Lab Exercize 1

US Wages

library("faraway")
data(uswages)
?uswages
names(uswages)
##  [1] "wage"  "educ"  "exper" "race"  "smsa"  "ne"    "mw"    "so"    "we"   
## [10] "pt"
formattable::formattable(uswages)
wage educ exper race smsa ne mw so we pt
6085 771.60 18 18 0 1 1 0 0 0 0
23701 617.28 15 20 0 1 0 0 0 1 0
16208 957.83 16 9 0 1 0 0 1 0 0
2720 617.28 12 24 0 1 1 0 0 0 0
9723 902.18 14 12 0 1 0 1 0 0 0
22239 299.15 12 33 0 1 0 0 0 1 0
14379 541.31 16 42 0 1 0 0 1 0 1
12878 148.39 16 0 0 1 0 1 0 0 1
23121 273.19 12 36 0 1 0 0 0 1 1
13086 666.67 12 37 0 0 0 1 0 0 0
19913 241.50 9 20 1 1 0 0 1 0 1
20055 703.79 14 29 0 1 0 0 1 0 0
6076 550.81 17 16 0 0 1 0 0 0 0
24050 807.22 14 21 0 1 0 0 0 1 1
11064 712.25 14 11 0 0 0 1 0 0 0
26395 351.46 10 10 0 1 0 0 0 1 0
15576 373.24 12 8 0 0 0 0 1 0 0
18936 759.73 13 19 0 1 0 0 1 0 0
4747 356.13 14 6 0 1 1 0 0 0 0
21572 308.64 16 0 0 1 0 0 1 0 0
14575 469.14 6 24 0 0 0 0 1 0 0
15065 617.28 16 -1 0 1 0 0 1 0 0
23270 123.46 16 1 0 1 0 0 0 1 1
11093 474.83 12 11 0 0 0 1 0 0 0
8830 261.16 12 40 0 1 0 1 0 0 0
9219 284.90 12 5 0 1 0 1 0 0 0
28065 1661.92 12 15 0 1 0 0 0 1 0
1339 629.15 12 44 0 1 1 0 0 0 0
13462 2374.15 12 35 0 1 0 0 1 0 0
10787 522.32 16 8 0 1 0 1 0 0 0
11423 688.51 14 12 0 1 0 1 0 0 0
15657 246.91 9 13 0 1 0 0 1 0 0
2698 949.67 5 55 1 1 1 0 0 0 0
14276 261.16 14 7 1 1 0 0 1 0 0
10854 106.86 10 52 0 1 0 1 0 0 1
7510 296.77 12 11 0 1 0 1 0 0 0
26838 379.87 14 8 0 1 0 0 0 1 0
21118 634.92 9 19 0 1 0 0 1 0 0
10875 1182.03 12 45 0 1 0 1 0 0 0
8891 740.74 12 9 0 1 0 1 0 0 0
15487 237.42 10 12 1 1 0 0 1 0 0
6090 144.03 12 0 0 1 1 0 0 0 0
2293 406.96 14 11 0 0 1 0 0 0 0
8794 351.61 9 10 0 0 0 1 0 0 0
3544 593.54 12 10 0 1 1 0 0 0 0
23320 273.03 14 4 0 1 0 0 0 1 0
23176 997.15 12 44 0 1 0 0 0 1 0
4938 1198.96 12 34 0 1 1 0 0 0 0
12672 569.80 15 15 0 1 0 1 0 0 0
8971 130.58 12 4 0 1 0 1 0 0 0
16287 641.03 13 16 1 1 0 0 1 0 0
15181 712.25 14 25 0 1 0 0 1 0 0
3554 1073.12 16 8 0 1 1 0 0 0 0
26446 712.25 16 13 0 1 0 0 0 1 0
8698 261.16 12 35 0 1 0 1 0 0 0
9899 783.48 16 4 0 1 0 1 0 0 0
18503 197.53 12 8 1 1 0 0 1 0 1
27829 720.16 12 28 1 1 0 0 0 1 0
10616 593.54 14 18 0 1 0 1 0 0 0
24172 1234.57 18 7 0 1 0 0 0 1 0
14806 533.87 12 9 0 0 0 0 1 0 0
4777 712.25 16 6 0 1 1 0 0 0 0
9322 909.31 16 9 0 1 0 1 0 0 0
16555 356.13 12 14 1 1 0 0 1 0 0
26982 759.73 14 11 0 1 0 0 0 1 0
19738 382.74 8 42 0 1 0 0 1 0 0
16707 53.70 9 22 1 1 0 0 1 0 1
6352 403.61 12 12 0 0 1 0 0 0 0
19667 664.77 12 15 0 1 0 0 1 0 0
17679 415.48 13 21 0 1 0 0 1 0 0
17796 949.67 16 21 0 1 0 0 1 0 0
27009 664.77 12 15 0 1 0 0 0 1 0
3901 308.64 10 51 0 0 1 0 0 0 0
27986 997.15 12 11 0 1 0 0 0 1 0
3303 2374.15 18 27 0 1 1 0 0 0 0
15785 259.73 12 1 0 0 0 0 1 0 0
119 641.03 13 27 0 0 1 0 0 0 0
11397 411.52 12 11 0 1 0 1 0 0 0
7461 379.87 12 23 1 1 0 1 0 0 0
6106 231.48 16 11 0 1 1 0 0 0 0
12956 142.45 12 4 0 0 0 1 0 0 0
7371 503.70 11 6 0 0 0 1 0 0 0
8854 94.59 14 4 0 1 0 1 0 0 1
5540 1234.57 18 3 0 1 1 0 0 0 0
21727 379.87 4 34 0 0 0 0 1 0 0
7385 391.74 12 15 0 1 0 1 0 0 0
612 411.70 12 19 0 0 1 0 0 0 0
21394 1068.38 14 31 0 1 0 0 1 0 0
9748 123.46 15 -1 0 1 0 1 0 0 0
10401 569.80 12 37 0 1 0 1 0 0 0
8748 94.97 13 32 0 0 0 1 0 0 1
7702 474.83 8 46 0 1 0 1 0 0 0
18839 379.87 12 12 0 1 0 0 1 0 0
16131 118.71 3 56 0 0 0 0 1 0 1
10609 90.22 12 1 0 0 0 1 0 0 0
3648 402.17 10 8 0 1 1 0 0 0 0
20327 1344.78 16 12 0 1 0 0 1 0 0
26747 474.83 16 27 0 1 0 0 0 1 0
24480 356.13 9 45 0 1 0 0 0 1 0
25209 197.53 12 2 0 1 0 0 0 1 0
4795 949.67 11 19 1 1 1 0 0 0 0
10301 531.81 18 11 0 0 0 1 0 0 1
22061 522.32 12 16 0 0 0 0 1 0 0
12857 356.13 18 32 0 1 0 1 0 0 0
24745 949.67 12 35 0 1 0 0 0 1 0
16118 902.18 18 14 0 1 0 0 1 0 0
27977 1697.72 18 12 0 0 0 0 0 1 0
25363 451.09 14 16 0 0 0 0 0 1 0
6986 830.96 16 37 0 1 0 1 0 0 0
24174 807.22 14 16 0 1 0 0 0 1 0
26144 617.28 6 23 0 1 0 0 0 1 0
9238 271.60 13 1 0 1 0 1 0 0 0
7572 462.99 12 10 0 0 0 1 0 0 0
22024 336.70 13 17 0 1 0 0 1 0 0
20215 593.54 16 4 0 1 0 0 1 0 0
26010 189.93 8 43 0 1 0 0 0 1 0
7945 119.66 14 3 0 0 0 1 0 0 0
18821 641.03 13 15 0 0 0 0 1 0 0
3395 76.43 13 -1 0 1 1 0 0 0 1
4310 493.83 14 0 0 1 1 0 0 0 0
22040 679.01 16 23 0 0 0 0 1 0 0
18395 308.64 10 10 0 1 0 0 1 0 0
26521 130.58 12 11 0 1 0 0 0 1 1
6305 56.79 14 0 0 0 1 0 0 0 1
2330 1899.34 14 30 0 1 1 0 0 0 0
27898 1316.87 12 15 0 0 0 0 0 1 0
2245 830.96 18 0 0 1 1 0 0 0 0
23041 784.69 14 15 0 0 0 0 0 1 0
6736 1139.60 16 5 0 1 0 1 0 0 0
27500 167.55 12 2 0 1 0 0 0 1 0
2224 712.25 12 42 0 1 1 0 0 0 0
6712 845.20 14 13 0 1 0 1 0 0 0
15738 315.82 12 18 0 1 0 0 1 0 0
25092 183.42 10 6 0 1 0 0 0 1 0
5494 337.08 9 43 0 1 1 0 0 0 0
13670 493.83 11 3 0 1 0 0 1 0 0
20453 854.70 18 25 0 0 0 0 1 0 0
14818 885.57 12 20 0 0 0 0 1 0 0
24711 1033.01 18 3 0 0 0 0 0 1 0
4526 403.61 13 5 0 1 1 0 0 0 0
7363 522.32 16 7 0 1 0 1 0 0 0
18966 197.53 12 19 1 1 0 0 1 0 0
10371 308.64 12 4 0 1 0 1 0 0 0
22716 521.94 12 42 0 0 0 0 0 1 0
3094 367.74 16 8 0 1 1 0 0 0 0
6244 236.42 12 13 0 1 1 0 0 0 0
85 569.80 8 36 0 1 1 0 0 0 0
10912 641.03 16 16 0 1 0 1 0 0 0
26199 783.48 16 10 0 1 0 0 0 1 0
1514 189.93 15 -1 0 1 1 0 0 0 0
13332 500.95 17 1 0 1 0 0 1 0 0
13016 593.54 12 12 0 1 0 1 0 0 0
8931 154.32 13 1 0 1 0 1 0 0 1
12447 721.45 8 47 0 1 0 1 0 0 0
6079 522.32 10 24 1 1 1 0 0 0 0
6635 1234.57 14 21 0 1 0 1 0 0 0
25763 123.46 16 9 0 1 0 0 0 1 1
18783 546.06 12 21 0 0 0 0 1 0 0
24442 1305.79 18 19 0 0 0 0 0 1 0
20029 522.32 18 12 0 1 0 0 1 0 0
16431 379.87 12 19 0 0 0 0 1 0 0
977 866.57 18 14 0 1 1 0 0 0 0
4269 689.53 11 38 0 1 1 0 0 0 0
19267 346.63 12 38 0 0 0 0 1 0 0
19620 379.87 13 5 0 0 0 0 1 0 0
15685 370.37 3 49 0 1 0 0 1 0 0
26 546.06 12 16 0 1 1 0 0 0 0
9511 1305.79 12 18 0 1 0 1 0 0 0
6369 498.58 12 17 0 0 1 0 0 0 0
3858 241.21 12 0 0 0 1 0 0 0 0
4020 195.46 12 5 1 1 1 0 0 0 0
17173 160.49 12 21 1 1 0 0 1 0 0
25293 470.09 12 25 0 1 0 0 0 1 0
19611 415.48 12 40 0 0 0 0 1 0 0
749 830.96 12 27 0 0 1 0 0 0 0
23472 668.47 14 21 0 1 0 0 0 1 0
4190 997.15 18 6 0 1 1 0 0 0 0
24273 1111.11 18 28 0 1 0 0 0 1 0
5642 384.62 12 31 0 1 1 0 0 0 0
1845 462.96 12 13 0 1 1 0 0 0 0
25642 189.93 1 49 0 1 0 0 0 1 0
1776 683.76 9 46 0 1 1 0 0 0 0
19914 61.73 12 17 1 1 0 0 1 0 1
11450 664.77 16 9 0 1 0 1 0 0 0
23203 679.01 16 7 0 1 0 0 0 1 0
26631 740.74 13 13 0 1 0 0 0 1 0
5814 617.28 12 25 0 1 1 0 0 0 0
18808 142.45 9 46 0 0 0 0 1 0 0
12836 1264.13 18 36 0 1 0 1 0 0 0
9363 830.96 12 25 0 1 0 1 0 0 0
15041 747.86 16 12 0 1 0 0 1 0 0
21760 284.90 12 9 0 1 0 0 1 0 0
27384 1049.38 12 9 0 1 0 0 0 1 0
19119 213.68 12 2 1 0 0 0 1 0 0
18296 854.70 13 38 0 0 0 0 1 0 0
7176 617.28 11 15 0 1 0 1 0 0 0
5405 284.90 5 54 0 1 1 0 0 0 0
19662 403.61 12 23 0 0 0 0 1 0 0
21531 498.58 12 46 0 0 0 0 1 0 0
22603 346.63 12 3 0 0 0 0 0 1 0
19901 403.61 14 12 1 1 0 0 1 0 0
12690 249.29 12 47 1 1 0 1 0 0 0
7329 664.77 12 34 0 0 0 1 0 0 0
7441 807.22 12 22 0 0 0 1 0 0 0
1860 1412.63 18 14 0 1 1 0 0 0 0
7539 807.22 10 27 0 0 0 1 0 0 0
20745 902.18 14 16 0 1 0 0 1 0 0
9449 98.77 13 -1 0 1 0 1 0 0 1
21575 474.83 10 12 0 0 0 0 1 0 0
2445 1020.89 13 42 0 1 1 0 0 0 0
23322 830.96 12 16 0 1 0 0 0 1 0
14657 830.96 18 29 0 0 0 0 1 0 0
24374 569.80 15 21 0 0 0 0 0 1 0
4022 1135.80 13 33 0 1 1 0 0 0 0
4371 379.87 16 17 0 1 1 0 0 0 0
19006 521.60 12 27 0 1 0 0 1 0 0
26989 345.68 16 8 0 1 0 0 0 1 0
24343 593.54 14 32 0 1 0 0 0 1 0
21663 284.90 8 29 0 1 0 0 1 0 0
6648 712.25 11 42 0 1 0 1 0 0 0
4625 593.54 16 5 0 1 1 0 0 0 0
7080 1103.40 12 40 0 1 0 1 0 0 0
22863 199.12 13 3 0 0 0 0 0 1 0
27419 142.45 12 0 0 1 0 0 0 1 0
3151 641.03 18 4 0 1 1 0 0 0 0
18806 261.16 13 7 0 0 0 0 1 0 0
17443 474.83 16 4 0 1 0 0 1 0 0
17341 641.03 14 20 0 1 0 0 1 0 0
437 607.05 7 41 0 0 1 0 0 0 0
14035 427.35 12 44 1 1 0 0 1 0 0
13930 1305.79 18 11 0 1 0 0 1 0 0
20996 261.16 12 4 0 1 0 0 1 0 0
27982 629.39 12 7 0 1 0 0 0 1 0
26901 546.06 15 39 0 1 0 0 0 1 0
8849 318.14 12 22 0 0 0 1 0 0 0
16676 1258.31 18 6 0 1 0 0 1 0 0
9533 664.77 12 19 0 1 0 1 0 0 0
27663 363.25 18 12 0 0 0 0 0 1 0
16411 322.89 13 10 0 0 0 0 1 0 0
25277 597.27 13 18 0 1 0 0 0 1 0
23436 323.34 16 8 0 1 0 0 0 1 0
12980 402.85 16 8 0 1 0 1 0 0 0
12567 522.32 12 14 0 1 0 1 0 0 0
5373 517.57 11 24 0 1 1 0 0 0 0
8028 664.77 8 43 0 1 0 1 0 0 0
11852 581.67 12 28 0 1 0 1 0 0 0
5797 493.83 16 18 0 1 1 0 0 0 0
26552 296.30 9 8 0 1 0 0 0 1 0
16842 92.59 11 1 1 0 0 0 1 0 1
14414 325.26 12 3 0 1 0 0 1 0 0
12109 320.51 15 1 0 1 0 1 0 0 0
10853 197.41 12 0 0 1 0 1 0 0 1
19360 226.76 10 12 1 0 0 0 1 0 0
1248 1471.98 18 27 0 1 1 0 0 0 0
8662 593.54 14 17 1 1 0 1 0 0 0
4606 849.50 8 18 0 1 1 0 0 0 0
9035 403.61 14 11 0 1 0 1 0 0 0
9600 690.77 12 17 0 1 0 1 0 0 0
4464 296.77 12 27 1 1 1 0 0 0 0
20562 783.48 15 18 0 1 0 0 1 0 0
20295 232.67 12 4 1 1 0 0 1 0 0
7684 415.48 12 11 0 0 0 1 0 0 0
7260 1210.83 12 30 0 0 0 1 0 0 0
2336 874.49 12 21 0 1 1 0 0 0 0
15120 830.96 9 30 0 1 0 0 1 0 0
15092 356.13 12 11 0 1 0 0 1 0 0
24227 546.06 18 11 0 1 0 0 0 1 0
6672 1020.89 12 34 0 1 0 1 0 0 0
12738 522.32 12 16 0 1 0 1 0 0 0
15601 522.32 9 15 0 0 0 0 1 0 0
21033 712.25 12 29 0 1 0 0 1 0 0
11576 283.95 16 0 0 1 0 1 0 0 0
21385 165.43 10 8 0 1 0 0 1 0 0
29 204.18 12 6 0 1 1 0 0 0 0
25909 4264.87 16 16 0 1 0 0 0 1 0
15411 422.36 12 42 1 1 0 0 1 0 0
12917 443.44 12 14 0 0 0 1 0 0 0
14404 997.15 12 31 0 1 0 0 1 0 0
11365 474.83 12 15 0 1 0 1 0 0 0
8296 717.77 16 13 0 1 0 1 0 0 0
28018 925.93 18 16 0 1 0 0 0 1 0
14754 1187.08 18 20 0 0 0 0 1 0 0
3850 474.83 15 33 0 0 1 0 0 0 0
4152 474.83 16 15 0 1 1 0 0 0 0
9332 1258.31 18 16 0 1 0 1 0 0 0
26049 237.42 12 4 0 1 0 0 0 1 0
8005 830.96 18 36 0 0 0 1 0 0 0
20100 466.39 14 34 0 0 0 0 1 0 0
18652 154.32 18 2 0 1 0 0 1 0 1
5279 498.58 12 44 0 1 1 0 0 0 0
5330 308.64 16 12 0 1 1 0 0 0 0
7104 375.31 12 4 0 1 0 1 0 0 0
3180 498.58 11 12 0 1 1 0 0 0 0
9092 123.46 12 4 0 0 0 1 0 0 0
779 432.10 12 6 0 0 1 0 0 0 0
3433 92.59 12 7 0 1 1 0 0 0 1
27388 474.83 12 5 0 1 0 0 0 1 0
14891 546.06 14 7 0 1 0 0 1 0 0
23821 246.91 12 11 0 1 0 0 0 1 0
25518 474.83 11 25 0 1 0 0 0 1 0
11203 427.35 13 12 0 0 0 1 0 0 0
11297 593.54 16 10 0 0 0 1 0 0 0
1598 949.67 16 28 0 1 1 0 0 0 0
1526 540.12 12 4 0 1 1 0 0 0 0
11462 391.74 16 3 0 0 0 1 0 0 0
2882 275.96 8 39 0 1 1 0 0 0 0
27774 347.22 14 0 0 1 0 0 0 1 0
23907 237.42 12 42 0 1 0 0 0 1 0
24169 144.75 10 6 0 1 0 0 0 1 0
14413 978.16 14 21 0 1 0 0 1 0 0
10163 444.44 13 14 0 0 0 1 0 0 0
12472 186.71 18 4 0 0 0 1 0 0 1
4195 918.38 9 16 0 1 1 0 0 0 0
16812 305.34 12 28 0 0 0 0 1 0 0
19068 1099.54 11 15 1 1 0 0 1 0 0
4182 205.76 14 1 0 1 1 0 0 0 0
17360 1006.50 18 27 0 1 0 0 1 0 0
14462 335.48 10 5 0 1 0 0 1 0 0
6216 949.67 12 23 0 1 1 0 0 0 0
2304 427.35 12 2 0 1 1 0 0 0 0
8453 1590.69 16 11 0 1 0 1 0 0 0
24281 356.13 16 5 0 1 0 0 0 1 0
26636 194.68 12 3 0 1 0 0 0 1 1
27901 1077.44 13 23 0 0 0 0 0 1 0
16165 332.38 12 4 0 1 0 0 1 0 0
17141 546.06 13 14 0 1 0 0 1 0 0
1647 522.32 12 38 0 0 1 0 0 0 0
24284 1039.89 13 34 0 1 0 0 0 1 0
3190 1780.63 14 33 0 1 1 0 0 0 0
12938 434.43 12 19 0 1 0 1 0 0 0
24346 760.78 16 20 0 1 0 0 0 1 0
235 1187.08 16 19 0 1 1 0 0 0 0
16899 819.09 11 13 0 1 0 0 1 0 0
15546 284.90 12 7 0 0 0 0 1 0 0
25398 498.58 13 9 0 1 0 0 0 1 0
23289 1187.08 11 35 0 1 0 0 0 1 0
15909 474.83 12 33 0 1 0 0 1 0 0
14036 451.09 12 32 1 1 0 0 1 0 0
6151 949.67 16 13 0 1 1 0 0 0 0
18163 1042.52 16 22 0 1 0 0 1 0 0
18669 92.59 8 11 0 1 0 0 1 0 0
8707 949.67 14 7 0 1 0 1 0 0 0
14308 474.83 16 9 0 1 0 0 1 0 0
27271 403.61 17 26 0 1 0 0 0 1 0
27392 569.80 14 7 0 1 0 0 0 1 0
22670 451.09 11 9 0 0 0 0 0 1 0
3113 830.96 14 12 0 1 1 0 0 0 0
16188 297.42 12 3 0 1 0 0 1 0 0
26129 118.71 11 6 0 1 0 0 0 1 1
2567 271.60 9 37 0 1 1 0 0 0 0
9537 878.44 16 1 0 1 0 1 0 0 0
21330 462.96 12 4 0 1 0 0 1 0 0
670 462.96 11 4 0 1 1 0 0 0 0
13060 534.19 8 48 0 0 0 1 0 0 0
4542 356.13 12 6 0 1 1 0 0 0 0
17364 155.27 12 7 0 1 0 0 1 0 0
15992 534.19 12 10 0 1 0 0 1 0 0
17619 854.70 14 19 0 1 0 0 1 0 0
8683 830.96 16 7 0 1 0 1 0 0 0
21652 949.67 18 5 0 1 0 0 1 0 0
5130 641.03 12 9 0 1 1 0 0 0 0
26158 835.45 10 41 0 1 0 0 0 1 0
10083 308.64 13 3 0 0 0 1 0 0 0
13333 712.25 13 11 0 1 0 0 1 0 0
28027 812.32 12 17 0 0 0 0 0 1 0
5320 555.56 12 5 1 1 1 0 0 0 0
19603 2374.15 12 5 1 0 0 0 1 0 0
19834 61.73 13 0 0 0 0 0 1 0 1
16099 664.77 12 19 0 0 0 0 1 0 0
19056 474.83 17 2 0 1 0 0 1 0 0
11956 668.85 10 48 0 0 0 1 0 0 1
20004 470.37 12 25 1 1 0 0 1 0 0
20846 189.93 16 0 0 1 0 0 1 0 1
17260 237.42 3 39 0 1 0 0 1 0 0
7710 830.96 12 27 0 1 0 1 0 0 0
6956 180.44 15 -1 0 1 0 1 0 0 0
23236 397.81 13 2 0 1 0 0 0 1 0
26071 617.28 16 45 0 1 0 0 0 1 1
4543 474.83 10 24 0 1 1 0 0 0 0
4591 1234.57 13 23 0 1 1 0 0 0 0
4759 1733.14 16 26 0 1 1 0 0 0 0
1549 593.54 12 9 0 1 1 0 0 0 0
22000 379.87 7 29 0 1 0 0 1 0 0
23393 498.58 12 13 0 1 0 0 0 1 0
171 653.59 16 36 0 0 1 0 0 0 0
17677 712.25 14 27 0 1 0 0 1 0 0
8175 344.25 6 15 0 1 0 1 0 0 0
5714 883.71 12 22 0 1 1 0 0 0 0
5838 356.13 16 9 0 1 1 0 0 0 0
2772 451.09 12 37 0 1 1 0 0 0 0
20542 506.49 12 11 0 1 0 0 1 0 0
20024 1092.12 18 3 0 1 0 0 1 0 0
10115 522.32 11 12 0 0 0 1 0 0 0
20508 474.83 18 18 0 1 0 0 1 0 0
13129 231.48 12 8 0 0 0 1 0 0 0
21674 470.09 16 9 0 0 0 0 1 0 0
8006 56.98 14 0 0 0 0 1 0 0 1
993 181.28 18 37 0 1 1 0 0 0 1
22765 1080.25 16 3 0 0 0 0 0 1 0
17040 474.83 12 10 0 1 0 0 1 0 0
1624 189.93 13 1 0 0 1 0 0 0 0
8468 514.40 12 42 0 1 0 1 0 0 0
24052 370.37 12 22 1 1 0 0 0 1 0
7686 496.11 12 13 0 0 0 1 0 0 0
23789 345.68 12 8 0 1 0 0 0 1 0
201 451.09 12 3 0 0 1 0 0 0 0
9268 878.44 16 16 1 1 0 1 0 0 0
11083 227.92 12 15 0 0 0 1 0 0 0
12213 188.46 16 28 0 0 0 1 0 0 0
7889 1020.89 13 21 0 0 0 1 0 0 0
21422 284.90 12 5 0 1 0 0 1 0 0
4243 391.74 12 43 0 1 1 0 0 0 0
2285 854.70 14 34 0 1 1 0 0 0 0
18466 688.51 12 20 0 0 0 0 1 0 0
5088 854.70 12 28 0 1 1 0 0 0 0
828 277.78 12 36 0 1 1 0 0 0 0
11936 593.54 12 17 0 0 0 1 0 0 0
9602 514.40 12 36 0 1 0 1 0 0 0
9655 1497.13 16 23 0 1 0 1 0 0 0
26927 902.18 18 7 0 1 0 0 0 1 0
23395 532.56 12 13 0 1 0 0 0 1 0
18750 252.53 9 15 0 0 0 0 1 0 0
13826 296.77 7 37 1 1 0 0 1 0 0
14532 408.36 11 16 1 1 0 0 1 0 0
4219 498.58 14 24 0 1 1 0 0 0 0
27787 892.59 13 0 0 0 0 0 0 1 0
4042 403.61 13 14 0 0 1 0 0 0 0
5758 408.73 12 4 0 1 1 0 0 0 0
23716 2374.15 17 23 0 0 0 0 0 1 0
25294 668.23 12 17 0 1 0 0 0 1 0
22710 354.94 12 16 0 0 0 0 0 1 0
4014 78.56 14 0 0 0 1 0 0 0 1
25636 493.83 12 10 0 1 0 0 0 1 0
24920 455.84 12 23 0 1 0 0 0 1 0
4078 389.36 12 6 0 0 1 0 0 0 0
2241 474.43 12 13 0 1 1 0 0 0 0
24463 474.83 12 13 0 0 0 0 0 1 0
392 522.32 12 5 0 1 1 0 0 0 0
24992 353.75 15 14 0 1 0 0 0 1 0
27585 308.64 16 0 0 1 0 0 0 1 0
22703 783.48 12 12 0 0 0 0 0 1 0
13041 254.04 13 12 0 1 0 1 0 0 0
6449 90.22 18 44 1 1 0 1 0 0 1
18076 121.91 12 7 1 0 0 0 1 0 0
21619 759.73 17 18 0 1 0 0 1 0 0
13842 1220.77 14 38 0 1 0 0 1 0 0
1547 246.91 4 36 0 1 1 0 0 0 0
22126 712.25 13 7 0 0 0 0 0 1 0
1983 987.65 17 4 0 1 1 0 0 0 1
25674 356.13 4 28 0 1 0 0 0 1 0
25309 664.77 14 33 0 0 0 0 0 1 0
355 451.09 12 7 0 0 1 0 0 0 0
9316 313.63 14 17 0 1 0 1 0 0 0
9675 386.99 12 18 0 1 0 1 0 0 0
1682 356.13 15 15 0 1 1 0 0 0 0
18010 149.00 13 1 0 1 0 0 1 0 0
8730 474.83 14 7 0 1 0 1 0 0 0
20754 617.28 16 3 0 1 0 0 1 0 0
12845 188.27 15 31 0 0 0 1 0 0 1
6952 664.77 14 26 0 1 0 1 0 0 0
937 735.99 12 18 0 1 1 0 0 0 0
1482 498.58 14 4 0 1 1 0 0 0 0
9096 557.12 12 12 0 0 0 1 0 0 0
2266 506.49 15 4 0 1 1 0 0 0 0
1182 308.64 12 3 0 1 1 0 0 0 0
24810 411.52 16 4 0 1 0 0 0 1 0
25028 688.51 12 25 0 0 0 0 0 1 0
10005 782.38 9 36 0 1 0 1 0 0 0
3788 439.22 10 24 0 0 1 0 0 0 0
11284 388.01 13 5 0 1 0 1 0 0 1
27779 664.77 14 9 0 1 0 0 0 1 0
22031 216.05 12 6 0 1 0 0 1 0 0
4379 1068.38 16 13 1 1 1 0 0 0 0
6393 759.73 10 48 0 1 1 0 0 0 0
21310 295.22 12 2 0 1 0 0 1 0 0
391 522.32 12 8 0 1 1 0 0 0 0
6733 949.67 16 40 0 1 0 1 0 0 0
24776 807.22 12 26 0 1 0 0 0 1 0
10469 830.96 12 14 0 1 0 1 0 0 0
21100 498.58 12 23 0 1 0 0 1 0 0
17462 604.69 18 24 0 1 0 0 1 0 0
25981 804.84 5 21 0 1 0 0 0 1 0
12633 121.08 13 -1 0 1 0 1 0 0 1
20805 142.45 6 11 0 1 0 0 1 0 0
17528 349.79 12 48 0 1 0 0 1 0 0
15354 335.10 12 0 0 1 0 0 1 0 0
7267 949.67 13 31 0 1 0 1 0 0 0
21730 427.35 14 23 0 1 0 0 1 0 0
4154 1424.50 17 26 0 1 1 0 0 0 0
16185 641.03 16 13 0 1 0 0 1 0 0
27997 1282.05 12 43 0 1 0 0 0 1 0
4503 522.32 12 3 0 1 1 0 0 0 0
22990 569.80 14 36 0 0 0 0 0 1 0
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15222 546.06 12 39 0 1 0 0 1 0 0
20536 356.13 12 11 0 1 0 0 1 0 0
6113 385.09 13 13 0 1 1 0 0 0 0
23938 474.83 12 17 0 1 0 0 0 1 0
9690 1780.63 16 38 0 1 0 1 0 0 0
16173 118.71 13 10 1 1 0 0 1 0 0
12323 580.97 12 43 0 0 0 1 0 0 0
13197 494.78 18 38 0 0 0 1 0 0 0
20826 961.54 16 30 0 1 0 0 1 0 0
1011 688.51 10 16 0 1 1 0 0 0 0
1400 807.22 16 15 0 0 1 0 0 0 0
19615 712.25 7 38 0 1 0 0 1 0 0
15406 332.38 15 10 1 1 0 0 1 0 0
10918 468.09 16 18 0 1 0 1 0 0 0
24255 584.00 16 15 0 1 0 0 0 1 0
3639 427.35 13 4 0 1 1 0 0 0 0
5906 185.19 18 25 0 1 1 0 0 0 0
14914 712.25 12 10 0 1 0 0 1 0 0

Data cleaning

  • Let’s check to see if the data need cleaning

Check for unusual values

summary(uswages)
##       wage              educ           exper            race      
##  Min.   :  50.39   Min.   : 0.00   Min.   :-2.00   Min.   :0.000  
##  1st Qu.: 308.64   1st Qu.:12.00   1st Qu.: 8.00   1st Qu.:0.000  
##  Median : 522.32   Median :12.00   Median :15.00   Median :0.000  
##  Mean   : 608.12   Mean   :13.11   Mean   :18.41   Mean   :0.078  
##  3rd Qu.: 783.48   3rd Qu.:16.00   3rd Qu.:27.00   3rd Qu.:0.000  
##  Max.   :7716.05   Max.   :18.00   Max.   :59.00   Max.   :1.000  
##       smsa             ne              mw               so        
##  Min.   :0.000   Min.   :0.000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:1.000   1st Qu.:0.000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :1.000   Median :0.000   Median :0.0000   Median :0.0000  
##  Mean   :0.756   Mean   :0.229   Mean   :0.2485   Mean   :0.3125  
##  3rd Qu.:1.000   3rd Qu.:0.000   3rd Qu.:0.0000   3rd Qu.:1.0000  
##  Max.   :1.000   Max.   :1.000   Max.   :1.0000   Max.   :1.0000  
##        we             pt        
##  Min.   :0.00   Min.   :0.0000  
##  1st Qu.:0.00   1st Qu.:0.0000  
##  Median :0.00   Median :0.0000  
##  Mean   :0.21   Mean   :0.0925  
##  3rd Qu.:0.00   3rd Qu.:0.0000  
##  Max.   :1.00   Max.   :1.0000
  • exper cannot be negative
  • convert negatives to NA
# we see that exper has neg. values
uswages$exper[uswages$exper <0] <-NA

Convert catagorical variables to factors

  • We see that race, smsa, and pt are categorical variables
  • convert to factor variables
  • apply appropriate labels
# convert race, smsa, and pt to factor variables
uswages$race <- factor(uswages$race)
levels(uswages$race) <- c("White","Black")
uswages$smsa <- factor(uswages$smsa)
levels(uswages$smsa) <- c("No","Yes")
uswages$pt <- factor(uswages$pt)
levels(uswages$pt) <- c("No","Yes")

Convert a set of dummy variables to one factor

  • The four regions ne, mw, so, we are dummy (or indicator or binary) variables
  • create a new variable and call it region, make it a factor variable based on the four regions, give it appropriate labels
# create region, a factor variable based on the four regions ne, mw, so, we
uswages <- data.frame(uswages, region = 
                        1*uswages$ne +
                        2*uswages$mw +
                        3*uswages$so +
                        4*uswages$we)
uswages$region <- factor(uswages$region)
levels(uswages$region) <- c("ne","mw","so","we")
formattable::formattable(uswages)
wage educ exper race smsa ne mw so we pt region
6085 771.60 18 18 White Yes 1 0 0 0 No ne
23701 617.28 15 20 White Yes 0 0 0 1 No we
16208 957.83 16 9 White Yes 0 0 1 0 No so
2720 617.28 12 24 White Yes 1 0 0 0 No ne
9723 902.18 14 12 White Yes 0 1 0 0 No mw
22239 299.15 12 33 White Yes 0 0 0 1 No we
14379 541.31 16 42 White Yes 0 0 1 0 Yes so
12878 148.39 16 0 White Yes 0 1 0 0 Yes mw
23121 273.19 12 36 White Yes 0 0 0 1 Yes we
13086 666.67 12 37 White No 0 1 0 0 No mw
19913 241.50 9 20 Black Yes 0 0 1 0 Yes so
20055 703.79 14 29 White Yes 0 0 1 0 No so
6076 550.81 17 16 White No 1 0 0 0 No ne
24050 807.22 14 21 White Yes 0 0 0 1 Yes we
11064 712.25 14 11 White No 0 1 0 0 No mw
26395 351.46 10 10 White Yes 0 0 0 1 No we
15576 373.24 12 8 White No 0 0 1 0 No so
18936 759.73 13 19 White Yes 0 0 1 0 No so
4747 356.13 14 6 White Yes 1 0 0 0 No ne
21572 308.64 16 0 White Yes 0 0 1 0 No so
14575 469.14 6 24 White No 0 0 1 0 No so
15065 617.28 16 NA White Yes 0 0 1 0 No so
23270 123.46 16 1 White Yes 0 0 0 1 Yes we
11093 474.83 12 11 White No 0 1 0 0 No mw
8830 261.16 12 40 White Yes 0 1 0 0 No mw
9219 284.90 12 5 White Yes 0 1 0 0 No mw
28065 1661.92 12 15 White Yes 0 0 0 1 No we
1339 629.15 12 44 White Yes 1 0 0 0 No ne
13462 2374.15 12 35 White Yes 0 0 1 0 No so
10787 522.32 16 8 White Yes 0 1 0 0 No mw
11423 688.51 14 12 White Yes 0 1 0 0 No mw
15657 246.91 9 13 White Yes 0 0 1 0 No so
2698 949.67 5 55 Black Yes 1 0 0 0 No ne
14276 261.16 14 7 Black Yes 0 0 1 0 No so
10854 106.86 10 52 White Yes 0 1 0 0 Yes mw
7510 296.77 12 11 White Yes 0 1 0 0 No mw
26838 379.87 14 8 White Yes 0 0 0 1 No we
21118 634.92 9 19 White Yes 0 0 1 0 No so
10875 1182.03 12 45 White Yes 0 1 0 0 No mw
8891 740.74 12 9 White Yes 0 1 0 0 No mw
15487 237.42 10 12 Black Yes 0 0 1 0 No so
6090 144.03 12 0 White Yes 1 0 0 0 No ne
2293 406.96 14 11 White No 1 0 0 0 No ne
8794 351.61 9 10 White No 0 1 0 0 No mw
3544 593.54 12 10 White Yes 1 0 0 0 No ne
23320 273.03 14 4 White Yes 0 0 0 1 No we
23176 997.15 12 44 White Yes 0 0 0 1 No we
4938 1198.96 12 34 White Yes 1 0 0 0 No ne
12672 569.80 15 15 White Yes 0 1 0 0 No mw
8971 130.58 12 4 White Yes 0 1 0 0 No mw
16287 641.03 13 16 Black Yes 0 0 1 0 No so
15181 712.25 14 25 White Yes 0 0 1 0 No so
3554 1073.12 16 8 White Yes 1 0 0 0 No ne
26446 712.25 16 13 White Yes 0 0 0 1 No we
8698 261.16 12 35 White Yes 0 1 0 0 No mw
9899 783.48 16 4 White Yes 0 1 0 0 No mw
18503 197.53 12 8 Black Yes 0 0 1 0 Yes so
27829 720.16 12 28 Black Yes 0 0 0 1 No we
10616 593.54 14 18 White Yes 0 1 0 0 No mw
24172 1234.57 18 7 White Yes 0 0 0 1 No we
14806 533.87 12 9 White No 0 0 1 0 No so
4777 712.25 16 6 White Yes 1 0 0 0 No ne
9322 909.31 16 9 White Yes 0 1 0 0 No mw
16555 356.13 12 14 Black Yes 0 0 1 0 No so
26982 759.73 14 11 White Yes 0 0 0 1 No we
19738 382.74 8 42 White Yes 0 0 1 0 No so
16707 53.70 9 22 Black Yes 0 0 1 0 Yes so
6352 403.61 12 12 White No 1 0 0 0 No ne
19667 664.77 12 15 White Yes 0 0 1 0 No so
17679 415.48 13 21 White Yes 0 0 1 0 No so
17796 949.67 16 21 White Yes 0 0 1 0 No so
27009 664.77 12 15 White Yes 0 0 0 1 No we
3901 308.64 10 51 White No 1 0 0 0 No ne
27986 997.15 12 11 White Yes 0 0 0 1 No we
3303 2374.15 18 27 White Yes 1 0 0 0 No ne
15785 259.73 12 1 White No 0 0 1 0 No so
119 641.03 13 27 White No 1 0 0 0 No ne
11397 411.52 12 11 White Yes 0 1 0 0 No mw
7461 379.87 12 23 Black Yes 0 1 0 0 No mw
6106 231.48 16 11 White Yes 1 0 0 0 No ne
12956 142.45 12 4 White No 0 1 0 0 No mw
7371 503.70 11 6 White No 0 1 0 0 No mw
8854 94.59 14 4 White Yes 0 1 0 0 Yes mw
5540 1234.57 18 3 White Yes 1 0 0 0 No ne
21727 379.87 4 34 White No 0 0 1 0 No so
7385 391.74 12 15 White Yes 0 1 0 0 No mw
612 411.70 12 19 White No 1 0 0 0 No ne
21394 1068.38 14 31 White Yes 0 0 1 0 No so
9748 123.46 15 NA White Yes 0 1 0 0 No mw
10401 569.80 12 37 White Yes 0 1 0 0 No mw
8748 94.97 13 32 White No 0 1 0 0 Yes mw
7702 474.83 8 46 White Yes 0 1 0 0 No mw
18839 379.87 12 12 White Yes 0 0 1 0 No so
16131 118.71 3 56 White No 0 0 1 0 Yes so
10609 90.22 12 1 White No 0 1 0 0 No mw
3648 402.17 10 8 White Yes 1 0 0 0 No ne
20327 1344.78 16 12 White Yes 0 0 1 0 No so
26747 474.83 16 27 White Yes 0 0 0 1 No we
24480 356.13 9 45 White Yes 0 0 0 1 No we
25209 197.53 12 2 White Yes 0 0 0 1 No we
4795 949.67 11 19 Black Yes 1 0 0 0 No ne
10301 531.81 18 11 White No 0 1 0 0 Yes mw
22061 522.32 12 16 White No 0 0 1 0 No so
12857 356.13 18 32 White Yes 0 1 0 0 No mw
24745 949.67 12 35 White Yes 0 0 0 1 No we
16118 902.18 18 14 White Yes 0 0 1 0 No so
27977 1697.72 18 12 White No 0 0 0 1 No we
25363 451.09 14 16 White No 0 0 0 1 No we
6986 830.96 16 37 White Yes 0 1 0 0 No mw
24174 807.22 14 16 White Yes 0 0 0 1 No we
26144 617.28 6 23 White Yes 0 0 0 1 No we
9238 271.60 13 1 White Yes 0 1 0 0 No mw
7572 462.99 12 10 White No 0 1 0 0 No mw
22024 336.70 13 17 White Yes 0 0 1 0 No so
20215 593.54 16 4 White Yes 0 0 1 0 No so
26010 189.93 8 43 White Yes 0 0 0 1 No we
7945 119.66 14 3 White No 0 1 0 0 No mw
18821 641.03 13 15 White No 0 0 1 0 No so
3395 76.43 13 NA White Yes 1 0 0 0 Yes ne
4310 493.83 14 0 White Yes 1 0 0 0 No ne
22040 679.01 16 23 White No 0 0 1 0 No so
18395 308.64 10 10 White Yes 0 0 1 0 No so
26521 130.58 12 11 White Yes 0 0 0 1 Yes we
6305 56.79 14 0 White No 1 0 0 0 Yes ne
2330 1899.34 14 30 White Yes 1 0 0 0 No ne
27898 1316.87 12 15 White No 0 0 0 1 No we
2245 830.96 18 0 White Yes 1 0 0 0 No ne
23041 784.69 14 15 White No 0 0 0 1 No we
6736 1139.60 16 5 White Yes 0 1 0 0 No mw
27500 167.55 12 2 White Yes 0 0 0 1 No we
2224 712.25 12 42 White Yes 1 0 0 0 No ne
6712 845.20 14 13 White Yes 0 1 0 0 No mw
15738 315.82 12 18 White Yes 0 0 1 0 No so
25092 183.42 10 6 White Yes 0 0 0 1 No we
5494 337.08 9 43 White Yes 1 0 0 0 No ne
13670 493.83 11 3 White Yes 0 0 1 0 No so
20453 854.70 18 25 White No 0 0 1 0 No so
14818 885.57 12 20 White No 0 0 1 0 No so
24711 1033.01 18 3 White No 0 0 0 1 No we
4526 403.61 13 5 White Yes 1 0 0 0 No ne
7363 522.32 16 7 White Yes 0 1 0 0 No mw
18966 197.53 12 19 Black Yes 0 0 1 0 No so
10371 308.64 12 4 White Yes 0 1 0 0 No mw
22716 521.94 12 42 White No 0 0 0 1 No we
3094 367.74 16 8 White Yes 1 0 0 0 No ne
6244 236.42 12 13 White Yes 1 0 0 0 No ne
85 569.80 8 36 White Yes 1 0 0 0 No ne
10912 641.03 16 16 White Yes 0 1 0 0 No mw
26199 783.48 16 10 White Yes 0 0 0 1 No we
1514 189.93 15 NA White Yes 1 0 0 0 No ne
13332 500.95 17 1 White Yes 0 0 1 0 No so
13016 593.54 12 12 White Yes 0 1 0 0 No mw
8931 154.32 13 1 White Yes 0 1 0 0 Yes mw
12447 721.45 8 47 White Yes 0 1 0 0 No mw
6079 522.32 10 24 Black Yes 1 0 0 0 No ne
6635 1234.57 14 21 White Yes 0 1 0 0 No mw
25763 123.46 16 9 White Yes 0 0 0 1 Yes we
18783 546.06 12 21 White No 0 0 1 0 No so
24442 1305.79 18 19 White No 0 0 0 1 No we
20029 522.32 18 12 White Yes 0 0 1 0 No so
16431 379.87 12 19 White No 0 0 1 0 No so
977 866.57 18 14 White Yes 1 0 0 0 No ne
4269 689.53 11 38 White Yes 1 0 0 0 No ne
19267 346.63 12 38 White No 0 0 1 0 No so
19620 379.87 13 5 White No 0 0 1 0 No so
15685 370.37 3 49 White Yes 0 0 1 0 No so
26 546.06 12 16 White Yes 1 0 0 0 No ne
9511 1305.79 12 18 White Yes 0 1 0 0 No mw
6369 498.58 12 17 White No 1 0 0 0 No ne
3858 241.21 12 0 White No 1 0 0 0 No ne
4020 195.46 12 5 Black Yes 1 0 0 0 No ne
17173 160.49 12 21 Black Yes 0 0 1 0 No so
25293 470.09 12 25 White Yes 0 0 0 1 No we
19611 415.48 12 40 White No 0 0 1 0 No so
749 830.96 12 27 White No 1 0 0 0 No ne
23472 668.47 14 21 White Yes 0 0 0 1 No we
4190 997.15 18 6 White Yes 1 0 0 0 No ne
24273 1111.11 18 28 White Yes 0 0 0 1 No we
5642 384.62 12 31 White Yes 1 0 0 0 No ne
1845 462.96 12 13 White Yes 1 0 0 0 No ne
25642 189.93 1 49 White Yes 0 0 0 1 No we
1776 683.76 9 46 White Yes 1 0 0 0 No ne
19914 61.73 12 17 Black Yes 0 0 1 0 Yes so
11450 664.77 16 9 White Yes 0 1 0 0 No mw
23203 679.01 16 7 White Yes 0 0 0 1 No we
26631 740.74 13 13 White Yes 0 0 0 1 No we
5814 617.28 12 25 White Yes 1 0 0 0 No ne
18808 142.45 9 46 White No 0 0 1 0 No so
12836 1264.13 18 36 White Yes 0 1 0 0 No mw
9363 830.96 12 25 White Yes 0 1 0 0 No mw
15041 747.86 16 12 White Yes 0 0 1 0 No so
21760 284.90 12 9 White Yes 0 0 1 0 No so
27384 1049.38 12 9 White Yes 0 0 0 1 No we
19119 213.68 12 2 Black No 0 0 1 0 No so
18296 854.70 13 38 White No 0 0 1 0 No so
7176 617.28 11 15 White Yes 0 1 0 0 No mw
5405 284.90 5 54 White Yes 1 0 0 0 No ne
19662 403.61 12 23 White No 0 0 1 0 No so
21531 498.58 12 46 White No 0 0 1 0 No so
22603 346.63 12 3 White No 0 0 0 1 No we
19901 403.61 14 12 Black Yes 0 0 1 0 No so
12690 249.29 12 47 Black Yes 0 1 0 0 No mw
7329 664.77 12 34 White No 0 1 0 0 No mw
7441 807.22 12 22 White No 0 1 0 0 No mw
1860 1412.63 18 14 White Yes 1 0 0 0 No ne
7539 807.22 10 27 White No 0 1 0 0 No mw
20745 902.18 14 16 White Yes 0 0 1 0 No so
9449 98.77 13 NA White Yes 0 1 0 0 Yes mw
21575 474.83 10 12 White No 0 0 1 0 No so
2445 1020.89 13 42 White Yes 1 0 0 0 No ne
23322 830.96 12 16 White Yes 0 0 0 1 No we
14657 830.96 18 29 White No 0 0 1 0 No so
24374 569.80 15 21 White No 0 0 0 1 No we
4022 1135.80 13 33 White Yes 1 0 0 0 No ne
4371 379.87 16 17 White Yes 1 0 0 0 No ne
19006 521.60 12 27 White Yes 0 0 1 0 No so
26989 345.68 16 8 White Yes 0 0 0 1 No we
24343 593.54 14 32 White Yes 0 0 0 1 No we
21663 284.90 8 29 White Yes 0 0 1 0 No so
6648 712.25 11 42 White Yes 0 1 0 0 No mw
4625 593.54 16 5 White Yes 1 0 0 0 No ne
7080 1103.40 12 40 White Yes 0 1 0 0 No mw
22863 199.12 13 3 White No 0 0 0 1 No we
27419 142.45 12 0 White Yes 0 0 0 1 No we
3151 641.03 18 4 White Yes 1 0 0 0 No ne
18806 261.16 13 7 White No 0 0 1 0 No so
17443 474.83 16 4 White Yes 0 0 1 0 No so
17341 641.03 14 20 White Yes 0 0 1 0 No so
437 607.05 7 41 White No 1 0 0 0 No ne
14035 427.35 12 44 Black Yes 0 0 1 0 No so
13930 1305.79 18 11 White Yes 0 0 1 0 No so
20996 261.16 12 4 White Yes 0 0 1 0 No so
27982 629.39 12 7 White Yes 0 0 0 1 No we
26901 546.06 15 39 White Yes 0 0 0 1 No we
8849 318.14 12 22 White No 0 1 0 0 No mw
16676 1258.31 18 6 White Yes 0 0 1 0 No so
9533 664.77 12 19 White Yes 0 1 0 0 No mw
27663 363.25 18 12 White No 0 0 0 1 No we
16411 322.89 13 10 White No 0 0 1 0 No so
25277 597.27 13 18 White Yes 0 0 0 1 No we
23436 323.34 16 8 White Yes 0 0 0 1 No we
12980 402.85 16 8 White Yes 0 1 0 0 No mw
12567 522.32 12 14 White Yes 0 1 0 0 No mw
5373 517.57 11 24 White Yes 1 0 0 0 No ne
8028 664.77 8 43 White Yes 0 1 0 0 No mw
11852 581.67 12 28 White Yes 0 1 0 0 No mw
5797 493.83 16 18 White Yes 1 0 0 0 No ne
26552 296.30 9 8 White Yes 0 0 0 1 No we
16842 92.59 11 1 Black No 0 0 1 0 Yes so
14414 325.26 12 3 White Yes 0 0 1 0 No so
12109 320.51 15 1 White Yes 0 1 0 0 No mw
10853 197.41 12 0 White Yes 0 1 0 0 Yes mw
19360 226.76 10 12 Black No 0 0 1 0 No so
1248 1471.98 18 27 White Yes 1 0 0 0 No ne
8662 593.54 14 17 Black Yes 0 1 0 0 No mw
4606 849.50 8 18 White Yes 1 0 0 0 No ne
9035 403.61 14 11 White Yes 0 1 0 0 No mw
9600 690.77 12 17 White Yes 0 1 0 0 No mw
4464 296.77 12 27 Black Yes 1 0 0 0 No ne
20562 783.48 15 18 White Yes 0 0 1 0 No so
20295 232.67 12 4 Black Yes 0 0 1 0 No so
7684 415.48 12 11 White No 0 1 0 0 No mw
7260 1210.83 12 30 White No 0 1 0 0 No mw
2336 874.49 12 21 White Yes 1 0 0 0 No ne
15120 830.96 9 30 White Yes 0 0 1 0 No so
15092 356.13 12 11 White Yes 0 0 1 0 No so
24227 546.06 18 11 White Yes 0 0 0 1 No we
6672 1020.89 12 34 White Yes 0 1 0 0 No mw
12738 522.32 12 16 White Yes 0 1 0 0 No mw
15601 522.32 9 15 White No 0 0 1 0 No so
21033 712.25 12 29 White Yes 0 0 1 0 No so
11576 283.95 16 0 White Yes 0 1 0 0 No mw
21385 165.43 10 8 White Yes 0 0 1 0 No so
29 204.18 12 6 White Yes 1 0 0 0 No ne
25909 4264.87 16 16 White Yes 0 0 0 1 No we
15411 422.36 12 42 Black Yes 0 0 1 0 No so
12917 443.44 12 14 White No 0 1 0 0 No mw
14404 997.15 12 31 White Yes 0 0 1 0 No so
11365 474.83 12 15 White Yes 0 1 0 0 No mw
8296 717.77 16 13 White Yes 0 1 0 0 No mw
28018 925.93 18 16 White Yes 0 0 0 1 No we
14754 1187.08 18 20 White No 0 0 1 0 No so
3850 474.83 15 33 White No 1 0 0 0 No ne
4152 474.83 16 15 White Yes 1 0 0 0 No ne
9332 1258.31 18 16 White Yes 0 1 0 0 No mw
26049 237.42 12 4 White Yes 0 0 0 1 No we
8005 830.96 18 36 White No 0 1 0 0 No mw
20100 466.39 14 34 White No 0 0 1 0 No so
18652 154.32 18 2 White Yes 0 0 1 0 Yes so
5279 498.58 12 44 White Yes 1 0 0 0 No ne
5330 308.64 16 12 White Yes 1 0 0 0 No ne
7104 375.31 12 4 White Yes 0 1 0 0 No mw
3180 498.58 11 12 White Yes 1 0 0 0 No ne
9092 123.46 12 4 White No 0 1 0 0 No mw
779 432.10 12 6 White No 1 0 0 0 No ne
3433 92.59 12 7 White Yes 1 0 0 0 Yes ne
27388 474.83 12 5 White Yes 0 0 0 1 No we
14891 546.06 14 7 White Yes 0 0 1 0 No so
23821 246.91 12 11 White Yes 0 0 0 1 No we
25518 474.83 11 25 White Yes 0 0 0 1 No we
11203 427.35 13 12 White No 0 1 0 0 No mw
11297 593.54 16 10 White No 0 1 0 0 No mw
1598 949.67 16 28 White Yes 1 0 0 0 No ne
1526 540.12 12 4 White Yes 1 0 0 0 No ne
11462 391.74 16 3 White No 0 1 0 0 No mw
2882 275.96 8 39 White Yes 1 0 0 0 No ne
27774 347.22 14 0 White Yes 0 0 0 1 No we
23907 237.42 12 42 White Yes 0 0 0 1 No we
24169 144.75 10 6 White Yes 0 0 0 1 No we
14413 978.16 14 21 White Yes 0 0 1 0 No so
10163 444.44 13 14 White No 0 1 0 0 No mw
12472 186.71 18 4 White No 0 1 0 0 Yes mw
4195 918.38 9 16 White Yes 1 0 0 0 No ne
16812 305.34 12 28 White No 0 0 1 0 No so
19068 1099.54 11 15 Black Yes 0 0 1 0 No so
4182 205.76 14 1 White Yes 1 0 0 0 No ne
17360 1006.50 18 27 White Yes 0 0 1 0 No so
14462 335.48 10 5 White Yes 0 0 1 0 No so
6216 949.67 12 23 White Yes 1 0 0 0 No ne
2304 427.35 12 2 White Yes 1 0 0 0 No ne
8453 1590.69 16 11 White Yes 0 1 0 0 No mw
24281 356.13 16 5 White Yes 0 0 0 1 No we
26636 194.68 12 3 White Yes 0 0 0 1 Yes we
27901 1077.44 13 23 White No 0 0 0 1 No we
16165 332.38 12 4 White Yes 0 0 1 0 No so
17141 546.06 13 14 White Yes 0 0 1 0 No so
1647 522.32 12 38 White No 1 0 0 0 No ne
24284 1039.89 13 34 White Yes 0 0 0 1 No we
3190 1780.63 14 33 White Yes 1 0 0 0 No ne
12938 434.43 12 19 White Yes 0 1 0 0 No mw
24346 760.78 16 20 White Yes 0 0 0 1 No we
235 1187.08 16 19 White Yes 1 0 0 0 No ne
16899 819.09 11 13 White Yes 0 0 1 0 No so
15546 284.90 12 7 White No 0 0 1 0 No so
25398 498.58 13 9 White Yes 0 0 0 1 No we
23289 1187.08 11 35 White Yes 0 0 0 1 No we
15909 474.83 12 33 White Yes 0 0 1 0 No so
14036 451.09 12 32 Black Yes 0 0 1 0 No so
6151 949.67 16 13 White Yes 1 0 0 0 No ne
18163 1042.52 16 22 White Yes 0 0 1 0 No so
18669 92.59 8 11 White Yes 0 0 1 0 No so
8707 949.67 14 7 White Yes 0 1 0 0 No mw
14308 474.83 16 9 White Yes 0 0 1 0 No so
27271 403.61 17 26 White Yes 0 0 0 1 No we
27392 569.80 14 7 White Yes 0 0 0 1 No we
22670 451.09 11 9 White No 0 0 0 1 No we
3113 830.96 14 12 White Yes 1 0 0 0 No ne
16188 297.42 12 3 White Yes 0 0 1 0 No so
26129 118.71 11 6 White Yes 0 0 0 1 Yes we
2567 271.60 9 37 White Yes 1 0 0 0 No ne
9537 878.44 16 1 White Yes 0 1 0 0 No mw
21330 462.96 12 4 White Yes 0 0 1 0 No so
670 462.96 11 4 White Yes 1 0 0 0 No ne
13060 534.19 8 48 White No 0 1 0 0 No mw
4542 356.13 12 6 White Yes 1 0 0 0 No ne
17364 155.27 12 7 White Yes 0 0 1 0 No so
15992 534.19 12 10 White Yes 0 0 1 0 No so
17619 854.70 14 19 White Yes 0 0 1 0 No so
8683 830.96 16 7 White Yes 0 1 0 0 No mw
21652 949.67 18 5 White Yes 0 0 1 0 No so
5130 641.03 12 9 White Yes 1 0 0 0 No ne
26158 835.45 10 41 White Yes 0 0 0 1 No we
10083 308.64 13 3 White No 0 1 0 0 No mw
13333 712.25 13 11 White Yes 0 0 1 0 No so
28027 812.32 12 17 White No 0 0 0 1 No we
5320 555.56 12 5 Black Yes 1 0 0 0 No ne
19603 2374.15 12 5 Black No 0 0 1 0 No so
19834 61.73 13 0 White No 0 0 1 0 Yes so
16099 664.77 12 19 White No 0 0 1 0 No so
19056 474.83 17 2 White Yes 0 0 1 0 No so
11956 668.85 10 48 White No 0 1 0 0 Yes mw
20004 470.37 12 25 Black Yes 0 0 1 0 No so
20846 189.93 16 0 White Yes 0 0 1 0 Yes so
17260 237.42 3 39 White Yes 0 0 1 0 No so
7710 830.96 12 27 White Yes 0 1 0 0 No mw
6956 180.44 15 NA White Yes 0 1 0 0 No mw
23236 397.81 13 2 White Yes 0 0 0 1 No we
26071 617.28 16 45 White Yes 0 0 0 1 Yes we
4543 474.83 10 24 White Yes 1 0 0 0 No ne
4591 1234.57 13 23 White Yes 1 0 0 0 No ne
4759 1733.14 16 26 White Yes 1 0 0 0 No ne
1549 593.54 12 9 White Yes 1 0 0 0 No ne
22000 379.87 7 29 White Yes 0 0 1 0 No so
23393 498.58 12 13 White Yes 0 0 0 1 No we
171 653.59 16 36 White No 1 0 0 0 No ne
17677 712.25 14 27 White Yes 0 0 1 0 No so
8175 344.25 6 15 White Yes 0 1 0 0 No mw
5714 883.71 12 22 White Yes 1 0 0 0 No ne
5838 356.13 16 9 White Yes 1 0 0 0 No ne
2772 451.09 12 37 White Yes 1 0 0 0 No ne
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7 284.90 8 51 White Yes 1 0 0 0 No ne
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23400 118.71 15 11 White Yes 0 0 0 1 Yes we
5398 588.21 12 7 White Yes 1 0 0 0 No ne
23739 231.48 12 32 White No 0 0 0 1 No we
21587 830.96 17 4 White Yes 0 0 1 0 No so
17911 515.19 16 22 White Yes 0 0 1 0 No so
18311 759.73 12 13 White No 0 0 1 0 No so
574 510.45 15 19 White Yes 1 0 0 0 No ne
694 759.73 16 33 White No 1 0 0 0 No ne
5444 54.01 12 0 White Yes 1 0 0 0 Yes ne
23627 148.15 6 11 White No 0 0 0 1 No we
10738 102.88 12 0 White Yes 0 1 0 0 Yes mw
26011 86.13 12 0 White Yes 0 0 0 1 Yes we
25476 498.58 14 9 Black Yes 0 0 0 1 No we
16563 664.77 13 32 White Yes 0 0 1 0 No so
17498 679.01 13 20 White Yes 0 0 1 0 No so
15230 274.35 12 9 White Yes 0 0 1 0 No so
4878 1068.38 16 38 White Yes 1 0 0 0 No ne
14623 459.94 11 16 White No 0 0 1 0 No so
16934 356.13 13 30 White Yes 0 0 1 0 No so
1136 1424.50 16 19 White Yes 1 0 0 0 No ne
5437 949.67 18 27 White Yes 1 0 0 0 No ne
16074 455.65 14 8 White No 0 0 1 0 No so
8235 85.66 13 0 Black Yes 0 1 0 0 Yes mw
4994 329.22 15 NA White Yes 1 0 0 0 No ne
3265 1329.53 15 10 White Yes 1 0 0 0 No ne
7596 2374.15 18 30 White No 0 1 0 0 No mw
7007 522.32 12 7 White Yes 0 1 0 0 No mw
8467 949.67 11 43 White Yes 0 1 0 0 No mw
8392 958.62 12 30 White Yes 0 1 0 0 No mw
3558 66.48 12 52 White Yes 1 0 0 0 Yes ne
16239 1266.22 16 6 White Yes 0 0 1 0 No so
10486 123.46 12 43 White Yes 0 1 0 0 No mw
15378 759.73 11 20 White Yes 0 0 1 0 No so
17885 356.13 14 35 Black Yes 0 0 1 0 No so
27881 854.70 12 23 White Yes 0 0 0 1 No we
20159 688.51 15 29 White Yes 0 0 1 0 No so
27692 53.83 12 1 Black Yes 0 0 0 1 No we
9106 333.33 12 7 White No 0 1 0 0 No mw
28073 1068.38 18 23 White No 0 0 0 1 No we
60 752.54 14 29 White Yes 1 0 0 0 No ne
4789 1056.51 16 19 White Yes 1 0 0 0 No ne
13387 522.32 14 14 White Yes 0 0 1 0 No so
15606 148.15 15 NA White Yes 0 0 1 0 No so
14256 1132.48 18 4 White Yes 0 0 1 0 No so
12981 1210.83 16 21 White Yes 0 1 0 0 No mw
16651 284.90 12 2 White Yes 0 0 1 0 No so
22810 142.45 13 0 White No 0 0 0 1 No we
8364 740.74 12 35 White Yes 0 1 0 0 No mw
16726 324.89 8 38 Black No 0 0 1 0 No so
9722 740.74 14 9 White Yes 0 1 0 0 No mw
7785 252.06 11 1 White Yes 0 1 0 0 No mw
16863 875.69 12 8 White Yes 0 0 1 0 No so
25107 119.90 14 5 White Yes 0 0 0 1 Yes we
19709 621.31 13 17 White No 0 0 1 0 No so
12324 91.62 12 5 White No 0 1 0 0 No mw
13094 498.58 18 7 White Yes 0 1 0 0 No mw
9978 783.48 12 33 White Yes 0 1 0 0 No mw
1159 2057.61 16 27 White Yes 1 0 0 0 No ne
7513 759.73 12 20 White Yes 0 1 0 0 No mw
9812 274.35 18 1 White Yes 0 1 0 0 No mw
4450 2374.15 18 19 White Yes 1 0 0 0 No ne
11465 451.09 12 5 White No 0 1 0 0 No mw
17925 740.74 12 12 White Yes 0 0 1 0 No so
19460 929.84 16 23 White Yes 0 0 1 0 No so
17107 347.22 12 10 White Yes 0 0 1 0 No so
4434 498.58 12 20 Black Yes 1 0 0 0 No ne
24038 352.73 10 24 White Yes 0 0 0 1 No we
20519 1448.24 16 7 White Yes 0 0 1 0 No so
8414 451.09 16 32 White Yes 0 1 0 0 No mw
5557 525.43 10 43 White Yes 1 0 0 0 No ne
20308 213.68 12 11 White Yes 0 0 1 0 No so
8440 64.98 12 1 White Yes 0 1 0 0 Yes mw
3657 689.96 12 28 White Yes 1 0 0 0 No ne
23368 498.58 15 10 White Yes 0 0 0 1 No we
21611 189.93 2 12 White Yes 0 0 1 0 No so
8206 58.10 14 5 White Yes 0 1 0 0 Yes mw
15859 474.83 12 9 White Yes 0 0 1 0 No so
17823 249.85 12 3 White Yes 0 0 1 0 No so
25377 253.24 12 1 White No 0 0 0 1 Yes we
13585 976.97 17 13 White No 0 0 1 0 No so
4728 51.44 16 NA White Yes 1 0 0 0 Yes ne
21943 949.67 12 13 White Yes 0 0 1 0 No so
10862 818.11 12 11 White Yes 0 1 0 0 No mw
14237 157.02 14 NA Black Yes 0 0 1 0 Yes so
25532 712.25 16 6 Black Yes 0 0 0 1 No we
8839 420.88 13 28 White No 0 1 0 0 No mw
6389 528.37 11 43 White Yes 1 0 0 0 No ne
6600 320.99 12 1 White Yes 0 1 0 0 No mw
11135 92.59 12 2 White No 0 1 0 0 No mw
9143 125.85 8 18 White No 0 1 0 0 No mw
12585 451.09 16 14 White No 0 1 0 0 No mw
18558 284.90 16 2 White Yes 0 0 1 0 No so
969 2374.15 18 16 White Yes 1 0 0 0 No ne
4708 205.76 12 3 White Yes 1 0 0 0 No ne
25553 284.90 10 10 White Yes 0 0 0 1 No we
16444 530.06 12 45 White Yes 0 0 1 0 Yes so
16616 370.37 12 16 White Yes 0 0 1 0 No so
27521 1975.31 18 29 White Yes 0 0 0 1 No we
23105 1899.34 18 17 White Yes 0 0 0 1 No we
20555 1020.89 14 10 White Yes 0 0 1 0 No so
8321 830.96 16 20 White Yes 0 1 0 0 No mw
12740 474.83 16 7 White Yes 0 1 0 0 No mw
3385 765.43 12 40 White Yes 1 0 0 0 No ne
26329 370.37 16 5 White Yes 0 0 0 1 No we
7105 590.08 12 6 White Yes 0 1 0 0 No mw
6895 1068.38 18 24 White Yes 0 1 0 0 No mw
23825 565.84 18 35 White Yes 0 0 0 1 Yes we
6073 94.97 12 7 White Yes 1 0 0 0 No ne
6855 807.22 12 22 White Yes 0 1 0 0 No mw
9099 379.87 12 10 White No 0 1 0 0 No mw
27883 2292.77 13 NA White Yes 0 0 0 1 No we
25598 237.42 12 3 White Yes 0 0 0 1 No we
11361 971.89 12 18 White Yes 0 1 0 0 No mw
10626 878.44 18 20 White Yes 0 1 0 0 No mw
20621 790.12 14 12 White Yes 0 0 1 0 No so
24126 154.32 12 45 White Yes 0 0 0 1 No we
18732 231.48 12 26 White No 0 0 1 0 No so
10042 498.58 15 6 White Yes 0 1 0 0 No mw
22182 412.77 9 11 White Yes 0 0 0 1 No we
144 617.28 12 20 White No 1 0 0 0 No ne
15040 763.30 18 13 White Yes 0 0 1 0 No so
979 830.96 16 13 White Yes 1 0 0 0 No ne
20217 783.48 16 13 White Yes 0 0 1 0 No so
5668 720.61 16 19 White Yes 1 0 0 0 No ne
8097 222.22 2 35 White Yes 0 1 0 0 No mw
15823 1424.50 16 35 White No 0 0 1 0 No so
6759 688.51 12 24 White Yes 0 1 0 0 No mw
18376 641.03 12 7 White Yes 0 0 1 0 No so
17630 592.59 11 10 White Yes 0 0 1 0 No so
12830 527.07 18 11 White No 0 1 0 0 No mw
17938 1377.02 16 24 White Yes 0 0 1 0 No so
20113 282.47 10 4 White No 0 0 1 0 No so
11624 427.35 12 3 White Yes 0 1 0 0 Yes mw
198 189.93 12 16 White No 1 0 0 0 No ne
14970 759.73 12 13 White Yes 0 0 1 0 No so
798 498.58 12 16 White No 1 0 0 0 No ne
6083 410.73 11 12 White Yes 1 0 0 0 No ne
6995 284.90 12 8 White Yes 0 1 0 0 No mw
26839 899.02 12 10 White Yes 0 0 0 1 No we
7180 546.06 12 17 White Yes 0 1 0 0 No mw
2799 783.48 14 19 White Yes 1 0 0 0 No ne
18268 688.51 13 19 White Yes 0 0 1 0 No so
8408 405.64 13 11 White Yes 0 1 0 0 No mw
25047 593.54 0 56 White Yes 0 0 0 1 No we
9563 902.18 12 30 White Yes 0 1 0 0 No mw
6783 1519.47 16 10 White Yes 0 1 0 0 No mw
6440 123.46 12 45 White Yes 1 0 0 0 Yes ne
5808 759.73 12 37 White Yes 1 0 0 0 No ne
691 379.87 16 13 White No 1 0 0 0 No ne
24057 166.19 14 47 White No 0 0 0 1 No we
20036 830.96 18 31 White Yes 0 0 1 0 No so
21618 246.91 6 9 White Yes 0 0 1 0 Yes so
14484 411.52 14 39 White Yes 0 0 1 0 No so
4003 759.73 14 22 White Yes 1 0 0 0 No ne
11924 396.79 12 22 White No 0 1 0 0 No mw
20469 166.19 16 2 White Yes 0 0 1 0 No so
20933 406.33 14 11 Black Yes 0 0 1 0 No so
15884 379.87 11 12 White No 0 0 1 0 No so
881 997.15 18 19 White Yes 1 0 0 0 No ne
12749 207.74 10 3 White No 0 1 0 0 No mw
6056 130.58 14 2 White Yes 1 0 0 0 Yes ne
11703 1092.32 12 17 White Yes 0 1 0 0 No mw
22442 365.62 12 12 White No 0 0 0 1 No we
26119 1187.08 16 12 White Yes 0 0 0 1 No we
13968 1187.08 18 17 White No 0 0 1 0 No so
5228 451.09 10 34 White Yes 1 0 0 0 No ne
3270 546.06 14 3 White Yes 1 0 0 0 No ne
5286 973.41 14 27 White Yes 1 0 0 0 No ne
16626 415.48 11 31 White Yes 0 0 1 0 No so
23631 382.98 12 27 White Yes 0 0 0 1 No we
19078 451.09 12 18 White No 0 0 1 0 No so
25406 183.60 15 5 White Yes 0 0 0 1 No we
8497 379.87 13 31 White Yes 0 1 0 0 No mw
28050 1377.02 16 32 White Yes 0 0 0 1 No we
11972 77.16 12 28 White No 0 1 0 0 No mw
27070 680.27 12 16 White Yes 0 0 0 1 No we
15053 2374.15 16 22 White Yes 0 0 1 0 No so
19203 189.93 5 24 Black No 0 0 1 0 No so
17905 284.90 10 28 White No 0 0 1 0 No so
7460 129.18 12 13 White No 0 1 0 0 No mw
428 759.73 14 29 White Yes 1 0 0 0 No ne
520 517.19 12 26 White Yes 1 0 0 0 No ne
22986 781.10 16 11 White No 0 0 0 1 No we
17882 2393.55 7 19 White Yes 0 0 1 0 Yes so
4875 2374.15 12 26 White Yes 1 0 0 0 No ne
16781 261.16 12 25 Black No 0 0 1 0 No so
3063 830.96 12 40 White Yes 1 0 0 0 No ne
16534 308.64 10 45 White No 0 0 1 0 No so
12408 178.60 16 0 White No 0 1 0 0 Yes mw
20401 281.48 13 15 White No 0 0 1 0 No so
14601 641.03 16 4 White Yes 0 0 1 0 No so
7993 158.72 9 8 White Yes 0 1 0 0 No mw
956 712.25 18 16 White Yes 1 0 0 0 No ne
3889 296.30 18 19 White Yes 1 0 0 0 No ne
22759 728.87 18 21 White Yes 0 0 0 1 No we
8999 132.10 11 14 Black Yes 0 1 0 0 No mw
1307 701.23 14 37 White Yes 1 0 0 0 No ne
13591 222.22 9 24 White No 0 0 1 0 No so
7228 78.35 12 3 White Yes 0 1 0 0 Yes mw
11663 332.38 10 9 White Yes 0 1 0 0 No mw
1478 569.80 11 18 White No 1 0 0 0 No ne
9668 130.58 17 NA White Yes 0 1 0 0 Yes mw
16375 891.47 12 47 White Yes 0 0 1 0 No so
5763 735.99 12 15 White Yes 1 0 0 0 No ne
6188 427.35 8 48 White Yes 1 0 0 0 No ne
21096 245.63 12 10 White Yes 0 0 1 0 No so
606 90.22 12 43 White No 1 0 0 0 No ne
15222 546.06 12 39 White Yes 0 0 1 0 No so
20536 356.13 12 11 White Yes 0 0 1 0 No so
6113 385.09 13 13 White Yes 1 0 0 0 No ne
23938 474.83 12 17 White Yes 0 0 0 1 No we
9690 1780.63 16 38 White Yes 0 1 0 0 No mw
16173 118.71 13 10 Black Yes 0 0 1 0 No so
12323 580.97 12 43 White No 0 1 0 0 No mw
13197 494.78 18 38 White No 0 1 0 0 No mw
20826 961.54 16 30 White Yes 0 0 1 0 No so
1011 688.51 10 16 White Yes 1 0 0 0 No ne
1400 807.22 16 15 White No 1 0 0 0 No ne
19615 712.25 7 38 White Yes 0 0 1 0 No so
15406 332.38 15 10 Black Yes 0 0 1 0 No so
10918 468.09 16 18 White Yes 0 1 0 0 No mw
24255 584.00 16 15 White Yes 0 0 0 1 No we
3639 427.35 13 4 White Yes 1 0 0 0 No ne
5906 185.19 18 25 White Yes 1 0 0 0 No ne
14914 712.25 12 10 White Yes 0 0 1 0 No so
  • In specifying a model using the region grouping, it easier to use the factor region than the dummy variables
  • Delete the four region dummy variables - we don’t need them anymore
  • The R lm() function will recreate them
# delete the four regions ne, mw, so, we
uswages <- subset(uswages,select=-c(ne:we))
# alternative
# uswages$ne <- NULL
# uswages$mw <- NULL
# uswages$so <- NULL
# uswages$we <- NULL
summary(uswages)
##       wage              educ           exper          race       smsa     
##  Min.   :  50.39   Min.   : 0.00   Min.   : 0.00   White:1844   No : 488  
##  1st Qu.: 308.64   1st Qu.:12.00   1st Qu.: 8.00   Black: 156   Yes:1512  
##  Median : 522.32   Median :12.00   Median :16.00                          
##  Mean   : 608.12   Mean   :13.11   Mean   :18.74                          
##  3rd Qu.: 783.48   3rd Qu.:16.00   3rd Qu.:27.00                          
##  Max.   :7716.05   Max.   :18.00   Max.   :59.00                          
##                                    NA's   :33                             
##    pt       region  
##  No :1815   ne:458  
##  Yes: 185   mw:497  
##             so:625  
##             we:420  
##                     
##                     
## 

Missing data

  • Delete all the missing data
# Take care of NAs
uswages <- na.omit(uswages)

See summary of finished product

  • Have one more look at the data summary
summary(uswages)
##       wage              educ           exper          race       smsa     
##  Min.   :  50.39   Min.   : 0.00   Min.   : 0.00   White:1812   No : 483  
##  1st Qu.: 314.69   1st Qu.:12.00   1st Qu.: 8.00   Black: 155   Yes:1484  
##  Median : 522.32   Median :12.00   Median :16.00                          
##  Mean   : 613.99   Mean   :13.08   Mean   :18.74                          
##  3rd Qu.: 783.48   3rd Qu.:16.00   3rd Qu.:27.00                          
##  Max.   :7716.05   Max.   :18.00   Max.   :59.00                          
##    pt       region  
##  No :1802   ne:448  
##  Yes: 165   mw:488  
##             so:616  
##             we:415  
##                     
## 

Explore scatterplot matrix using the continuous predictors

library("GGally")
## Loading required package: ggplot2
## Registered S3 method overwritten by 'GGally':
##   method from   
##   +.gg   ggplot2
## 
## Attaching package: 'GGally'
## The following object is masked from 'package:faraway':
## 
##     happy
ggpairs(uswages, columns = c("educ", "exper", "wage"), alpha = I(1/100), size = .1)
## Warning in warn_if_args_exist(list(...)): Extra arguments: 'alpha', 'size'
## are being ignored. If these are meant to be aesthetics, submit them using the
## 'mapping' variable within ggpairs with ggplot2::aes or ggplot2::aes_string.

  • It appears that educ and exper have a stronger relationship than either have with wage

  • The relationship with wage may become clearer if we condition with a factor such as region

  • wage is skewed to the right

  • Conclusion: Start with a simple model using educ as a predictor

Explore scatterplot matrix using the continuous predictors plus one factor, include fitted lines

library("GGally")

p1 <- ggpairs(uswages, 
        columns = c("region" ,"educ", "exper", "wage"),
        lower = list(
          continuous = wrap("smooth", se = FALSE),
          combo = "facetdensity",
          mapping = aes(color = region),
          alpha=I(1/100)
          )
)
p1  

#### Pick out the wage vs educ and wage vs exper scatterplots

p1[4, 2]

Observations : - As expected, we do see wages rising as the education increases for all of the regions. - There are a few outliers that can be seen. - West region seems to have lowest wages (for lower education).

p1[4, 3]

Use log(wage) in place of wage

  • The pattern in “wage vs exper” needs a closer look

  • This plot features loess (default) smoother-fits per region

library("ggplot2")
qplot(exper, 
      log(wage), 
      data = uswages, 
      color = region, 
      alpha = I(1/10)
      ) +
  geom_smooth(method = "loess", se = FALSE)

Observation : - We do see a steady increase in wages as the experience increases (till 20-30) but it shows a downward trend as experience increases beyond 30 - It essentially shows that the older working population is not paid as much as their younger counterparts.

  • Let’s explore fitting a quadratic model per region using log(wage) as the outcome
library("ggplot2")
plot1 <- qplot(exper, 
      log(wage), 
      data = uswages, 
      color = region, 
      alpha = I(1/5)
      ) +
  geom_smooth(method = "lm", 
              formula = y~poly(x, degree=2),
              se=FALSE
              ) +
  ggtitle("Quadratic Regressions per Region using exper ")
plot1

  • This is further exploration of the relation between wage and exper within the part time and full time workers using pt
plot3 <- plot1 +
  facet_grid(. ~ pt) +
  ggtitle("Quadratic Regressions per (`region`, `pt`) using `exper`")
plot3

Observations : - We do see the same trend as plots before this, but we see slightly different trend for southern region part time working population.

# Upon having a closer look at the kernel density plot of `educ`

qplot(educ, data = uswages, geom = "density")

# It appears there are distinct clusters that coincide with "highschool","college", and "graduate" levels of education

# Creating a factor variable out of "educ" 
# with levels equal to "high_school","college", and "graduate"

uswages$education <- cut(uswages$educ,
                     breaks=c(-Inf, 15, 17, Inf),
                     labels=c("high_school","college","graduate"))
# A boxplot of "log(wage)" per "education"

qplot(education, 
      log(wage), 
      data = uswages, 
      geom = "boxplot")

# This idea was suggested by my student Keegan McWilliam-Ward

Observations : - We see that the graduates were paid most, followed by college educated and high school educated people. - We see a few major outliers in high school category

Observation : - We do see a steady increase in wages as the experience increases (till 20-30) but it shows a downward trend as experience increases beyond 30 - It essentially shows that the older working population is not paid as much as their younger counterparts.

Observations : - We can see that a major part of dataset are high school graduates but they are also the ones that are towards the lower end of payscale - We can see graduates and college population getting paid better but as the experience increases, we do see a decline in pay - We see outliers wherein high school population is getting paid better than graduates and college population

Observations : - Among the part time working population we see that majority are high school graduates - Also we do not see a downward trend in wages for college population wuth respect to experience when it comes to part-time workers.

Lab Exercise 2

Galton’s Original Data

  • Sir Francis Galton, the originator of regression analysis, demonstrated his technique with the data on the heights of parents and their children as collected during a census in France during the time of Napoleon.
library("mosaic")
library("ggplot2")
data("Galton")
names(Galton)
## [1] "family" "father" "mother" "sex"    "height" "nkids"
str(Galton)
## 'data.frame':    898 obs. of  6 variables:
##  $ family: Factor w/ 197 levels "1","10","100",..: 1 1 1 1 108 108 108 108 123 123 ...
##  $ father: num  78.5 78.5 78.5 78.5 75.5 75.5 75.5 75.5 75 75 ...
##  $ mother: num  67 67 67 67 66.5 66.5 66.5 66.5 64 64 ...
##  $ sex   : Factor w/ 2 levels "F","M": 2 1 1 1 2 2 1 1 2 1 ...
##  $ height: num  73.2 69.2 69 69 73.5 72.5 65.5 65.5 71 68 ...
##  $ nkids : int  4 4 4 4 4 4 4 4 2 2 ...
formattable::formattable(Galton)
family father mother sex height nkids
1 78.5 67.0 M 73.2 4
1 78.5 67.0 F 69.2 4
1 78.5 67.0 F 69.0 4
1 78.5 67.0 F 69.0 4
2 75.5 66.5 M 73.5 4
2 75.5 66.5 M 72.5 4
2 75.5 66.5 F 65.5 4
2 75.5 66.5 F 65.5 4
3 75.0 64.0 M 71.0 2
3 75.0 64.0 F 68.0 2
4 75.0 64.0 M 70.5 5
4 75.0 64.0 M 68.5 5
4 75.0 64.0 F 67.0 5
4 75.0 64.0 F 64.5 5
4 75.0 64.0 F 63.0 5
5 75.0 58.5 M 72.0 6
5 75.0 58.5 M 69.0 6
5 75.0 58.5 M 68.0 6
5 75.0 58.5 F 66.5 6
5 75.0 58.5 F 62.5 6
5 75.0 58.5 F 62.5 6
6 74.0 68.0 F 69.5 1
7 74.0 68.0 M 76.5 6
7 74.0 68.0 M 74.0 6
7 74.0 68.0 M 73.0 6
7 74.0 68.0 M 73.0 6
7 74.0 68.0 F 70.5 6
7 74.0 68.0 F 64.0 6
8 74.0 66.5 F 70.5 3
8 74.0 66.5 F 68.0 3
8 74.0 66.5 F 66.0 3
9 74.5 66.0 F 66.0 1
10 74.0 65.5 F 65.5 1
11 74.0 62.0 M 74.0 8
11 74.0 62.0 M 70.0 8
11 74.0 62.0 F 68.0 8
11 74.0 62.0 F 67.0 8
11 74.0 62.0 F 67.0 8
11 74.0 62.0 F 66.0 8
11 74.0 62.0 F 63.5 8
11 74.0 62.0 F 63.0 8
12 74.0 61.0 F 65.0 1
14 73.0 67.0 M 68.0 2
14 73.0 67.0 M 67.0 2
15 73.0 66.5 M 71.0 3
15 73.0 66.5 M 70.5 3
15 73.0 66.5 F 66.7 3
16 73.0 65.0 M 72.0 9
16 73.0 65.0 M 70.5 9
16 73.0 65.0 M 70.2 9
16 73.0 65.0 M 70.2 9
16 73.0 65.0 M 69.2 9
16 73.0 65.0 F 68.7 9
16 73.0 65.0 F 66.5 9
16 73.0 65.0 F 64.5 9
16 73.0 65.0 F 63.5 9
17 73.0 64.5 M 74.0 6
17 73.0 64.5 M 73.0 6
17 73.0 64.5 M 71.5 6
17 73.0 64.5 M 62.5 6
17 73.0 64.5 F 66.5 6
17 73.0 64.5 F 62.3 6
18 73.0 64.0 F 66.0 3
18 73.0 64.0 F 64.5 3
18 73.0 64.0 F 64.0 3
19 73.2 63.0 F 62.7 1
20 72.7 69.0 M 73.2 8
20 72.7 69.0 M 73.0 8
20 72.7 69.0 M 72.7 8
20 72.7 69.0 F 70.0 8
20 72.7 69.0 F 69.0 8
20 72.7 69.0 F 68.5 8
20 72.7 69.0 F 68.0 8
20 72.7 69.0 F 66.0 8
21 72.0 68.0 M 73.0 3
21 72.0 68.0 F 68.5 3
21 72.0 68.0 F 68.0 3
22 72.0 67.0 M 73.0 3
22 72.0 67.0 M 71.0 3
22 72.0 67.0 F 67.0 3
23 72.0 65.0 M 74.2 7
23 72.0 65.0 M 70.5 7
23 72.0 65.0 M 69.5 7
23 72.0 65.0 F 66.0 7
23 72.0 65.0 F 65.5 7
23 72.0 65.0 F 65.0 7
23 72.0 65.0 F 65.0 7
24 72.0 65.5 F 65.5 1
25 72.0 64.0 F 66.0 2
25 72.0 64.0 F 63.0 2
26 72.0 63.0 M 70.5 5
26 72.0 63.0 M 70.5 5
26 72.0 63.0 M 69.0 5
26 72.0 63.0 F 65.0 5
26 72.0 63.0 F 63.0 5
27 72.0 63.0 M 69.0 3
27 72.0 63.0 M 67.0 3
27 72.0 63.0 F 63.0 3
28 72.0 63.0 M 73.0 6
28 72.0 63.0 M 67.0 6
28 72.0 63.0 F 70.5 6
28 72.0 63.0 F 70.0 6
28 72.0 63.0 F 66.5 6
28 72.0 63.0 F 63.0 6
29 72.5 63.5 F 67.5 3
29 72.5 63.5 F 67.2 3
29 72.5 63.5 F 66.7 3
30 72.0 62.0 F 64.0 1
31 72.5 62.0 M 71.0 6
31 72.5 62.0 M 70.0 6
31 72.5 62.0 M 70.0 6
31 72.5 62.0 F 66.0 6
31 72.5 62.0 F 65.0 6
31 72.5 62.0 F 65.0 6
32 72.0 62.0 M 74.0 5
32 72.0 62.0 M 72.0 5
32 72.0 62.0 M 69.0 5
32 72.0 62.0 F 67.5 5
32 72.0 62.0 F 63.5 5
33 72.0 62.0 M 72.0 5
33 72.0 62.0 M 71.5 5
33 72.0 62.0 M 71.5 5
33 72.0 62.0 M 70.0 5
33 72.0 62.0 F 68.0 5
34 72.0 61.0 F 65.7 1
35 71.0 69.0 M 78.0 5
35 71.0 69.0 M 74.0 5
35 71.0 69.0 M 73.0 5
35 71.0 69.0 M 72.0 5
35 71.0 69.0 F 67.0 5
36 71.0 67.0 M 73.2 4
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166 67.5 65.0 F 64.0 11
166 67.5 65.0 F 64.0 11
166 67.5 65.0 F 63.0 11
166 67.5 65.0 F 63.0 11
166 67.5 65.0 F 63.0 11
166 67.5 65.0 F 63.0 11
166 67.5 65.0 F 63.0 11
166 67.5 65.0 F 62.5 11
166 67.5 65.0 F 62.0 11
167 67.0 64.0 M 71.5 4
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168 67.0 63.5 M 71.0 8
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168 67.0 63.5 M 68.0 8
168 67.0 63.5 M 67.0 8
168 67.0 63.5 M 65.5 8
168 67.0 63.5 F 63.5 8
169 67.0 63.0 M 69.0 3
169 67.0 63.0 M 68.0 3
169 67.0 63.0 F 63.0 3
170 67.5 62.0 M 70.0 5
170 67.5 62.0 M 69.5 5
170 67.5 62.0 M 69.0 5
170 67.5 62.0 M 68.5 5
170 67.5 62.0 F 66.0 5
171 67.0 61.0 M 67.0 1
172 66.0 67.0 M 70.5 8
172 66.0 67.0 M 70.5 8
172 66.0 67.0 M 67.0 8
172 66.0 67.0 M 66.0 8
172 66.0 67.0 M 66.0 8
172 66.0 67.0 F 62.0 8
172 66.0 67.0 F 62.0 8
172 66.0 67.0 F 61.5 8
173 66.0 67.0 M 72.0 9
173 66.0 67.0 M 65.0 9
173 66.0 67.0 M 65.0 9
173 66.0 67.0 F 67.0 9
173 66.0 67.0 F 64.0 9
173 66.0 67.0 F 64.0 9
173 66.0 67.0 F 62.0 9
173 66.0 67.0 F 60.0 9
173 66.0 67.0 F 60.0 9
174 66.0 66.0 M 66.0 5
174 66.0 66.0 M 65.0 5
174 66.0 66.0 F 67.0 5
174 66.0 66.0 F 66.5 5
174 66.0 66.0 F 65.5 5
175 66.0 66.0 M 72.0 6
175 66.0 66.0 M 68.0 6
175 66.0 66.0 F 66.0 6
175 66.0 66.0 F 65.0 6
175 66.0 66.0 F 62.0 6
175 66.0 66.0 F 61.0 6
176 66.5 65.0 M 68.7 8
176 66.5 65.0 M 68.5 8
176 66.5 65.0 M 66.5 8
176 66.5 65.0 M 64.5 8
176 66.5 65.0 F 62.5 8
176 66.5 65.0 F 60.5 8
176 66.5 65.0 F 60.5 8
176 66.5 65.0 F 57.5 8
177 66.0 65.5 M 72.0 5
177 66.0 65.5 M 71.0 5
177 66.0 65.5 M 67.0 5
177 66.0 65.5 F 66.0 5
177 66.0 65.5 F 65.0 5
178 66.0 63.0 M 70.0 1
179 66.0 63.5 F 64.5 2
179 66.0 63.5 F 62.0 2
180 66.5 63.0 M 67.2 6
180 66.5 63.0 M 67.0 6
180 66.5 63.0 M 65.0 6
180 66.5 63.0 F 65.0 6
180 66.5 63.0 F 65.0 6
180 66.5 63.0 F 63.0 6
181 66.5 62.5 M 70.0 7
181 66.5 62.5 M 68.0 7
181 66.5 62.5 F 63.5 7
181 66.5 62.5 F 62.5 7
181 66.5 62.5 F 62.5 7
181 66.5 62.5 F 62.5 7
181 66.5 62.5 F 62.5 7
182 66.0 61.5 M 70.0 1
183 66.0 60.0 M 68.0 4
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183 66.0 60.0 M 65.0 4
183 66.0 60.0 F 60.0 4
184 66.0 60.0 M 65.0 1
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185 66.0 59.0 M 67.0 15
185 66.0 59.0 M 66.5 15
185 66.0 59.0 M 66.0 15
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185 66.0 59.0 M 65.5 15
185 66.0 59.0 M 65.0 15
185 66.0 59.0 F 65.0 15
185 66.0 59.0 F 64.0 15
185 66.0 59.0 F 63.0 15
185 66.0 59.0 F 62.0 15
185 66.0 59.0 F 61.0 15
185 66.0 59.0 F 60.0 15
185 66.0 59.0 F 58.0 15
185 66.0 59.0 F 57.0 15
186 65.0 67.0 M 66.5 4
186 65.0 67.0 M 66.0 4
186 65.0 67.0 M 66.0 4
186 65.0 67.0 F 65.0 4
187 65.0 67.0 F 63.0 1
188 65.0 66.0 M 63.0 4
188 65.0 66.0 F 63.0 4
188 65.0 66.0 F 63.0 4
188 65.0 66.0 F 60.0 4
190 65.0 65.0 M 69.0 9
190 65.0 65.0 M 68.0 9
190 65.0 65.0 M 68.0 9
190 65.0 65.0 F 65.0 9
190 65.0 65.0 F 65.0 9
190 65.0 65.0 F 62.0 9
190 65.0 65.0 F 62.0 9
190 65.0 65.0 F 61.0 9
190 65.0 65.0 F 59.0 9
191 65.0 65.5 M 70.7 2
191 65.0 65.5 F 65.5 2
192 65.0 65.0 M 69.2 6
192 65.0 65.0 M 69.0 6
192 65.0 65.0 M 68.0 6
192 65.0 65.0 M 67.7 6
192 65.0 65.0 F 64.5 6
192 65.0 65.0 F 60.5 6
193 65.0 64.0 M 67.0 6
193 65.0 64.0 M 67.0 6
193 65.0 64.0 F 64.0 6
193 65.0 64.0 F 64.0 6
193 65.0 64.0 F 62.5 6
193 65.0 64.0 F 60.5 6
194 65.0 63.0 M 70.0 2
194 65.0 63.0 F 63.0 2
195 65.0 63.0 M 66.0 3
195 65.0 63.0 M 66.0 3
195 65.0 63.0 F 63.0 3
196 65.5 63.0 M 71.0 4
196 65.5 63.0 M 71.0 4
196 65.5 63.0 M 69.0 4
196 65.5 63.0 F 63.5 4
197 65.5 60.0 M 68.0 5
197 65.5 60.0 M 68.0 5
197 65.5 60.0 M 67.0 5
197 65.5 60.0 M 67.0 5
197 65.5 60.0 F 62.0 5
198 64.0 64.0 M 71.5 7
198 64.0 64.0 M 68.0 7
198 64.0 64.0 F 65.5 7
198 64.0 64.0 F 64.0 7
198 64.0 64.0 F 62.0 7
198 64.0 64.0 F 62.0 7
198 64.0 64.0 F 61.0 7
199 64.0 64.0 M 70.5 7
199 64.0 64.0 M 68.0 7
199 64.0 64.0 F 67.0 7
199 64.0 64.0 F 65.0 7
199 64.0 64.0 F 64.0 7
199 64.0 64.0 F 64.0 7
199 64.0 64.0 F 60.0 7
200 64.0 63.0 M 64.5 1
201 64.0 60.0 M 66.0 2
201 64.0 60.0 F 60.0 2
203 62.0 66.0 M 64.0 3
203 62.0 66.0 F 62.0 3
203 62.0 66.0 F 61.0 3
204 62.5 63.0 M 66.5 2
204 62.5 63.0 F 57.0 2
136A 68.5 65.0 M 72.0 8
136A 68.5 65.0 M 70.5 8
136A 68.5 65.0 M 68.7 8
136A 68.5 65.0 M 68.5 8
136A 68.5 65.0 M 67.7 8
136A 68.5 65.0 F 64.0 8
136A 68.5 65.0 F 63.5 8
136A 68.5 65.0 F 63.0 8
  • Let’s plot the data and fit a linear model of child’s height versus father’s height in the two sex groups

Data plotting

# Scatterplot with regression fit of child's height vs. father's height for each sex, sex type is represented by shape and color
plot <- qplot(father,
              height, 
      data=Galton, 
      shape=sex, 
      color=sex
      ) +
  geom_smooth(method="lm", 
      formula=y~x,
      se=FALSE
      ) + 
  ggtitle("Regression of Child's Height on Fathers' Height"
          ) +
  xlab("Father's Height"
       ) +
  ylab("Child's Height")
plot

# Alternate plotting method using ggplot2
# p <- ggplot(Galton, aes(x = father, y = height, colour = sex))
# p <- p + geom_point()
# p <- p + geom_smooth(aes(group=sex), method="lm", fullrange=FALSE)
# p <- p + ggtitle("Galton Data 1885")
# p
  • Another graphic is the facet plot
  • Rather than putting the two groups in the same plot we separate then into two facets
plot <- plot + facet_grid(. ~ sex)
plot

Main Effects Model Fitting

  • The fit of the linear model within the two sex groups is obtained with a main effects model as follows;
g1 <- lm(height ~ father + sex, data = Galton)
summary(g1)
## 
## Call:
## lm(formula = height ~ father + sex, data = Galton)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -9.3708 -1.4808  0.0192  1.5616  9.4153 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 34.46113    2.13628   16.13   <2e-16 ***
## father       0.42782    0.03079   13.90   <2e-16 ***
## sexM         5.17604    0.15211   34.03   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.277 on 895 degrees of freedom
## Multiple R-squared:  0.5971, Adjusted R-squared:  0.5962 
## F-statistic: 663.2 on 2 and 895 DF,  p-value: < 2.2e-16
summary(g1)$r.square
## [1] 0.5971034

Residual Plots

Let’s check the residual plot and the normal Q-Q plot of the residuals

library("ggplot2")
mod <- fortify(g1)

plot1 <- qplot(.fitted, .stdresid, data=mod) + 
  geom_hline(yintercept = c(-2, 0, 2), color = c(2,1,2), linetype="dashed")
plot2 <- qplot(sample =.stdresid, data = mod, geom = "qq") + geom_abline()

library("gridExtra")
## 
## Attaching package: 'gridExtra'
## The following object is masked from 'package:dplyr':
## 
##     combine
grid.arrange(plot1, plot2, nrow = 1)

Observations : - From the QQ plot of the residual values, we do see the data to be normally distributed. - We see quite a few outliers, and some departure from normality

  • Note the use of the ggplot2::fortify() function, it combines all the data with the model calculations, you can explore what is does with str(mod) and View(mod)

Interaction Model Fitting

  • We note from the scatterplot matrix, the slopes of the regression lines for the two groups may not be the same
  • This means that the appropriate fit could be an interaction model
  • Fit the following interaction model
g2 <- lm(height ~ father*sex, data = Galton)
summary(g2)
## 
## Call:
## lm(formula = height ~ father * sex, data = Galton)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -9.3774 -1.4857  0.0088  1.6017  9.3987 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 35.58523    2.87662  12.370   <2e-16 ***
## father       0.41160    0.04148   9.923   <2e-16 ***
## sexM         2.67368    4.28926   0.623    0.533    
## father:sexM  0.03615    0.06192   0.584    0.560    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.278 on 894 degrees of freedom
## Multiple R-squared:  0.5973, Adjusted R-squared:  0.5959 
## F-statistic: 441.9 on 3 and 894 DF,  p-value: < 2.2e-16
summary(g2)$r.square
## [1] 0.5972569

Residual Plots

Let’s check the residual plot and the normal Q-Q plot of the residuals

library("ggplot2")
mod <- fortify(g2)
plot1 <- qplot(.fitted, .stdresid, data=mod) + 
  geom_hline(yintercept = c(-2, 0, 2), color = c(2,1,2), linetype="dashed")
plot2 <- qplot(sample =.stdresid, data = mod, geom = "qq") + geom_abline()

library("gridExtra")
grid.arrange(plot1, plot2, nrow = 1)

### More data modeling

  • Another interaction model with \(sex \times father\) and \(sex \times mother\)
g3 <- lm(height ~ sex*(father + mother), data = Galton)
summary(g3)
## 
## Call:
## lm(formula = height ~ sex * (father + mother), data = Galton)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -9.5305 -1.4399  0.1257  1.4638  9.0968 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 16.61023    3.91658   4.241 2.46e-05 ***
## sexM         2.78965    5.51014   0.506    0.613    
## father       0.40072    0.03931  10.195  < 2e-16 ***
## mother       0.30746    0.04560   6.742 2.81e-11 ***
## sexM:father  0.01103    0.05883   0.188    0.851    
## sexM:mother  0.02609    0.06277   0.416    0.678    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.156 on 892 degrees of freedom
## Multiple R-squared:  0.6398, Adjusted R-squared:  0.6377 
## F-statistic: 316.8 on 5 and 892 DF,  p-value: < 2.2e-16

Observations : - We see a much better \(R^2\) value here : 0.6377 but it is not a significant correlation value.