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AppliedMultivariate Data Analaysis-HW3:

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(1) Suppose ?? ∼ ??2 ��
5

10
� , �2 1

1 2
��. Complete the following:

(a)Which of the plots below is the correct contour plot for the distribution? Explain your choice by
specifying particular characteristics of the plot that correspond to this distribution.

(b) Roughly indicate on your chosen plot from a) where you would expect most of the (x1, x2) data values
to be for a random sample. In your answer, indicate where the concentration of (x1, x2) data values
would be the largest. Note that you should be able to answer this entire part without actually simulating
data.

(c) Using R to draw a contour plot for X (a) and add 100 points in it.

(d) Calculate the correlation matrix for X

(f) Find f(x) at x = µ (hint use dmvnorm()).

(g)Find f(x) at x = [6, 11]′ by using dmvnorm().

(Q2)There are three typos in the dataset typo.csv, where the original point was shifted by a factor of
ten. Find them as outliers using Chi-squared QQ plot of squared Mahalanobis distances

(Q3)We investigate graphically the R internal dataset swiss which you can load by data(swiss). The data
contains the variables

Fertility common standardized fertility measure

Catholic #of catholics

Agriculture # of men working in agriculture environment

Examination # draftees receiving highest mark on army examination

Education # education beyond primary school for draftees

Infant.Mortality # of live births who live less than 1 year

of 47 counties in the west of switzerland dated at 1888. With ?swiss you get more information on the
meaning of the variables.

a) Read the help file of stars()
b) Make a star plot of all variables. What can you say about Sierre? R-Hint: data(swiss), stars(swiss, ..
c) We are interested in the relation between Fertility and Education. Therefore we would like to make

a scatter-plot of Fertility against Education whose points are stars with the information of the other
variables. In addition we need the argument location. R-Hint: stars(swiss[, c(2,3,5,6)], location =
swiss[, c(4,1)], axes = T, …)

d) Set the argument draw.segments to TRUE to get segments instead of stars. Place a legend with
key.loc.

e) Which relation do you get from the plots?

Hep R files for Question3

?stars

data(swiss)

stars(swiss, key.loc = c(15.5,1.5))

stars(swiss[,c(2,3,5,6)],location=swiss[,c(4,1)], key.loc = c(45,90),

labels=NULL, len=3, axes=T, xlab=”Education”, ylab=”Fertility”)

stars(swiss[,c(2,3,5,6)],location=swiss[,c(4,1)], draw.segments=T,

key.loc=c(45,90), labels=NULL, len=3, axes=T, xlab=”Education”,

ylab=”Fertility”, cex=0.8)

(Q4) (Visualization: parallel coordinate plot and conditioning plot)

The data quakes.csv contains the measurements of latitude (lat), longitude (long), depth (depth),
magnitude (mag) and the number of reporting stations (stations) for 1000 seismic events of Mb >4.0
(body wave magnitude) that occurred in a cube near Fiji since 1964.
a) Load the data saved in quakes.csv.
b) Does the magnitude of the earthquake depend on the depth? (Make a scatterplot)
R-Hint: You can use the command jitter(…) to plot points next to each other rather than
overlapping them.
c) Does the number of reporting stations depend on the magnitude? (Make a scatterplot)
d) Investigate the relationships between all variables in the data using a parallel coordinate plot and
a scatterplot matrix. Which method do you find more useful?
R-Hint:
library(MASS)
parcoord(…)
e) How does the depth depend on longitude and latitude? (Plot a point (pch = 20) at the position of the
earthquake; the color should be green, orange or red according to the depth)
R-Hint:
deepVec <- cut(quakes$depth, breaks=c(0,250,450,700), labels=c("green","orange", "red")) deepVecString <- as.character(deepVec) f) Look at the help _le of coplot() to see how you could answer question e) with this command. Also use coplot() to display how depth and magnitude depend on longitude and latitude.

(Q5) The data consists of the emissions of three different pollutants from 46 different engines. A
data engine.csv is available.

(a)For each pollutant verify the normality (hint: use histogram,qqnorm, shapiro test and chi-
square plot)

(b) Test for Multivariate Normal for the engine data.

(c) Check for Outliers

(d) Draw pairwise bivariate boxplot and bagplot

(6) For the following null and alternative hypothesis interpret the type 1 and type 2 error

(a) Ho: The person is healthy
H1: The person has Alzheimer’s

(b) Ho: Message is real
H1: Message is spam

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181.57 579 4.9 49

562

40 4.7 17

563

182.1 62 4.9 25

564

182.8 273 5.3 78

565 -25.04

393 4.2 21

264 4.2 23

174 4.5 18

568

574 5.2 67

569 -19.6 183.84 309 4.5 23
570

179.82 75 5.6 79

571

167.26 195 5.2 87

572

44 4.8 35

573

420 4.5 29

574 -20.41

63 5 28

575 -18.18 182.04 609 4.4 26
576

40 4.5 18

577

181.31 575 4.6 42

181.69 559 4.5 24

579

405 5.2 74

183.4 70 5.1 54

-15.9 167.16 41 4.8 42

582

605 4.3 18

583

166.36 130 5.1 55

584 -20.04

577 4.7 19

585

4.6 20

586

82 4.8 51

587

50 4.6 23

-24.96

480 4.4 25

589

181.42 559 4.6 27

590

566 5.1 49

591 -20.95

4.3 20

181.9 409 4.4 19

593

209 4.7 30

594

70 4.8 47

595 -21.79 185 74 4.1 15

134 4.6 33

597

150 4.9 35

598 -17.02 182.93 406 4 17
599

182.39 243 4.7 32

600

89 4.7 32

601

53 5.2 89

602

68 4.6 18

603

180.81 605 4.6 34

604 -21.24 180.86

4.9 23

605 -19.89

546 5.7 99

606

179.8 176 4.7 26

607 -22 185.5 52 4.4 18
608

66 4.9 38

609 -24.5

377 4.8 43

180.2 186 4.6 27

611

182.4 51 4.4 18

67 4.8 35

613 -17.99

234 4.7 28

614 -19.6 181.87 597 4.2 18
615

64 5.1 54

511 4.8 56

617

47 4.9 47

618

49 5.1 49

619 -18.07

546 4.3 28

75 4.4 30

181.3 60 4.7 33

278 4.7 24

550 5.3 86

624

518 5.1 71

171.5 116 4.9 38

626

518 4.5 23

627

181.75 75 4.7 41

628

491 4.2 23

629

56 5.1 50

630

182.37 376 4.8 57

181.02 584 4.2 18

632

48 4.8 56

-28.56 183.59 53 4.4 20

-21.3 180.92 617 4.5 26

-20.08

294 4.3 18

636

417 5.6 129

637

280 4 16

638

332 5 36

639 -17.4

85 4.2 28

640

180.18 525 4.6 31

641

181.09 613 4.6 18

-16.23

182 4.5 28

183.4 57 5 32

644 -20.81

79 4.7 42

181.41 595 4.6 36

646

184 164 4.8 50

148 4.6 44

-15.48

82 4.4 17

153 5.6 87

-20.48 181.38 556 4.2 13

649 5.4 88

651 4.8 43

-11.4 166.07 93 5.6 94

654 -23.1

533 4.4 27

-14.28

642 4.7 29

-22.87

47 4.6 27

-17.59 180.98 548 5.1 79

658 -27.6 182.1 154 4.6 22

-17.94 180.6 627 4.5 29

-17.88

622 4.2 23

180.8 286 4.8 43

182.3 390 4.9 48

624 5.5 105

664 -23.46

539 5 41

624 4.2 21

180.87 631 5.2 69

180.98 631 4.8 36

-15.85

299 4.4 30

180.09 498 4.8 40

-18.6 184.28 255 4.4 31

671 -17.8 181.32 539 4.1 12

-10.78 166.1 195 4.9 45

-18.12 181.71 594 4.6 24

573 4.5 32

167.1 128 5.3 18

137 4.8 40

143 4.6 41

511 4.8 37

564 4.7 17

680

181.66 559 4.9 50

248 5.3 60

-20.16

210 4.4 27

180.94 390 4.6 33

181.74 616 4.3 17

186.4 98 4.4 17

169.1 218 4.2 27

-18.89 181.24 655 4.1 14

-17.61

356 4.2 15

181.54 564 5 64

-17.6 181.5 548 4.1 10

181.4 655 4.3 20

-18.8 182.41 385 5.2 67

-20.61

518 4.2 10

181.53 598 4.5 36

179.86 476 4.4 29

-23.9 179.9 579 4.4 16

-18.07 181.58 603 5 65

-15.43

249 4 11

-14.3 167.32 208 4.8 25

-18.04 181.57 587 5 51

167.18 221 4.2 21

545 5.2 91

-17.98 181.51 586 5.2 68

-25 180 488 4.5 10

184.48 246 4.3 15

61 4.5 19

-23.73

524 4.6 11

-17.74

104 5.1 71

271 4.4 36

487 4.3 16

186.73 83 4.7 37

167.91 183 5.6 109

185.86 55 4.9 46

166 5.1 22

586 4.6 13

-13.36

618 4.4 18

181.51 524 4.8 49

-26.1 182.5 133 4.2 17

201 4.7 57

182.9 383 4.1 11

171.4 86 4.7 33

181.48 555 4 17

-26.53 178.3 605 4.9 43

-26.5

609 5 50

204 4.5 16

169.71 287 4.4 23

-17.1 182.8 390 4 14

348 4.5 30

-23.5 180 550 4.7 23

181.69 487 4.4 20

-17.97 181.48 578 4.7 43

181.2 361 4.7 32

180.8 275 4 14

498 4.2 14

167.24 162 4.5 18

-15.4

78 4.7 44

-22.06 183.95 134 4.5 17

554 4.1 15

-20.3 181.4 608 4.6 13

367 4.3 25

599 4.6 30

-19.02

45 5.2 65

-22.1 185.3 50 4.6 22

162 4.7 36

-19.3 183 302 5 65

181.59 57 5.2 49

181.3 203 4.4 20

-22.55

66 4.6 18

180.64 591 4.5 18

-25.6 180.3 440 4 12

-18.04

611 4.2 20

-21.29 185.77 57 5.3 69

180.85 627 5.9 119

-20.64

89 4.9 42

500 4.5 34

264 4.4 14

-17.1 185.9 127 5.4 75

-21.13 185.6 85 5.3 86

50 5.1 47

186.73 75 4.1 20

-20.7 184.3 182 4.3 17

180.92 619 4.5 18

-17.78

223 4.1 10

-21.57

156 5.1 70

46 5.3 71

50 4.5 29

-19.1 184.52 230 4.1 16

-19.85

184 4.4 26

188 4.7 24

-20.7 186.3 80 4 10

185.1 86 5.1 61

-16.4

391 4 16

-19.6

199 4.3 21

592 4.3 21

-21.6 180.5 595 4 22

181 618 4.1 10

-21.8 183.6 213 4.4 17

-21.05 180.9 616 4.3 10

175 4.2 12

-17.9 181.5 589 4 12

83 4.5 25

119 4.7 32

70 5 48

-20.4 186.1 74 4.3 22

-15

40 5.1 54

183.4 87 4.7 34

2

63 5.3 69

-23.61 180.27 537 5 63

-21.56 185.5 47 4.5 29

181.58 490 5 77

-18.07 181.65 593 4.1 16

-26

644 4.9 27

-20.21 181.9 576 4.1 16

-28 182 199 4 16

-20.74 180.7 589 4.4 27

180.6 178 4.5 19

169.46 248 4.4 33

-20.45 182.1 500 4.5 37

-22.9 183.8 71 4.3 19

-18.11 181.63 568 4.3 36

-23.8 184.7 42 5 36

180.21 510 4.5 37

-23.2 184.8 97 4.5 13

-12.93

663 4.4 30

181.06 625 4.5 35

-19.13

210 4.1 22

-21.08 181.3 557 4.9 78

-20.07 181.75 582 4.7 27

-20.9 182.02 402 4.3 18

-25.04

474 4.6 32

577 4.6 43

-19.34

56 5.2 49

-15.83 167.1 43 4.5 19

-23.73 183 118 4.3 11

-18.1 181.72 544 4.6 52

180.49 532 4 14

185.1 237 4.5 39

111 4.8 30

595 4.6 30

-22.1 180.4 603 4.1 11

-24.97

505 4.9 50

100 4.7 40

-22.14

587 4.1 23

-21.48 182.44 364 4.3 20

100 4.4 17

182.4 350 4 12

-13.4 166.9 228 4.8 15

-15.5 185.3 93 4.4 25

185.23 66 4.4 34

225 4.6 21

180.9 334 4.2 28

-15.7 185.1 70 4.1 15

-19.2

220 4.2 18

-19.7 182.44 397 4 12

-19.4

326 4.1 15

-15.85 185.9 121 4.1 17

209 4.7 29

510 4.8 44

-20.89

54 5.1 44

-18.97

242 5 41

-17.99

574 4.8 38

-15.8

82 4.4 39

102 5 36

-21.6

43 5.2 56

432 4.2 19

-17.56 181.23 580 4.1 16

180.26 464 4.8 60

179.98 479 4.5 27

581 5 54

-21.55 181.39 513 5.1 81

77 4.1 16

68 4.7 41

-15.18

71 5.2 59

68 4.8 48

-17.9 181.41 586 4.5 33

-18.5 185.4 243 4 11

-14.82

658 4.7 49

-15.65

315 4.1 15

-30.01 181.15 210 4.3 17

167.24 278 4.3 17

638 4 14

-21.4 180.78 615 4.7 51

-17.93

567 4.1 27

181.7 560 4.2 13

-12.01

99 4.8 36

-19.1 169.63 266 4.8 31

397 4.2 15

180 4.2 29

-21.14

40 5.7 78

242 6 132

181.57 530 4.2 20

133 4.5 32

167.01 62 4.9 36

-22.09 180.58 580 4.4 22

-17.8 181.2 530 4 15

182.43 566 4.3 20

-18.85 182.2 501 4.2 23

548 4.5 30

587 4.8 31

-18.1 181.63 592 4.4 28

-18.4

221 4.2 18

-21.2 181.4 560 4.2 12

-12 166.2 94 5 31

-11.7 166.3 139 4.2 15

-26.72

162 5.2 64

562 4.5 30

169.5 204 4.6 35

56 5 22

184.52 49 5 52

100 5.4 71

231 4.8 28

-22.24

601 4.2 21

-13.8 166.53 42 5.5 70

-21.07 183.78 180 4.3 25

-17.74 181.25 559 4.1 16

180.15 524 4.4 22

-21.29 185.8 69 4.9 74

-22.2 180.58 594 4.5 45

-15.24

262 4.9 56

-17.82

538 4 33

-32.14 180 331 4.5 27

-19.3 185.86 48 5 40

180.94 47 4.9 47

181.62 558 4.5 31

-17.46 181.42 524 4.2 16

-17.44 181.33 545 4.2 37

179.85 477 4.2 34

129 5.2 30

268 4.3 21

182.39 117 5.1 43

179.97 541 4.6 50

-22.33

112 4.6 14

162 4.4 36

181.51 609 4.4 32

76 4.9 64

61 5.1 40

184.47 202 4.2 28

90 4.7 30

182.8 133 4 14

589 5.6 115

167.95 190 5.3 81

-20.56

138 5 82

-17.98 181.61 598 4.3 27

-18.4

600 4.1 11

182.22 162 5.1 67

181.02 626 4.5 36

167.32 137 4.9 22

57 5.4 61

182.54 201 4.7 40

-14.1

69 4.8 29

185.13 219 4.5 28

-23.47 180.21 553 4.2 23

-23.92 180.21 524 4.6 50

51 4.6 28

107 5.6 121

44 5.4 110

-18.14 181.71 574 4 20

128 5.2 72

181.16 568 4.2 12

-17.95

583 4.7 57

-20.83

622 4.3 15

182.1 193 4.8 27

182.39 544 4.6 30

-23.6 183.99 118 5.4 88

-23.7

51 4.8 27

182.4 63 4.6 22

182.32 442 4.2 22

87 5.5 67

-23.5 184.9 61 4.7 16

-23.73

60 4.7 35

-17.93 181.62 561 4.5 32

138 5.5 78

184.5 174 4.5 34

-23.47

543 4.1 21

-23.49

530 4 23

-23.85 180.26 497 4.3 32

63 4.7 27

-20.88

82 4.9 50

-20.97 181.2 605 4.5 31

234 4.7 55

-23.9 184.6 41 4.5 22

40 4.8 42

-12.57

137 4.3 20

184.23 223 4.1 23

-22.04 183.95 109 5.4 61

-17.99 181.59 595 4.1 26

-23.5 180.13 512 4.8 40

-21.4

613 4.2 20

-15.86

60 4.8 25

43 5.4 45

182.38 172 4.4 14

184.5 54 5.2 74

-24.1 184.5 68 4.7 23

217 4.9 35

-23.3 184.68 102 4.9 27

185.74 178 4.2 32

-20.77

251 4.4 47

-28.1 183.5 42 4.4 17

182.26 575 4.3 11

-23

43 4.9 20

181.67 577 5 67

42 4.7 21

183.6 75 4.9 49

183.5 71 4.3 22

-15.54 187.15 60 4.5 17

291 4.2 16

-22.33

125 5.2 51

-22.7 170.3 69 4.8 27

181.3 614 4 12

-16 184.53 108 4.7 33

181.42 575 4.3 18

-15.45 181.42 409 4.3 27

183.86 243 4.9 65

-17.95 181.37 642 4 17

-17.7 188.1 45 4.2 10

179.54 470 4.4 22

167.06 248 4.7 35

184.2 244 4.5 34

-17.4 187.8 40 4.5 14

170.56 165 6 119

lat long depth mag stations
1

2 4 1

8 6 5 62 4.8 41

20 18 3 6

50 4.2 15

26 18

4.1 42 5.4 43
-1

7 9 1

81 66 626 19
-20.4 181 96 6

49 11
-19 68 18

4.3 1

95 12
-11.7 16 6.1 82

28 181.

93 1

94 4.4
-28 74 181.7 21 4.7 35
10

17 47 1

79 59 6

22
-21 44 1

80 5

83 13
-12 1

67 24 4.6
-18 54 182 55
14 181.6 60
-20.7 1

69 92 1

39
-1

5.9 18

4.9 30
-13.

64 1

65
-17.8 181.5 5

90 4.5

23 179 78 57
-22 63 180 31 5

98
-20.

84 181.16 5

76
-10.98 166 32 211
-23 180.1 51
-30.2 1

25
-19.6 180.2 431
-17.9 181.4 5

37
27 -14.

72 167 155
-16 46 180.7 498 5.2
29 -20.

97 181.47 58
-19.84 182.3 328
-22.5 179.2 5

53
-16.3 166.74
33 -1

5.5 1

85 292
34 -23.5 180.8 349
1

86 48
36 -25 179.33 600
-18.

73 169 206
38 -17.6 181.2 574
-17.66 585
40 -18.8 169.33 230
-37.37 176 263
-1

5.3 186
-24 179.8 511
-15 186.04
45 -19.2 169.41 246
-30.1 56
-2

6.4 329
-11.

77 166.3 70
-24.1 180.08 493
-18.97 185 129 5.1
-18.

75 182.35 554
52 -19.26 184 223
-22.7 173
-21.3 180.6 593
-20.1 182.1 4

89
-19.85 182.13 562
445
-22.06 584
181.3 535
-24.2 530
61 -20.6 181.55 582
-21.16 182.4 260
-13.8 172 613
-11.4 166.2
-20.68 181.41
-17.1 184.9 286
-20.14 5

87
-21.96 179.6 627
181.8
-15.46 187 91
71 185.8 152
-19.86 184.3 201
-11.55
-23.7 179.

99 506
-17.7 181.23 546
-23.54 180.04 564
-19.21 184.7 197
-12.11 167.06 265
-21.8 181.71 323
-28.98 181.11 304
-34.02 180.21
-23.8 180.9 367
-19.5 182.38 579
-20.12 183 284
450
184.31 170
-21.5 170.5 117
88 -23.6 179.9 538
-15.43 186.3 123
-15.41 186.4
-15.48 167.5 128
-13.36 236
-20.64 182.02 497
-19.7 169.71 271
-15.44 185.2 224
-19.73 375
-27 365
-18.1 183.4 306
-13.66 166.54
100 -24.5 179.92 484
101 -16.9 18

5.6 108
102 -26 178 583
103 -21.88 180.3 608
104 -33
105 -21.33 180.69 636
106 -19.4 183.5 293
107 -34.89
-20.2 169.49
109 -22.55 185.9 5.7
110 -36.95 177 146
111 -15.7 185.23 280
112 -16.85 182.31 388
113 -19.06 182.45 477
114 -26.1 178.3 617
115 178.35 606
116 -26.13 178.31 609
172.23
118 -13.4 172.29
119 -14.6 167.4
120 -18.96 169.48 248
121 -14.65 166.9
122 -19.9 178.9
-22.05 180.4
124 -19.22 182.43 571
125 -31.24
126 -17.93 167.89
127 -19.3 183.8 517
-26.5 178.57
-27.72
130 -19.1 183.51 307
131 -17.4 185.4 189
132 -17.05 181.22 527
133 -19.52 168
134 -23.71 510
135 180.82 624
136 -16.2 168.02
137 -16.1 187.32
138 -23.9 182.8 199
139 -25.2 182.6 149
140 -18.84 184.1 210
141 -12.66 169.46 658
142 -20.65
143 -13.23 167.1 220
144 -29.9 181.43 205
145 -14.3 173.5 614
147 185.1
148 -21.2 173.49
-23.58 180.17 462
150 573
151 -23.34 184.5
-15.5 167.62
153 -23.83 182.5 229
154 -11.8 165
-15.54 167.68
156 181.32 597
157 -11.75 166.07
158 -24.81 452
159 -20.9 169.84
160 -11.34 166.24
161 -17.98 180.5
162 -24.34 179.5 504
163 -13.86 167.16 202
164 -35.56
-35.48
-34.2 179.43
182.12
-19.89 244
-23.43 553
-18.89 169.42 239
171 -17.82 181.83 640
-25.6 180.34 434
174 -15.2 184.6
175 -15.03 182.2 399
-32.2 216
-22.64 180.64 544
-17.42 185.16
-17.84 181.48 542
-15.02 184.2 339
-18.04 181.75
-24.6
-19.88
-20.3
-20.45 181.85 534
-17.67 187.09
-22.3 181.9 309
188 576
-24.27 179.88 523
190 -15.8 185.13 290
191 -20.02 184.09 234
192 -18.5 169.31
193 -17.87 569
194 -24.08 605
195 179.61 422
196 -20.36 181.19 637
-23.85 182.53 204
198 182.75
-20.41 181.74
200 -17.72 595
-19.67 182.18 360
203 -16.23 183.59
-26.72 183.3
-12.95 169.09 629
-21.97 182.32 261
207 180.54 603
208 -20.32 181.69 508
209 -30.28 180.62 350
533
-30.66 180.13 411
212 -16.17 338
213 -28.25 226
214 -20.47 185.6
215 180.27
-20.94 181.58
217 -26.6
218 -18.13 181.52 618
219 -20.21 183.83 242
-18.3 182.39 342
221 -16.52 185.7
222 -22.36 171.65
-22.43 184.48
-20.37 397
225 -23.77 505
-13.65 166.6
227 -21.55 182.9
228 185.75
-23.73 232
-22.34 171.5
231 180.94 664
-24.64 180.81
233 182.82
-19.62 185.3
235 525
179.93
237 -28.23 182.68
238 -21.6 180.63
-13.44 166.53
240 -24.96 180.22 470
241 -20.08 182.74 298
-24.36 182.84
243 -14.7
-18.2 183.6
245 -16.65 185.5
-18.11 181.67
247 -17.95 181.65 619
186.9
249 -23.36 180.01
250 -19.15 169.5
251 -10.97 166.26
252 -14.85 167.24
253 181.38 587
254 170.4
255 -29.1
256 180.88 680
257 -16.09 184.8
258 -19.18
259 -23.81 179.36 521
-23.79 179.89 526
-19.02 184.23 270
262 181.51 548
169.01
264 -17.88
-19.41 183.05 300
266 -26.17
267 -14.95
268 -18.73 168.8
269 182.37 482
-21.29 180.85 607
-19.76
272 -22.09 180.38 590
273
274 -20.16 181.99
275 -22.1 577
276 -17.44 529
277 -23.33 180.18 528
278 -24.78 179.22 492
279 180.52 561
-19.13 182.51
281 -30.72 413
282 -22.32 565
283 -16.4 177.77
383
285 184.68
-24.4 179.85 522
287 671
288 -21.13 185.32
289 -18.07 181.57 572
182.28
291 -18.4 181.49 641
-13.34
-20.92
294 -25.31 179.69 507
295 -15.24 186.2
296 185.86
297 178.4
-17.94 601
299 -30.64
-18.6 169.32
301 -13.09 169.28 654
302 -19.68 184.14
303 -16.44 185.74
-21.09 555
305 -14.99 171.39
179.7 500
-17.68 181.36 515
308 180.53
-21.38 181.39 501
310 -32.6
311 -13.05 169.58 644
312 -12.93 169.63
313 181.91 442
314 -21.34 464
315 -21.4 183.78
316 181.02 479
317 -17.32 181.03
318 -18.77 169.24
319 -26.16
320 -12.59 325
321 -14.82 167.32
322 -21.79 183.48
-19.83 182.04 575
324 -29.5
-12.49 166.36
326
327 -21.04 483
-10.78 165.77
-20.76 185.77
330 -11.41
331 183.87
332 -23.91
333 -27.33
334 -12.25
335 -23.49 179.07
336 -27.1
337
-27.19
-27.27
340
341 -27.22
-27.38
343
344 -27.54
345
346 -27.71 182.47
347 -27.6
348
-21.54 185.48
-27.21
351 -28.96 182.61
352 -12.01 166.29
353 -17.46
354 -30.17
355 182.36
356 -17.79
357 -22.19 171.4
358 403
359 -27.18
-11.64 166.47
361
362 185.72
363 -21.98
364 -32.14 406
169.21
366 -26.78 183.61
-20.43 502
368 183.2
369 -15.83 423
370 -23.44 182.93
371 179.99
372 184.08
373 -17.59 181.09 536
374 -19.77 630
-20.31 184.06
376 -15.33 186.75
377
378 -15.36 186.66
379 -15.29 186.42
380 186.71
381 167.95
382 167.14
-25.5
384 -14.32 167.33
385 -20.04 182.01
386 -28.83 181.66
387
-27.23 180.98 401
389 -10.72 165.99
390 183.88
391 186.1
392 -27.17
393 181.26 556
394 417
395 591
396 646
181.42
398 -15.87 188.1
400 -13.45 170.3
-30.8 182.16
402 -11.63 166.1
-30.4
404 -26.18 178.59
405
407 -20.51
408 167.51
409 -23.61 180.23 475
410 -33.2
186.8
412 -22.2 184.56
-20.07 169.1
414 -25.04 481
415
416 -14.28 167.26
-14.43
418 -32.7
419 -34.1
420
421 -24.19
182.77
-17.04
424 179.71
425
426
427 -20.58 181.24 602
428 -20.61 488
429 -19.47 169.15
430 -17.47 180.96
432 180.26
433 -18.55 182.23 563
178.47 537
435
436 -27.63
437
438 476
439 -20.56 499
440
441 166.37
-21.05
443 -17.97 168.52
444 182.54 524
183.81
446 -22.28 183.52
447 -15.72 185.64
448 -20.85 181.59
449 -21.11
180.15 467
451 -26.46
-24.09 179.68
453 -16.96 167.7
454 -23.1
455 -20.81
456
457 -18.06 604
458
459 -23.53
460 -18.18 639
461 -15.66
463 -18.08 628
-18.05 180.86 632
465
466
-15.61
468 -16.03
469 568
-31.94 180.57
471 -19.14 184.36
472
473 -16.95 185.94
474 -10.79 166.06
-20.83
-32.9
-37.93 177.47
478 -29.09
-23.56
480
-21.39 180.68
184.87
-32.42 181.21
485
486
487 -34.4
-17.61
489 -21.07 181.13 594
490 -13.84 170.62 638
491 -30.24 181.63
-18.49 169.04
-23.45 520
494 -16.04 183.54
495 -17.14 185.31
496 -22.54 172.91
-15.9
-30.04
-24.03
184.46
-16.51 187.1
503 -21.06
-13.07 166.8
-23.46 180.09 543
589
-11.81 165.98
-11.76 165.96
509 -12.08 165.76
-25.59 180.02
-26.54 183.63
512 184.28
513 -16.99
514 541
-17.81 181.82 598
516 -15.17 187.2
-11.67 166.02
518 -20.75 184.52
519
179.79
-20.66
570
-24.68 183.33
167.38
-32.45 181.15
-21.31 180.84 586
167.18
-13.26 167.01
-15.26 183.13
-33.57
531 -15.77
532 -15.79 166.83
-16.28 166.94
-23.2
167.25
181.31 549
-15.96 166.69
539 -15.95 167.34
540 -17.56
167.42
-15.86 166.85
545 -15.71 166.91
-16.45 167.54
547 -11.54 166.18
-19.61
187.15
550
551 182.22
552 -20.33 168.71
-15.08 166.62
184.61
-23.12 184.42
557 -23.65
558 -22.9 183.95
559 180.47
560 -13.56 166.49
-17.99
-23.92 184.47
-30.69
-21.92
180.97
566 -19.92 183.91
567 -27.75 182.26
-17.71 181.18
-34.68
-14.46
-18.85 187.55
-17.02 182.41
186.51
-16.49 187.8
-17.74
578 -20.49
-18.51 182.64
580 -27.28
581
-20.57 181.33
-11.25
181.87
-20.89 181.25 599
-16.62 186.74
-20.09 168.75
588 179.87
-20.95
-23.31 179.27
181.06 611
592 -21.58
-13.62 167.15
-12.72 166.28
596 -20.48 169.76
-12.84 166.78
-23.89
-23.07 184.03
-27.98 181.96
-28.1 182.25
-21.24
615
174.46
-32.82
-21.57 185.62
180.92
610 -33.03
-30.09
612 -22.75 170.99
168.98
-15.65 186.26
616 -17.78 181.53
-22.04 184.91
-20.06 168.69
181.54
620 -12.85 165.67
621 -33.29
622 -34.63 179.1
623 -24.18 179.02
-23.78 180.31
625 -22.37
-23.97 179.91
-34.12
-25.25 179.86
-22.87 172.65
-18.48
631 -21.46
-28.56 183.47
633
634
635 183.22
-18.82 182.21
-19.51 183.97
-12.05 167.39
186.54
-23.93
-21.23
642 167.91
643 -28.15
185.01
645 -20.72
-23.29
647 -38.46 176.03
648 186.73
649 -37.03 177.52
650
651 -18.12 181.88
652 -18.17 181.98
653
180.12
655 170.34
656 171.72
657
659
660 180.58
661 -30.01
662 -19.19
663 -18.14 180.87
180.11
665 -18.44 181.04
666 -18.21
667 -18.26
668 184.83
669 -23.82
670
672
673
674 -19.34 182.62
675 -15.34
676 -24.97 182.85
677 -15.97 186.08
678 -23.47 180.24
679 -23.11 179.15
-20.54
681 -18.92 169.37
682 184.27
683 -25.48
684 -18.19
685 -15.35
686 -18.69
687
688 183.32
689 -20.93
690
691 -17.96
692
693 182.44
694 -20.74
695 -25.23
696
697
698 185.19
699
700
701 -13.9
702 -17.64 177.01
703
704
705 -19.45
706 -16.11 187.48
707 179.98
708 186.78
709 -21.56 183.23
710 -20.97 181.72
711 -15.45
712 -15.93
713 -21.47
714 -21.44 170.45
715 -22.16 180.49
716 172.76
717 -21.22
718
719 -18.35 185.27
720 -17.2
721 -22.42
722 -17.91
723
724 178.29
725 -16.31 168.08
726 -18.76
727
728 -19.28 182.78
729
730 -21.26
731
732 -26.02
733 -30.3
734 -24.89 179.67
735 -14.57
736 186.87
737
738 -25.14 178.42
739
740 -25.28 181.17
741 -20.63 181.61
742 186.83
743
744 -38.59 175.7
745
746 -31.03
747 -30.51
748 183.34
749 -22.14
750
751 181.84
752
753 -21.08
754 169.66
755 -24.41 180.03
756 -12.16 167.03
757
758
759 -12.34 167.43
760 -16.43
761
762 -21.18
763 185.33
764 183.86
765 -13.7 166.75
766 -12.27 167.41
767
768 184.51
769 -11.37 166.55
770
771 -20.24
772 182.73
773 184.53
774 -21.63 180.77
775
776 -21.77
777
778
779 -10.8 165.8
780
781 -22.26 171.44
782 -22.33 171.46
783 -24.04 184.85
784
785 184.62
786 -27.87
787 -14.1 166.64
788
789
790 -21.19
791
792 178.43
793
794
795
796 -31.8
797 -18.91
798
799
800
801
802 -23.42
803
804 169.52
805 -21.14
806 184.97
807
808
809
810 179.84
811 -21.85 180.89
812 186.59
813
814
815
816 -22.12
817 -15.39
818 -16.21 186.52
819 -21.75 180.67
820
821 179.54
822 -19.36 186.36
823 179.62
824
825 -18.54 168.93
826 -21.62
827
828
829 -15.67
830 -21.78 183.11
831 -30.63
832
833 184.37
834
835 182.29
836
837 -17.38 168.63
838 -24.33 179.97
839 185.26
840 169.44
841 181.62
842 185.25
843 -25.42 182.65
844 169.9
845 -26.06 180.05
846
847 -25.63
848 -25.46
849 -22.23 180.48
850
851 -15.18 185.93
852 -13.79 166.56
853 167.23
854 -18.78 186.72
855
856
857 171.17
858 185.17
859
860 -13.16
861 -21.03 180.78
862
863 181.89
864 -20.87
865 166.66
866
867 -22.85 181.37
868 -17.08 185.96
869 174.21
870 -12.23 167.02
871 -20.91
872 -11.38 167.05
873 -11.02
874
875
876 -18.94
877
878 -21.91 181.28
879 -22.03 179.77
880
881 184.84
882
883
884
885 182.69
886 -24.39 178.98
887 -19.64
888 -21.35 170.04
889 -22.82
890 -38.28 177.1
891 -12.57 167.11
892 180.28
893
894
895
896 -23.87
897
898
899 185.11
900 181.27
901
902
903 -33.09
904 -20.18
905
906
907 -24.71
908 -21.53 170.52
909 -19.17 169.53
910 -28.05
911 -23.39
912 171.51
913 -15.28 185.98
914 -20.27
915 -10.96 165.97
916 -21.52 169.75
917 -19.57
918 -23.08 183.45
919 -25.06
920 -17.85 181.44
921 -15.99
922 184.41
923
924 181.77
925 -27.64
926 -20.99
927 -14.86
928 -29.33 182.72
929 -25.81
930 166.01
931 -17.63
932
933
934 -20.88 185.18
935 -20.25 184.75
936 -19.33 186.16
937
938 -22.41 183.99
939 -20.77
940 181.73
941 181.01
942 -27.84
943 -19.94
944
945 184.13
946 -30.39
947 -18.98
948 -27.89 182.92
949
950 184.49
951
952 -35.94 178.52
953 -18.68
954 179.95
955 180.06
956
957 -27.08 183.44
958 184.95
959
960 -21.71 183.58
961
962 -15.78 167.44
963 166.72
964 -19.69
965
966
967
968 180.74
969 166.98
970 -23.95 184.64
971 -25.79
972 -23.75
973
974 -18.56 169.05
975
976 -17.03
977 183.71
978
979 -18.83
980 170.7
981 -20.82
982 -22.95 170.56
983 -28.22
984 -27.99
985
986 -12.37 166.93
987 171.66
988
989 -17.86
990
991 -20.73
992
993 -20.05
994
995
996 -25.93
997 -12.28
998 -20.13
999
1000 -21.59
1

3

4

2

4

1

543

8

2

9

5673

09

7

19

47

008

2

08

5

43

7

41

22

0

2

7

16

8

8

8

6

5

4

78

6018

5

805

19

49

081

489

42

64

78

943

7

93943

6993

6059

3

98438743

99

7673391

9

908

58

8729487

1

42

08940730878

738

68564

58968

894585

3857

4

00618

00

40474

8

965

1300225

577578

38739

889

12

9055

425

968

5

88

8

7064

14

60

45508

69

02

0703993

388

6

59

2

583477645653

460119

3696822

883809544357

4834

81

5

3

687

01

935

7

65394046704

517

166808

16

49

39746033

638100

07

5559

8

5771336

8737159

27

52

416

7729

54

354056061

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13

69536

9

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98

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5424

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596

4733617

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32397500115

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19511

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11

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658260178

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39

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9

26998330937

954

359

183848745876

716

9658022

8

168469634268

13

54484788995

045

65274

7

61

14

3129

8417522

797067

42988905

17085601

57607

15

1395562741

94881934915

171594

260458

5517505

16

819

3749

31923

9519

9976829

3

1763

612

17

24

9676

07

174

18

232

251

34566046

76

19

89007174

562893

1592442

918523445

485838236752

20

1

6470609

13164677

66642

10689939011

21

88786873

30845705238

22

4

258568778

64

23

0835300

5

32222694

24

1246158

65837979

6

998774452

25

494561

26

236614

27

241612

28

379013963

29

70240996778

30

91877493732

9543191124

31

38998322

088

32

33

34

35

36

37

38

24

59703986

39

40

41

02

42

8275824845

43

44

45

46

001771561

47

01332

48

49

50

51

0968190551

52

53

54

55

56

073774571

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

211

212

213

214

215

216

217

218

219

220

221

222

223

224

225

226

227

228

229

230

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

271

272

273

274

275

276

277

278

279

280

281

282

283

284

285

286

287

288

289

290

291

292

293

294

295

296

297

298

299

300

V

1 V

2 V

3 V

4 V

5 V

6 V

7 V

8 V

9 V

10
-1.0

48 89 14 35 86 54 -0.5

11 56 85 39 61 19 -0.

38 41 43 94 15 0.

73 22 26 68 23 77 0.

67 16 17 42 1.

27 20 47 50 62 -0.386

60 29 30 74 -0.

70 33 69 28 99 0.

91 98 55 81 79 65 -0.8

90 93 57 59 239
1.

294 63 25 45 84 1.014

52 24 96 82 0.

32 193 78 80 0.00

18 76 58 64 71 -0.

277 49 31 159 0.47096

279 72 -0.

147 97 87 108 0.2

36 262 95 0.4

40 300 206 0.9

180 265
0.825

53 34 0.6

116 37 0.77

66 117 51 -0.8

13 119 83 0.653909

139 100 -0.

290 1.

185 184 241 88 1.788

268 187 -0.

92 44 1.8800

168 288
-0.05568601

172 -0.77

225 133 -2.4

130 250 163 -0.479495534457026 0.080350

190 -1.063430

75 -2.

273 200 -0.93438659354

12 -2.65108

102 21 -1.24

46 196
-0.7843822

175 181 0.6809

155 238 1.

150 215 148 224 -0.48

259 145 0.45590

260 188 -0.755939591004849 1.04290497175446 -1.4

210 244 -0.488

131 179 115 3.7937630474411
-0.733503

222 149 -0.

207 -0.68002411966491 0.768721

192 0.834532060457924 0.99853

166 -0.

128 -0.685

266 236 1.

189 271 157 0.01858

129 284
-0.2

158 0.837426507279305 0.

293 201 -0.04602

223 118 -0.69

272 -1.31288379776602 -0.947808054035307 0.969704520629497 -1.

195 237 -1.0779619

103
-0.3349

127 -0.

291 287 -0.413969737

209 0.759870166

249 -1.57

178 156 -1.46

245 -0.573744095237

121 -1.47768813353584 -2.5

269 160 -0.9086327

137
-1.085699

135 0.3206010802

252 -0.

295 258 -2.

162 282 0.967507379847

173 0.71568

171 1.43987355831294 -1.03

186 213 0.467091506098809 2.8974866

226
-0.0854

232 -1.36977576086265 -2.96365835059083 -0.7

230 -1.59447513085598 -1.0439926094

170 -3.4560636

274 -2.740082

122 -0.73057070964

120 -6.52797831798

112
1.0706

105 143 0.291

229 0.867056928483376 -0.537076518743

183 0.

202 256 1.20935190758918 1.76

125 1.20037063318729 1.76904906948857 1.186079783

289
-0.14539355099

270 1.38554546858

176 1.

278 1.05079670

124 -0.411738034

228 0.

126 0.131183940

298 0.09044

275 0.71023651193

285 -0.0

109
-1.

165 0.

169 235 -2.8942887765

220 -1.46582307301181 0.750798131695606 -2.06570830348222 -1.86476023245272 0.467684224581887 -3.697548393

114 0.984086649374962
-0.81851572

251 1.0689

212 2.07295

297 0.2008

174 2.256

107 2.03758794322301 2.18734572459925 2.10818849586002 0.4602383

110 4.03817881963851
0.684936077925063 -1.58588915921206 -2.1

240 -0.4

253 -0.661869892228

233 -0.779416

247 -1.50795753019396 -0.477952294354622 -0.0673705

101 -3.4020

164
-0.320056419

276 -0.38385009

197 -0.150974987776029 1.542764

234 -0.12411433

246 1.9825

243 -0.13079239961725 -0.3027

141 153 1.68974988309147 -0.309470926

111
-1.31

152 113 0.864834417612731 1.073353

104 261 0.500707238958464 0.269395933461581 -0.349839383300

142 1.71787999

151 0.171769493872447 0.0346764615658556 1.49549358813359
-0.599608327943981 0.561250341094273 -0.544987903

146 1.10980861414807 -0.844573956

248 -1.6066459458021 1.063

154 0.3437036816

254 -3.94416671099523 -1.25403840583718
-0.1294

106 -1.43983705890361 -2.81012

231 -0.76124

194 -0.413722343348169 -0.588759900338305 -2.97393738963

299 0.148

134 0.

182 -3.48663301843564
0.886736147003819 -1.0061661467

123 0.62397

205 1.2071160988788 -1.

286 264 1.14881200652795 0.1473933

161 0.111974064414983 0.872722287111

263 -3.

280
-0.151395962335781 -0.940355026554107 1.07438649769442 0.447529832761294 -1.671

227 -0.523103030975376 1.67470833287137 1.90700970488473 -1.

138 0.345956287430998
0.329791200757734 0.053451332153781 0.64671945919

219 0.904

211 -0.940377247318525 1.014976721

208 0.377451223406648 1.17479974567585 1.68591008681761 -1.89345043438607
-3.2273228297675 -0.573945495641693 -0.351711397205462 -0.332790557094147 0.223232661640596 -0.851586552097446 1.

221 217 -0.1631

255 -4.56555648525086 -0.293184703561543
-0.77179

177 0.22054883007557 0.336393499041208 1.52009878365097 -0.0

136 296 1.28

216 0.590897052853454 -1.46411119515994 0.798400485588341 0.892228607540781
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0.689880912612876 0.849443442407863 0.63969329219827 -0.164941404465841 -0.190503607942915 0.842805186410222 -0.182602813347105 1.05617018286749 0.855395003195318 -0.265011938288247
-1.70446554880575 1.61090482414801 -1.14893047613666 -0.414581737624283 -1.02933989627099 1.34874501503087 -1.41251893462161 -1.59662916635434 2.14476765832609 0.881634254103988
1.10537213468354 0.0552999460562607 -0.186708778833374 0.95288095707738 0.590311039170979 0.439396729930229 -0.421432404013487 -0.230517033050334 1.58477309611316 -0.433808060510667
-0.313852814685915 1.2053964476066 2.21290155037126 -0.300182450475621 -0.438949049008103 0.788104181779212 1.33219980146524 1.5757067263248 0.307420309354325 0.611848996904082
-0.346692745478719 -1.74628449112984 -0.394192918455534 -0.0106887372616722 0.99634754876334 0.634687849707755 -0.529157318940961 -0.0295994416846092 1.63904652738618 1.48747122093567
1.0384404772982 -0.751873044369511 0.503111025219406 1.01912547691678 1.67509190068467 -1.2002430337711 0.227774534205532 -1.26959101757111 -1.17278570334435 1.71169288572813

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Areas of Expertise

Although you can leverage our expertise for any writing task, we have a knack for creating flawless papers for the following document types.

Areas of Expertise

Although you can leverage our expertise for any writing task, we have a knack for creating flawless papers for the following document types.

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Trusted Partner of 9650+ Students for Writing

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Our Services

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Check Out Our Sample Work

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It May Not Be Much, but It’s Honest Work!

Here is what we have achieved so far. These numbers are evidence that we go the extra mile to make your college journey successful.

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We Analyze Your Problem and Offer Customized Writing

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We Handle Your Writing Tasks to Ensure Excellent Grades

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