854  70   84.0  180.5    50
## 1855  43   85.5  173.6    62
## 1856  63   87.5  173.6    64
## 1857  80   51.7  164.3    52
## 1858  65   92.5  157.9    70
## 1859  61   65.9  155.4    80
## 1860  35   66.0  162.8    80
## 1861  39   79.4  178.4    68
## 1862  56  100.5  178.4    70
## 1863  70   81.0  174.5    58
## 1864  61   65.3  173.3    64
## 1865  36   82.7  161.4    78
## 1866  53   80.7  174.0    68
## 1867  32   92.2  179.5    78
## 1868  29   62.2  175.0    88
## 1869  44   75.9  167.1    68
## 1870  27   76.3  171.1    72
## 1871  42   70.7  181.6    66
## 1872  80   59.1  166.1    54
## 1873  56   75.9  160.5    70
## 1874  63   96.6  177.2    82
## 1875  61   68.0  163.1    72
## 1876  22   95.5  196.6    66
## 1877  46   78.1  150.0    90
## 1878  61   67.4  160.4    82
## 1879  80   84.7  174.1    48
## 1880  58   84.1  178.9    58
## 1881  32   70.3  149.3    70
## 1882  32   58.8  170.1    76
## 1883  50   91.2  171.3    82
## 1884  46   81.7  146.5    76
## 1885  29  103.1  173.3    94
## 1886  19   85.6  177.9    74
## 1887  48   74.8  173.3    76
## 1888  29   80.2  178.2    66
## 1889  28   71.3  160.3    64
## 1890  46   52.1  156.5    58
## 1891  45   86.1  171.8    74
## 1892  58   63.6  151.1    76
## 1893  27  108.4  189.4    66
## 1894  57  105.8  162.2    62
## 1895  27   70.6  175.9    72
## 1896  49   78.4  163.4    62
## 1897  28  116.9  189.0    86
## 1898  56   63.0  167.8    70
## 1899  50  104.4  175.4    74
## 1900  50   94.2  175.5    78
## 1901  23   90.4  169.5    90
## 1902  65   91.9  182.4    62
## 1903  41   91.1  183.3    66
## 1904  80   43.8  143.9    66
## 1905  67   75.9  179.3    56
## 1906  42   84.4  175.6    74
## 1907  19   65.8  175.9    90
## 1908  36   52.9  157.4    62
## 1909  17   77.5  186.2    58
## 1910  40  106.0  169.6    76
## 1911  28   69.5  176.8    70
## 1912  31  136.3  180.9    82
## 1913  30   72.7  183.6    84
## 1914  16  122.4  173.7    76
## 1915  68   64.9  149.4    80
## 1916  19   85.6  177.9    74
## 1917  72   79.1  166.6    60
## 1918  44   70.1  165.8    84
## 1919  57   68.9  153.8    90
## 1920  45  137.9  191.8    84
## 1921  26   80.4  158.4    92
## 1922  30   95.3  168.4    78
## 1923  26   64.0  165.7    60
## 1924  74  111.3  177.6   100
## 1925  43   87.8  167.9    60
## 1926  52   89.0  174.3    74
## 1927  22  116.4  184.2    78
## 1928  59   78.4  175.3    62
## 1929  58  103.5  163.2    62
## 1930  32   80.1  179.0    78
## 1931  58   73.0  164.4    60
## 1932  44  124.4  166.5    90
## 1933  70  103.8  174.3    68
## 1934  70   89.7  156.6    70
## 1935  64   67.8  163.1    72
## 1936  29   64.5  164.2    82
## 1937  61   71.3  176.7    72
## 1938  59  107.6  181.6    70
## 1939  37   81.3  168.8    76
## 1940  40   89.1  171.7    72
## 1941  40   40.8  144.2    66
## 1942  21   56.8  185.5    62
## 1943  62   99.0  166.1   118
## 1944  21   90.1  168.8    92
## 1945  54  110.0  183.7   102
## 1946  34   66.4  165.1    84
## 1947  47  131.5  173.2   114
## 1948  45   75.4  164.1    78
## 1949  40  121.4  176.2    72
## 1950  36  114.3  178.3   106
## 1951  80   57.7  160.0    80
## 1952  80   48.5  144.4    56
## 1953  19   56.1  166.5    72
## 1954  34   76.6  173.8    76
## 1955  25   91.5  181.5    66
## 1956  38   91.3  166.6    78
## 1957  25   62.2  176.0    66
## 1958  56   63.8  159.4    72
## 1959  52   65.4  155.5    72
## 1960  60   89.9  165.7    86
## 1961  20   81.9  184.9    62
## 1962  60   92.1  163.4    64
## 1963  21  100.5  149.0    92
## 1964  21   65.3  175.7    54
## 1965  65   73.8  181.0    68
## 1966  46   73.1  174.5    66
## 1967  44   62.3  171.6    76
## 1968  67   97.8  170.3    54
## 1969  59   54.3  145.1    84
## 1970  54   67.9  161.9    80
## 1971  28   57.7  164.7    72
## 1972  23   61.1  179.7    76
## 1973  18   58.7  162.2    68
## 1974  19   90.0  180.5    54
## 1975  50   96.1  181.5    80
## 1976  60   65.1  160.3    70
## 1977  54   79.7  168.6    66
## 1978  28   77.5  160.8    70
## 1979  57   81.2  173.0    74
## 1980  36  109.9  168.4    96
## 1981  18   75.2  183.0    92
## 1982  45   75.7  166.7    62
## 1983  29   75.6  170.2    58
## 1984  44   79.5  175.4    54
## 1985  50   65.1  164.9    78
## 1986  39  122.2  169.8    80
## 1987  31   74.5  159.3    74
## 1988  19   75.7  158.1    86
## 1989  57   48.6  145.2    78
## 1990  68   92.6  181.2    44
## 1991  16   60.1  160.8    70
## 1992  67   50.2  156.5    66
## 1993  21   69.2  164.4    58
## 1994  52   93.7  183.7    78
## 1995  33   82.1  166.6    74
## 1996  49  116.7  172.3    68
## 1997  25   87.5  186.1    82
## 1998  39   65.5  168.2    76
## 1999  17   63.5  166.4    86
## 2000  33   85.7  175.5    74
## 2001  28   77.4  171.4    92
## 2002  38   68.4  174.2    68
## 2003  80   66.7  158.6    78
## 2004  47  117.3  181.5    96
## 2005  32   80.1  179.0    78
## 2006  53   77.4  183.3   102
## 2007  57  105.0  176.9    78
## 2008  54  117.3  171.9    58
## 2009  40   91.3  188.9    82
## 2010  40   90.3  179.9    64
## 2011  41   84.1  170.6    80
## 2012  54   53.9  160.1    78
## 2013  53  106.2  176.6    84
## 2014  58   78.6  158.7    66
## 2015  39   56.4  157.5    64
## 2016  17  104.6  167.5    64
## 2017  72   71.9  157.5    66
## 2018  44   84.6  182.0    76
## 2019  25   64.9  154.6    76
## 2020  30   59.8  171.8    72
## 2021  31   86.2  172.5    68
## 2022  34   46.5  155.9    72
## 2023  71   44.0  160.6    64
## 2024  26   88.7  165.1    68
## 2025  70   90.8  166.9    76
## 2026  56  102.9  173.7    78
## 2027  63  113.4  193.7    58
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## 2030  28   57.7  164.7    72
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## 2043  46   84.4  176.8    82
## 2044  44   86.5  165.9    80
## 2045  43   89.4  173.4    64
## 2046  22   73.8  179.7    84
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## 2054  73  128.5  176.6    84
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## 2056  22   65.8  170.1    62
## 2057  43  105.3  199.6    52
## 2058  18  125.6  152.0    92
## 2059  31   62.1  151.2    98
## 2060  22   51.5  157.9    84
## 2061  37  114.0  172.6    68
## 2062  70  103.5  155.1    70
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## 2064  35   68.1  175.3    78
## 2065  24   88.5  168.9    72
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## 2074  32   74.5  164.0    68
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## 2082  64   93.5  162.4    62
## 2083  80   46.4  143.8    54
## 2084  21   60.9  162.5    70
## 2085  32   80.1  179.0    78
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## 2087  56  103.4  185.6    56
## 2088  37  106.0  168.3    96
## 2089  34   74.9  162.2    68
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## 2091  59   85.6  157.3    78
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## 2093  16   69.5  160.2    74
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## 2096  57  108.1  188.2    56
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## 2098  73   84.5  167.8    70
## 2099  46  102.1  185.5    64
## 2100  37   93.5  173.9    74
## 2101  64  102.9  162.6    68
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## 2107  24   50.7  168.8    68
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## 2110  62   78.1  155.7    68
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## 2123  35   70.5  161.7    68
## 2124  47   91.5  192.6    96
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## 2126  31   77.2  182.5    88
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## 2129  62   87.3  156.7    64
## 2130  44   81.0  159.4    70
## 2131  19   79.9  163.8    84
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## 2134  56   68.1  163.0    76
## 2135  31   60.5  158.9    62
## 2136  39   83.3  163.7    82
## 2137  24   98.3  177.0    72
## 2138  42   78.2  166.2    88
## 2139  18   60.9  180.1    74
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## 2141  74   79.8  164.7    64
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## 2143  62   88.1  166.4    64
## 2144  17   73.3  168.0    66
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## 2146  27   76.4  169.4    76
## 2147  26   54.6  168.5    78
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## 2149  47   63.0  164.6    76
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## 2152  62   75.7  156.4    72
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## 2154  48   82.1  179.2    60
## 2155  26   60.8  160.6    76
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## 2157  45   79.7  174.7    74
## 2158  50   57.9  162.2    58
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## 2160  53   95.2  167.1    64
## 2161  18   79.0  169.7    72
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## 2163  49  112.1  180.0    88
## 2164  64   82.0  154.3    76
## 2165  57   86.1  192.8    82
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## 2186  36   78.7  165.8    62
## 2187  34   60.8  163.9    90
## 2188  74   79.1  177.1    58
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## 2190  60  166.1  157.5    80
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## 2195  50   57.9  162.2    58
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## 2197  23   90.6  184.1    68
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## 2199  47   80.2  157.5    52
## 2200  46   43.7  148.1    88
## 2201  55   74.3  173.0    82
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## 2210  47  115.0  191.1    82
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## 2215  52  113.7  183.5    74
## 2216  44   76.6  160.0    72
## 2217  50  164.9  195.0    88
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## 2220  62  103.6  187.1    64
## 2221  31  110.5  169.1    66
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## 2245  21   72.7  170.7    74
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## 2247  65   85.3  182.4    68
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## 2265  35   91.5  185.7    68
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## 2287  52  103.5  186.2    70
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## 2291  62   99.6  172.0    74
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## 2344  60   84.6  186.9    62
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## 2352  23   65.8  183.2    64
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## 2391  31   62.3  154.8    66
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## 2393  34   98.3  159.3    74
## 2394  22   96.8  178.9    76
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## 2402  45  100.2  173.3    80
## 2403  27   71.8  167.7    70
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## 2405  31   76.0  155.6    84
## 2406  31   52.3  154.5    68
## 2407  35   71.1  159.8    68
## 2408  27   76.4  169.0    74
## 2409  28   80.9  177.1    58
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## 2420  46   83.6  166.1    80
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## 2423  32   85.7  164.1    82
## 2424  26   65.5  178.2    74
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## 2426  20   70.5  166.6    76
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## 2428  29   52.0  159.9    50
## 2429  59  100.3  174.1    64
## 2430  41  105.1  182.5    70
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## 2432  35  141.4  176.7    82
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## 2434  57   81.1  165.9    68
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## 2437  34   76.6  173.8    76
## 2438  29   98.4  176.0    60
## 2439  38   86.6  167.7    52
## 2440  43   55.0  169.2    64
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## 2442  27   73.4  173.2    92
## 2443  61   65.7  162.9    70
## 2444  45   92.5  166.5    74
## 2445  63   73.4  168.0    74
## 2446  19   76.8  182.6    72
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## 2450  21   77.8  153.0    84
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## 2452  59   53.6  155.8    68
## 2453  54   78.5  191.2    50
## 2454  29  117.6  173.5    78
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## 2456  80   70.1  172.6    62
## 2457  21   62.6  168.8    72
## 2458  64   93.5  162.4    62
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## 2460  21   41.9  151.6    78
## 2461  24   61.5  164.9    90
## 2462  41  116.8  160.3    96
## 2463  39  100.3  165.2    84
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## 2465  22   55.2  153.5    88
## 2466  19   80.0  181.5    62
## 2467  38  104.5  182.0    90
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## 2469  27   85.8  162.7    76
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## 2471  19   71.6  169.1    68
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## 2473  23  167.6  185.5    62
## 2474  49  105.0  174.4    64
## 2475  23   80.6  159.8    72
## 2476  71   76.6  157.7    54
## 2477  40   98.8  168.4    82
## 2478  34   53.1  153.9    54
## 2479  37   97.2  169.3    84
## 2480  48   89.2  186.5    70
## 2481  34   99.5  168.5    74
## 2482  42  105.0  177.1    88
## 2483  19   43.9  165.8    60
## 2484  45   94.8  180.4    70
## 2485  38   87.5  179.1    56
## 2486  30   76.3  181.1    64
## 2487  20   50.8  166.0    88
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## 2489  49  119.3  153.8    68
## 2490  30   70.9  171.0    74
## 2491  54  117.3  171.9    58
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## 2493  47   75.0  168.9    72
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## 2495  80   62.3  158.4    70
## 2496  51  119.3  178.7    82
## 2497  18  100.0  178.5    70
## 2498  59   63.0  162.1    90
## 2499  51   79.0  173.9    84
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## 2501  17   55.8  152.6    70
## 2502  77  104.7  179.3    68
## 2503  30   90.9  175.5    78
## 2504  18  120.4  181.3    72
## 2505  20   58.1  161.6    74
## 2506  26   99.4  183.4    90
## 2507  28   42.4  150.4    66
## 2508  24   96.4  160.9    76
## 2509  21   60.0  176.9    62
## 2510  33  106.7  180.4    86
## 2511  39   54.3  152.0    60
## 2512  39   76.2  183.5    64
## 2513  61   61.8  147.6    78
## 2514  41   91.7  162.8    52
## 2515  43  105.3  199.6    52
## 2516  58   80.1  170.1    76
## 2517  76   50.1  157.2    64
## 2518  71   77.5  167.6    92
## 2519  25  105.5  182.6    74
## 2520  60   88.0  167.1    88
## 2521  48   78.0  164.1    68
## 2522  59   79.5  172.9    66
## 2523  18   44.2  151.0    74
## 2524  28  131.1  180.2   108
## 2525  25  105.5  182.6    74
## 2526  53   72.5  160.4    58
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## 2678  52  128.4  180.8    64
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## 2719  50   75.7  171.5    56
## 2720  30   48.8  158.2    84
## 2721  39  102.8  173.3    74
## 2722  62   51.8  153.5    72
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## 2725  80   66.3  160.3    72
## 2726  58   53.8  157.9    64
## 2727  46  103.4  171.8    76
## 2728  18   70.1  168.5    82
## 2729  43   85.3  179.2    60
## 2730  27   61.4  158.1    64
## 2731  70   76.0  176.9    74
## 2732  20  128.3  176.9    62
## 2733  63   96.6  177.2    82
## 2734  34   69.3  184.1    72
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## 2736  70   75.3  165.0    80
## 2737  72   87.6  171.1    62
## 2738  54  135.4  167.8    68
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## 2740  79   79.2  161.7    76
## 2741  46   77.3  184.9    54
## 2742  27   99.9  175.7    74
## 2743  41   57.7  160.9    58
## 2744  56  100.6  182.3    64
## 2745  27   90.7  177.4    78
## 2746  67  128.3  180.2    70
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## 2748  57  105.4  165.3    78
## 2749  49   96.8  170.0    82
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## 2756  41   79.1  178.4    80
## 2757  30   54.0  162.4    94
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## 2759  27   77.6  173.6    88
## 2760  77   58.8  165.5    70
## 2761  52   83.9  170.4    60
## 2762  51   61.5  163.5    62
## 2763  80   75.0  161.6    64
## 2764  26   49.0  156.6    66
## 2765  27   57.1  164.2    60
## 2766  44   62.3  171.6    76
## 2767  50   72.7  168.0    84
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## 2769  59   86.1  183.7    72
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## 2771  29   87.8  164.4    66
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## 2784  16   89.4  190.9    60
## 2785  44   54.3  171.6    70
## 2786  68   72.7  159.2    62
## 2787  21   79.7  172.4    72
## 2788  43   96.2  159.8    68
## 2789  48   90.1  164.7    64
## 2790  80   76.1  177.4    62
## 2791  51   61.6  163.9    62
## 2792  50   58.3  169.7    82
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## 2794  52  113.7  183.5    74
## 2795  69   62.8  163.4    82
## 2796  56  100.5  178.4    70
## 2797  71   64.1  164.9    84
## 2798  71   76.2  166.1    66
## 2799  36   96.6  153.8    84
## 2800  19   59.6  181.3    84
## 2801  56   78.7  152.0    78
## 2802  35   89.1  177.9    64
## 2803  35   59.7  170.3    80
## 2804  20   51.0  157.9    78
## 2805  70   72.3  182.9    82
## 2806  64  106.1  164.2    70
## 2807  41  113.4  158.9    76
## 2808  50   76.9  173.9    72
## 2809  74   63.6  166.9    72
## 2810  50   92.6  176.9    62
## 2811  44  100.2  169.6    86
## 2812  28  112.2  152.7    70
## 2813  19   72.1  178.0    62
## 2814  19   59.6  162.1    88
## 2815  44   81.3  185.9    68
## 2816  72   86.6  171.8    64
## 2817  80   91.8  155.9    80
## 2818  45   65.0  150.5    68
## 2819  16   63.8  171.4    58
## 2820  17   64.1  161.8    78
## 2821  80   69.7  159.2    72
## 2822  29   75.6  170.2    58
## 2823  30   98.8  169.0    68
## 2824  74   81.3  165.1    62
## 2825  28   63.3  163.1    62
## 2826  40   83.0  173.6    82
## 2827  70  117.6  171.3    94
## 2828  21  127.4  158.8    84
## 2829  41   91.7  162.8    52
## 2830  35   85.3  171.3    70
## 2831  68   93.9  177.1    70
## 2832  34   62.5  153.9    92
## 2833  36  111.6  176.8    84
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## 2835  31   62.6  165.9    70
## 2836  70   91.7  177.0    82
## 2837  42   99.7  175.2    62
## 2838  21  103.7  161.0    86
## 2839  74   83.6  188.8    96
## 2840  42   87.9  185.9    60
## 2841  47   84.6  177.3    54
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## 2854  56   63.0  167.8    70
## 2855  56  102.9  173.7    78
## 2856  31  140.1  157.0    82
## 2857  72   92.4  157.3    48
## 2858  32  107.4  175.3    68
## 2859  55   75.3  173.1    50
## 2860  52   76.3  161.9    76
## 2861  26   64.0  165.7    60
## 2862  33   73.9  169.9    64
## 2863  33   50.9  166.2    60
## 2864  51  137.1  172.8    66
## 2865  22   70.3  184.1    72
## 2866  56   57.5  170.7    64
## 2867  65   59.4  163.7    70
## 2868  38   74.3  153.0    86
## 2869  35   58.8  169.8    62
## 2870  58   63.6  151.1    76
## 2871  50  164.9  195.0    88
  1. Develop analytical models to predict a person’s weight based on his/her age, height, and pulse (i.e., use the variable Weight as your target variable). In particular, create a regression model, a decision tree, a bagging model using 100 bootstrapped samples, a random forest with 200 trees, and a boosting model with 200 trees each having 5 splits and a shrinkage/weight of 0.03.
    ##Regression Model
nhanes_regression <- lm(Weight ~., data = nhanes_train)
summary(nhanes_regression)
## 
## Call:
## lm(formula = Weight ~ ., data = nhanes_train)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -43.860 -13.096  -3.099  10.227 116.080 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -112.64017    6.78932 -16.591  < 2e-16 ***
## Age            0.12471    0.02045   6.097 1.22e-09 ***
## Height         1.01324    0.03522  28.768  < 2e-16 ***
## Pulse          0.24685    0.03019   8.177 4.32e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 18.67 on 2867 degrees of freedom
## Multiple R-squared:  0.2311, Adjusted R-squared:  0.2303 
## F-statistic: 287.2 on 3 and 2867 DF,  p-value: < 2.2e-16

##Decision Tree

library(rpart)
library(rpart.plot)
nhanes_tree <- rpart(formula = Weight ~ ., data = nhanes_train)
prp(nhanes_tree, digits = 4, extra = 1) 

##Bagging Model
Using 100 bootstrapped samples.

library(ipred)
nhanes_bag <- bagging(formula = Weight ~., data = nhanes_train, nbagg = 100) 

##Random Florest
With 200 trees.

#install.packages('randomForest')
library(randomForest)
## randomForest 4.7-1.1
## Type rfNews() to see new features/changes/bug fixes.
nhanes_rf <- randomForest(Weight ~., data = nhanes_train, importance = TRUE, ntree = 200)

##Boosting Model
With 200 trees each having 5 splits and a shrinkage/weight of 0.03.

library(gbm)
## Loaded gbm 2.1.8.1
nhanes_boost <- gbm(formula = Weight ~., data = nhanes_train, distribution = "gaussian", n.trees = 200, shrinkage = 0.03, interaction.depth = 5)
  1. Load the nhanes_test csv file into R, and use this data to calculate the mean squared error (MSE) for each of the models that you developed in the previous question. Based on your results, which model is best for predicting body weight?
nhanes_test <- read.csv("/Users/jusimioni/Desktop/MSDA 2021-23/Spring 2023/Big Data/Data/nhanes_test.csv")

##MSE

#MSE Regression Model
MSE_reg <- predict(nhanes_regression, nhanes_test) 
mean((MSE_reg - nhanes_test$Weight)^2)
## [1] 332.8215
#MSE Decision Tree
MSE_tree = predict(nhanes_tree, nhanes_test)
mean((MSE_tree - nhanes_test$Weight)^2)
## [1] 334.6264
#MSE Bagging
MSE_bagg = predict(nhanes_bag, nhanes_test)
mean((MSE_bagg - nhanes_test$Weight)^2)
## [1] 327.0961
#MSE Random Florest
MSE_rf = predict(nhanes_rf, nhanes_test)
mean((MSE_rf - nhanes_test$Weight)^2)
## [1] 262.378
#MSE Boosting
MSE_boost = predict(nhanes_boost, nhanes_test)
## Using 200 trees...
mean((MSE_boost - nhanes_test$Weight)^2)
## [1] 314.1001

By looking at the MSE results the best model predicting body weight is Random Florest.

#Part 3: Clustering 1. Use R to compute the mean of each variable in the nhanes_train csv file.

colMeans(nhanes_train)
##       Age    Weight    Height     Pulse 
##  45.14699  82.63375 169.54650  72.32045
  1. Perform k-means clustering on the data in the nhanes_train csv file. Create 4 distinct clusters.
library(fpc)
nhanes_clus <- kmeans(nhanes_train[, 1:4], 4)
nhanes_clus
## K-means clustering with 4 clusters of sizes 722, 426, 694, 1029
## 
## Cluster means:
##        Age    Weight   Height    Pulse
## 1 63.13019  68.70402 162.5860 69.49030
## 2 35.10329 116.11033 175.9885 77.86854
## 3 54.87464  94.82695 174.8431 69.24207
## 4 30.12634  70.32488 168.1912 74.08552
## 
## Clustering vector:
##    [1] 3 2 4 2 2 3 3 3 3 1 4 4 4 2 3 2 4 4 4 1 3 4 1 2 1 3 1 3 4 4 4 1 4 2 4 1 1
##   [38] 1 4 2 3 1 1 4 3 1 4 1 3 1 1 1 4 2 4 1 2 1 1 3 3 4 1 4 1 4 3 2 4 1 3 1 3 1
##   [75] 2 4 4 4 4 2 1 4 3 4 3 4 4 1 3 3 4 1 4 2 2 3 4 4 4 4 1 3 1 4 4 3 1 4 1 4 4
##  [112] 4 2 2 3 4 1 4 1 4 4 3 3 1 1 3 4 3 2 4 3 4 1 3 1 4 4 2 3 1 1 1 4 3 3 2 1 2
##  [149] 4 3 4 4 3 4 1 1 2 4 4 4 2 4 2 4 3 4 4 4 4 1 2 3 4 4 2 2 4 3 4 1 4 4 4 4 4
##  [186] 1 2 3 3 4 3 3 2 3 1 3 1 4 4 1 2 1 4 4 2 1 3 1 3 4 3 3 3 3 2 3 1 4 4 3 4 4
##  [223] 4 2 2 4 4 2 1 1 4 3 2 1 2 2 3 1 1 4 4 4 3 1 1 3 4 3 3 3 4 4 3 4 4 2 1 3 1
##  [260] 4 1 3 3 1 4 1 2 3 1 4 4 4 4 2 4 3 4 2 4 3 1 1 3 1 3 3 4 4 4 4 3 2 3 4 1 4
##  [297] 1 3 3 4 4 3 4 4 2 2 1 4 4 1 1 4 4 3 4 1 4 4 1 4 2 3 3 3 4 4 2 1 4 4 4 1 3
##  [334] 4 1 1 1 4 1 3 1 3 3 1 3 3 4 4 2 3 3 1 3 4 2 4 2 4 2 4 1 1 4 4 4 4 1 4 1 4
##  [371] 1 4 4 4 4 4 1 3 1 3 3 1 3 4 1 4 4 4 2 4 1 3 1 4 1 2 4 3 4 3 4 4 4 4 1 3 1
##  [408] 1 3 4 4 4 1 4 1 3 1 3 4 1 1 1 1 4 4 4 1 3 3 3 2 4 4 4 3 4 4 3 3 1 1 4 4 3
##  [445] 4 1 4 4 4 2 1 3 1 3 3 3 2 1 4 4 3 2 3 2 2 2 3 3 3 1 4 1 4 2 4 4 3 4 3 2 4
##  [482] 4 1 4 4 3 2 1 2 4 2 4 4 1 1 4 2 3 1 4 1 3 3 4 3 4 3 4 4 1 1 4 1 4 1 1 2 2
##  [519] 3 4 4 4 3 3 3 1 4 2 4 4 1 1 1 1 4 2 4 4 4 1 2 3 1 3 4 4 3 4 4 4 1 3 4 3 4
##  [556] 3 1 4 3 4 3 2 1 1 4 4 4 1 1 1 3 4 1 3 4 3 2 4 1 4 4 1 3 4 1 4 4 3 3 2 1 4
##  [593] 2 3 1 3 1 1 3 4 4 3 4 3 1 4 1 2 4 3 3 4 4 1 1 3 4 3 1 1 4 3 4 3 4 3 2 3 3
##  [630] 3 1 3 1 1 3 1 1 2 2 3 3 3 1 1 4 3 2 4 1 3 4 3 1 4 1 3 2 1 4 1 2 4 1 4 4 1
##  [667] 3 2 4 4 4 4 2 1 2 4 3 2 2 2 3 3 4 2 2 4 4 4 3 3 1 2 4 3 1 1 4 2 1 3 2 4 4
##  [704] 2 2 2 1 1 3 1 4 4 1 1 4 4 4 4 4 1 3 1 1 4 4 4 4 3 3 1 2 2 4 4 4 1 1 2 3 3
##  [741] 4 1 2 4 4 1 4 4 1 4 1 4 2 1 1 1 1 1 3 4 4 4 4 1 4 2 4 3 4 1 4 2 3 3 4 2 3
##  [778] 4 1 4 4 4 3 1 4 1 4 2 4 4 3 1 4 3 3 1 1 2 1 2 4 4 1 4 3 4 3 1 1 4 4 2 3 3
##  [815] 2 4 2 4 4 3 1 4 4 4 3 4 1 3 3 1 1 2 1 3 4 1 1 4 4 3 3 4 1 1 2 1 4 2 3 1 4
##  [852] 3 1 3 4 2 4 4 3 4 1 2 1 4 4 3 4 1 1 1 1 3 3 4 3 4 1 1 4 4 3 1 2 1 4 3 3 2
##  [889] 2 1 3 3 2 1 4 4 3 1 2 2 3 2 1 3 4 1 1 4 1 3 2 4 4 2 4 3 4 4 4 3 4 4 2 2 4
##  [926] 4 2 1 1 4 4 2 1 4 3 1 4 4 1 1 1 4 4 1 4 1 3 4 2 3 4 4 3 1 1 4 3 4 1 4 4 4
##  [963] 4 3 4 4 4 3 3 4 1 4 1 4 3 3 4 4 2 3 1 2 1 2 2 1 4 1 4 1 4 4 4 2 4 1 3 3 3
## [1000] 1 4 3 1 2 1 3 4 2 1 4 2 4 1 1 4 2 3 3 3 4 4 3 2 1 3 1 1 2 4 2 1 4 4 3 2 4
## [1037] 3 3 4 1 3 4 4 2 4 1 2 4 1 4 4 4 4 3 2 1 4 4 2 4 2 4 4 1 1 1 4 4 1 1 3 4 4
## [1074] 3 3 1 4 2 3 1 1 2 2 4 4 2 1 4 4 4 4 1 1 2 2 3 4 3 3 4 2 3 2 1 1 4 4 2 2 4
## [1111] 4 4 3 4 2 1 3 2 4 1 2 2 3 3 4 1 4 3 3 1 1 2 4 4 4 4 3 1 3 4 2 2 3 4 1 4 3
## [1148] 1 4 1 1 1 4 4 4 1 1 4 4 3 1 4 4 2 4 3 3 4 3 4 4 2 3 3 1 2 4 2 1 4 2 4 4 1
## [1185] 1 4 1 4 2 2 4 3 3 3 2 3 1 3 4 1 4 1 3 4 4 4 3 1 4 4 2 2 3 3 3 1 4 1 1 2 4
## [1222] 3 4 4 1 1 4 3 1 1 3 3 4 4 2 1 4 2 3 3 3 1 1 4 3 3 4 3 1 1 4 4 4 1 3 4 2 3
## [1259] 3 1 1 3 4 3 4 4 4 1 1 4 1 3 3 4 4 2 3 2 3 1 3 1 1 1 4 3 1 3 4 4 4 1 4 4 4
## [1296] 1 2 3 4 2 3 3 3 1 1 1 1 2 3 1 2 4 3 4 1 4 2 4 1 1 3 3 4 4 4 1 3 1 1 3 2 2
## [1333] 1 1 4 3 2 3 3 2 1 1 1 3 3 2 1 4 2 4 4 4 1 3 3 1 3 4 1 2 3 1 1 3 1 2 3 4 3
## [1370] 2 2 1 4 3 3 2 4 1 4 3 3 4 1 1 1 1 1 4 4 1 2 1 3 4 2 4 1 2 3 1 1 4 1 4 3 4
## [1407] 1 2 2 1 2 3 3 3 4 2 1 4 1 1 4 3 3 1 2 3 3 1 1 1 1 2 1 3 3 4 1 4 3 1 3 4 3
## [1444] 2 3 4 4 1 1 1 3 3 1 4 2 4 4 4 1 3 4 3 3 4 3 4 4 3 4 4 4 4 3 1 2 4 4 4 4 1
## [1481] 1 1 2 3 4 2 4 1 3 4 4 1 2 4 1 4 2 1 2 4 1 3 3 3 1 1 1 3 3 4 3 4 3 4 1 4 1
## [1518] 3 3 3 1 4 1 2 2 1 1 1 4 1 2 2 1 4 4 3 4 1 3 2 1 2 2 4 4 3 4 1 3 2 3 4 4 3
## [1555] 2 1 1 4 4 1 3 1 1 1 4 4 3 1 4 2 3 4 3 2 4 4 1 3 3 2 1 4 2 3 3 4 2 1 4 4 3
## [1592] 1 2 4 4 4 1 4 2 4 1 4 1 1 3 3 1 3 1 3 4 3 2 3 3 3 3 3 1 3 4 2 4 1 3 4 2 3
## [1629] 3 1 3 1 4 4 4 4 2 3 1 4 3 4 1 4 2 4 3 1 4 1 4 4 3 1 2 2 4 4 1 3 3 3 3 1 3
## [1666] 1 1 4 4 4 3 4 4 4 2 1 4 4 2 3 3 4 4 4 4 3 1 3 4 4 2 1 1 1 4 3 2 4 3 2 4 4
## [1703] 2 4 1 1 4 3 4 1 1 2 3 1 1 3 2 1 2 4 4 3 3 1 3 4 3 4 4 2 1 2 1 4 1 4 3 4 2
## [1740] 2 2 3 4 4 1 3 3 3 4 3 4 1 2 1 4 4 4 3 4 1 4 1 1 4 2 4 2 4 4 4 3 1 4 4 4 4
## [1777] 1 2 1 2 3 4 4 4 4 1 4 4 4 1 3 1 3 4 2 4 3 4 1 3 4 1 1 1 3 4 1 3 3 1 1 2 3
## [1814] 1 4 2 4 4 4 3 1 4 4 1 3 1 4 1 1 1 1 1 4 1 4 1 4 1 3 1 2 3 2 4 4 1 1 4 3 4
## [1851] 2 4 1 3 3 3 1 3 1 4 4 3 1 1 4 3 2 4 4 4 4 1 1 3 1 2 4 1 1 3 4 4 3 1 2 4 4
## [1888] 4 4 1 3 1 2 3 4 1 2 1 3 3 4 3 3 1 1 3 4 4 4 2 4 2 4 2 1 4 1 4 1 2 4 2 4 3
## [1925] 3 3 2 1 3 4 1 2 3 1 1 4 1 3 4 3 4 4 3 4 2 4 2 4 2 2 1 1 4 4 4 3 4 1 1 3 4
## [1962] 3 2 4 1 4 4 3 1 1 4 4 4 4 3 1 1 4 3 2 4 4 4 3 1 2 4 4 1 3 4 1 4 3 4 2 4 4
## [1999] 4 4 4 4 1 2 4 3 3 3 3 3 4 1 3 1 4 2 1 3 4 4 4 4 1 4 3 3 3 3 3 4 4 2 4 2 1
## [2036] 1 3 4 4 2 1 4 3 3 3 4 2 3 4 4 2 4 3 2 4 4 3 2 4 4 2 3 1 4 4 2 4 3 2 3 3 2
## [2073] 4 4 4 1 2 2 1 2 4 3 1 4 4 3 3 2 4 1 1 2 4 3 4 3 4 1 3 3 3 4 1 1 2 1 4 4 2
## [2110] 1 4 4 4 4 3 4 2 3 2 4 3 4 4 3 4 4 3 1 1 4 4 1 4 1 4 4 2 4 4 4 1 4 3 4 1 4
## [2147] 4 2 1 4 2 1 3 3 4 4 3 1 1 3 4 2 2 1 3 3 3 1 3 3 4 4 2 2 4 2 1 3 3 1 1 1 2
## [2184] 3 3 4 4 1 1 2 2 4 4 3 1 3 4 4 1 1 1 2 3 3 4 1 3 3 3 2 4 2 4 4 2 4 2 4 4 3
## [2221] 2 4 1 3 4 4 2 4 3 4 2 3 4 4 4 4 3 1 3 4 1 3 2 3 4 1 3 4 4 4 1 1 4 4 2 3 3
## [2258] 4 3 4 4 3 3 1 3 1 2 2 1 4 2 3 4 3 2 4 4 2 3 4 1 4 3 3 4 4 3 4 2 4 3 1 2 4
## [2295] 3 4 3 4 4 1 3 4 1 2 2 4 4 1 3 4 4 1 4 4 4 1 4 3 2 3 1 1 4 4 3 1 2 2 1 4 3
## [2332] 3 4 1 3 4 1 1 1 2 4 4 1 3 2 2 4 4 4 3 1 4 4 2 3 3 1 3 1 4 1 1 2 4 1 4 3 3
## [2369] 2 4 4 3 1 3 2 2 3 4 1 4 4 1 2 1 3 2 3 1 1 4 4 4 2 2 2 2 3 1 1 1 3 3 4 1 4
## [2406] 4 4 4 4 1 4 4 1 4 2 3 3 4 3 3 4 3 4 4 4 4 1 4 3 2 3 2 1 1 4 4 4 2 3 4 1 4
## [2443] 1 3 1 4 1 1 4 4 4 1 3 2 3 1 4 3 3 4 4 2 2 4 4 4 2 3 4 4 4 4 2 3 4 1 2 4 2
## [2480] 3 2 2 4 3 3 4 4 1 2 4 3 4 4 1 1 2 2 1 3 1 4 3 4 2 4 2 4 2 4 2 4 4 1 3 3 1
## [2517] 1 1 2 3 1 1 4 2 2 1 1 1 4 2 3 4 1 3 3 4 2 4 2 2 3 4 4 1 4 1 4 4 3 2 4 3 1
## [2554] 1 3 1 4 3 1 4 3 4 1 4 4 3 3 4 3 4 2 3 3 4 3 3 4 3 4 3 1 4 2 3 1 1 3 3 2 4
## [2591] 1 3 2 1 1 3 1 3 4 1 3 1 2 2 4 4 3 3 2 1 4 4 2 1 4 4 3 2 4 4 1 4 1 3 1 3 3
## [2628] 3 3 2 1 3 4 4 2 1 3 4 1 4 4 1 1 4 3 2 3 4 3 1 4 4 4 3 4 2 4 3 2 1 1 1 4 1
## [2665] 4 3 1 3 2 3 2 4 1 4 3 4 4 2 3 4 2 1 3 3 1 3 4 1 4 3 3 4 3 3 3 1 3 4 4 4 1
## [2702] 3 3 4 1 1 1 3 1 4 1 1 4 4 2 4 3 4 1 4 2 1 1 1 1 1 3 4 3 4 1 2 3 4 4 1 3 2
## [2739] 3 1 3 2 4 3 4 2 3 3 3 2 2 2 1 4 1 4 4 4 4 1 3 1 1 4 4 4 1 3 3 2 4 3 4 2 4
## [2776] 1 4 4 2 3 1 4 3 4 4 1 4 3 3 1 1 1 1 2 1 3 1 1 2 4 1 3 4 4 1 3 2 3 1 3 2 2
## [2813] 4 4 3 3 1 1 4 4 1 4 2 1 4 4 3 2 3 4 3 4 2 3 4 3 3 2 3 3 3 1 1 3 1 4 3 2 2
## [2850] 2 2 1 2 1 3 2 3 2 1 1 4 4 4 2 4 1 1 4 4 1 2
## 
## Within cluster sum of squares by cluster:
## [1] 296828.7 306535.3 297261.0 418698.2
##  (between_SS / total_SS =  54.1 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
## [6] "betweenss"    "size"         "iter"         "ifault"
  1. Use R to display the mean of each variable in each cluster, and compare these means with those that you obtained in the previous question.
nhanes_clus$centers
##        Age    Weight   Height    Pulse
## 1 63.13019  68.70402 162.5860 69.49030
## 2 35.10329 116.11033 175.9885 77.86854
## 3 54.87464  94.82695 174.8431 69.24207
## 4 30.12634  70.32488 168.1912 74.08552
  1. Determine which cluster the data in row 2000 was placed in.
nhanes_clus$cluster[200]
## [1] 1