••
Submit your codes and outputs in a readable format (Word, HTML, Text, or PDF
file) for full credits!
Part1-Python Programming
Multiple Linear Regression Analysis
1) Download the file ‘bmi’ in the homework folder of the Course Blackboard
Read in the file and display the first 5 observations
2) Draw the histograms and pairwise scatter plots of all numeric columns using seaborn
pairplot.
3) Check the pairwise correlation coefficients between variables. Interpret the result and
state which variables have significant linear relationships with ‘BodyFatSiriEqu’.
4) Use ‘BodyFatSiriEqu’ as output variable and all other columns as input variables to
develop a regression model. Write the regression model equation.
5) Identify all significant coefficients of predictors at α=0.05 level using t-tests.
6) Interpret the meaning of coefficients. Compare and interpret the regression model to
the result of the pairwise correlation coefficients in (c).
7) Remove insignificant predictors from (e) and develop a regression model with
remaining significant input variables. Write the regression model equation. Compare
and interpret the regression models from (d) and (f)
8) Test the overall model using F-test of the regression output in (f). Interpret the result
of the test.
9) State the goodness-of-fit of the regression model
10) Draw the residual plots against each significant predictor, and output variable.
Interpret the results of the plots.
11) Describe any problem or issue of the above regression model and explain how to
improve the regression model.
Part2-Statistics
1) True/False Questions
1. Data points that lie apart from the rest of the points are called deviants.
2. In simple regression analysis the error terms are assumed to be independent and normally
distributed with zero mean and constant variance.
1
3. One of the major uses of residual analysis is to test some of the assumptions underlying
regression.
4. In the simple regression model, y = 21 − 5x, if the coefficient of determination is 0.81,
we can say that the coefficient of correlation between y and x is 0.90.
5. To determine whether the overall regression model is significant, the F-test is used.
6. The F-value to test the overall significance of a regression model is computed by dividing
the sum of squares regression (SSreg) by the sum of squares error (SSerr).
7. In a multiple regression model, the partial regression coefficient of an independent
variable represents the increase in the y variable when that independent variable is
increased by one unit if the values of all other independent variables are held constant.
8. In the model y = 0 + 1×1 + 2×2 + 3×3 + is a constant.
9. The F test is used to determine whether the overall regression model is significant.
10. If we reject H0: β1= β2=0 using the F-test, then we should conclude that both slopes are
different from zero.
2) Short Answer and Multiple-Choice Questions
11. The coefficient of correlation in a simple regression analysis is = – 0.6. The coefficient of
determination for this regression would be _______.
12. For the following scatter plot and regression line, at x = 65 the residual is _______.
2
Y
600
500
400
300
200
100
0
0
10
20
30
40
50
60
70
X
13. The following residuals plot indicates _______________.
a) a nonlinear relation
b) a nonconstant error variance
c) the simple regression assumptions are met
d) the sample is biased
e) the sample is random
14. The following residuals plot indicates _______________.
a) a nonlinear relation
b) a nonconstant error variance
c) the simple regression assumptions are met
d) the sample is biased
e) a random sample
15~18) Louis Katz, a cost accountant at Papalote Plastics, Inc. (PPI), is analyzing the
manufacturing costs of a molded plastic telephone handset produced by PPI. Louis’s independent
3
variable is production lot size (in 1,000’s of units), and his dependent variable is the total cost of
the lot (in $100’s). Regression analysis of the data yielded the following tables.
Intercept
x
Coefficients
3.996
0.358
Standard Error
1.161268
0.102397
t Statistic p-value
3.441065 0.004885
3.496205 0.004413
Source
df
Regression 1
SS
9.858769
MS
F
9.858769 12.22345
Residual
Total
8.872
18.73077
0.806545
11
12
Se = 0.898
r2 = 0.526341
15. Louis’s sample size (n) is ________________.
a) 13
b) 14
c) 12
d) 24
e) 1
16. Using = 0.05, Louis should ________________.
a) increase the sample size
b) suspend judgment
c) not reject H0: 1 = 0
d) reject H0: 1 = 0
e) do not reject H0: 0 = 0
17. For a lot size of 10,000 handsets, Louis’ model predicts total cost will be _____.
a) $4,031.80
b) $757.60
c) $3,960.20
d) $354.01
e) $1873.077
18. The multiple regression formulas used to estimate the regression coefficients are designed to
________________.
a) minimize the total sum of squares (SST)
b) minimize the sum of squares of error (SSE)
c) maximize the standard error of the estimate
d) maximize the p-value for the calculated F value
e) minimize the mean error
4
19~20) A multiple regression analysis produced the following tables.
Predictor Coefficients
Intercept
616.6849
x1
-3.33833
x2
1.780075
Source
Regression
Residual
Total
df
2
15
17
Standard Error
154.5534
2.333548
0.335605
t Statistic p-value
3.990108 0.000947
-1.43058 0.170675
5.30407 5.83E-05
SS
MS
F
p-value
121783 60891.48 14.76117 0.000286
61876.68 4125.112
183659.6
19. Using = 0.05 to test the null hypothesis H0: 1 = 0, the critical t value is ____.
20. These results indicate that ____________.
a) none of the predictor variables are significant at the 5% level
b) each predictor variable is significant at the 5% level
c) x1 is significant at the 5% level
d) x2 is significant at the 5% level
e) the intercept is not significant at 5% level
21~27) A multiple regression analysis produced the following tables.
21. Using = 0.01 to test the model, these results indicate that ____
a) at least one of the regression variables is a significant predictor of y
b) none of the regression variables are significant predictors of y
c) y cannot be sufficiently predicted using these data
d) y is a good predictor of the regression variables in the model
5
22. The regression equation for this analysis is ____________.
23. The sample size for this analysis is ____________.
24. . Using = 0.05 to test the null hypothesis H0: 1 = 0, the correct decision is ____.
25. Using = 0.05 to test the null hypothesis H0: 2 = 0, the correct decision is ____.
26. The correlation coefficient is ____________.
27. The overall proportion of variation of y accounted by x1 and x2 is _______
6
UnderwaterDens
BodyFatSiriEqu
ity
1.0708
Age
Height
Weight(kg)
NeckCircumf
Abdomen2Circu
HipCircumf
mf
ChestCircumf
12.3
23
172.085
69.96662
36.2
93.1
85.2
94.5
1.0853
6.1
22
183.515
78.58488
38.5
1.0414
25.3
22
168.275
69.85322
34
93.6
83
98.7
95.8
87.9
99.2
1.0751
10.4
26
183.515
83.80119
37.4
101.8
86.4
101.2
1.034
28.7
24
180.975
83.57439
34.4
97.3
100
101.9
1.0502
20.9
24
189.865
95.3678
39
104.5
94.4
107.8
1.0549
19.2
1.0704
12.4
26
177.165
82.10022
36.4
105.1
90.7
100.3
25
184.15
79.83226
37.8
99.6
88.5
97.1
1.09
4.1
25
187.96
86.63614
38.1
100.9
82.5
99.9
1.0722
11.7
23
186.69
89.92469
42.1
99.6
88.6
104.1
1.083
7.1
26
189.23
84.48158
38.5
101.5
83.6
98.2
1.0812
7.8
27
193.04
97.97595
39.4
103.6
90.9
107.7
1.0513
20.8
32
176.53
81.87342
38.4
102
91.6
103.9
1.0505
21.2
30
180.975
93.09983
39.4
104.1
101.8
108.6
1.0484
22.1
35
176.53
85.16197
40.5
101.3
96.4
100.1
1.0512
20.9
35
167.64
73.82216
36.4
99.1
92.8
99.2
1.0333
29
34
180.34
88.79071
38.9
101.9
96.4
105.2
1.0468
22.9
32
180.34
94.9142
42.1
107.6
97.5
107
1.0622
16
28
172.085
83.3476
38
106.8
89.6
102.4
1.061
16.5
33
186.69
96.04818
40
106.2
100.5
109
1.0551
19.1
28
172.72
81.19303
39.1
103.3
95.9
104.9
1.064
15.2
28
177.165
90.94527
41.3
111.4
98.8
104.8
1.0631
15.6
31
173.355
63.61633
33.9
86
76.4
94.6
1.0584
17.7
32
177.8
67.47187
35.5
86.7
80
93.4
1.0668
14
28
172.085
68.60585
34.5
90.2
76.3
95.8
1.0911
3.7
27
181.61
72.23458
35.7
89.6
79.7
96.5
1.0811
7.9
34
171.45
59.6474
36.2
88.6
74.6
85.3
1.0468
22.9
31
171.45
67.13167
38.8
97.4
88.7
94.7
1.091
3.7
27
164.465
60.44118
36.4
93.5
73.9
88.5
1.079
8.8
29
175.26
72.91497
36.7
97.4
83.5
98.7
1.0716
11.9
32
187.325
82.55381
38.7
100.5
88.7
99.8
1.0862
5.7
29
180.975
72.68818
37.3
93.5
84.5
100.6
1.0719
11.8
27
180.975
76.20352
38.1
93
79.1
94.5
1.0502
21.3
41
180.34
99.10993
39.8
111.7
100.5
108.3
1.0263
32.3
41
186.69
112.1507
42.1
117
115.6
116.1
1.0101
40.1
49
165.1
86.97634
38.4
118.5
113.1
113.8
1.0438
24.2
40
177.8
91.73906
38.5
106.5
100.9
106.2
1.0346
28.4
50
173.355
89.2443
42.1
105.6
98.8
104.8
1.0202
35.2
46
183.515
164.7221
51.2
136.2
148.1
147.7
1.0258
32.6
50
170.18
92.07925
40.2
114.8
108.1
102.5
1.0217
34.5
45
174.625
119.1814
43.2
128.3
126.2
125.6
1.025
32.9
44
74.93
92.98644
36.6
106
104.3
115.5
1.0279
31.6
48
177.8
98.42954
37.3
113.3
111.2
114.1
1.0269
32
41
181.61
96.16158
41.5
106.6
104.3
106
1.0814
7.7
39
172.72
56.81244
31.5
85.1
76
88.2
1.067
13.9
43
186.055
74.50255
35.7
96.6
81.5
97.2
1.0742
10.8
40
171.45
60.55458
33.6
88.2
73.7
88.5
1.0665
5.6
39
180.975
67.35847
34.6
89.8
79.5
92.7
1.0678
13.6
45
173.99
61.57516
32.8
92.3
83.4
90.4
1.0903
4
47
169.545
57.83303
34
83.4
70.4
87.2
1.0756
10.2
47
183.515
71.78099
34.9
90.2
86.7
98.3
1.084
6.6
40
175.26
63.16274
34.3
89.2
77.9
91
1.0807
8
51
172.085
62.25555
36.5
89.7
82
89.1
1.0848
6.3
49
186.69
69.28623
35.1
93.3
79.6
91.6
1.0906
3.9
42
171.45
61.80196
37.8
87.6
77.6
88.6
1.0473
22.6
54
182.88
89.81129
39.9
107.6
100
99.6
1.0524
20.4
58
172.72
82.32702
39.1
100
99.8
102.5
1.0356
28
62
176.53
91.28546
40.5
111.5
104.2
105.8
1.028
31.5
54
179.705
91.85245
40.5
115.4
105.3
97
1.043
24.6
61
167.005
81.53323
38.4
104.8
98.3
99.6
1.0396
26.1
62
186.055
97.97595
41.4
112.3
104.8
103.1
1.0317
29.8
56
173.99
81.07964
35.6
102.9
94.7
100.8
1.0298
30.7
54
178.435
87.65673
38
107.6
102.4
99.4
1.0403
25.8
61
170.18
80.73944
37.4
105.3
99.7
99.7
1.0264
32.3
57
177.8
93.21323
40.1
105.3
105.5
108.3
1.0313
30
55
171.45
83.2342
40.9
103
100.3
104.2
1.0499
21.5
54
179.705
68.71924
35.6
90
83.9
93.9
1.0673
13.8
55
181.61
70.19342
36.9
95.4
86.6
91.8
1.0847
6.3
54
175.895
70.42022
37.5
89.3
78.4
96.1
1.0693
12.9
55
181.61
71.1006
36.3
94.4
84.6
94.3
1.0439
24.3
62
181.61
75.97672
35.5
97.6
91.5
98.5
1.0788
8.8
55
174.625
66.56468
38.7
88.5
82.8
95.5
1.0796
8.5
56
187.325
72.91497
36.4
93.6
82.9
96.3
1.068
13.5
55
162.56
56.69905
33.2
87.7
76
88.6
1.072
11.8
61
167.005
64.86371
36.5
93.4
83.3
93
1.0666
18.5
61
171.45
67.24507
36
91.6
81.8
94.8
1.079
8.8
57
176.53
73.70876
38.7
91.6
78.8
94.3
1.0483
22.2
69
173.99
80.62604
38.7
102
95
98.3
1.0498
21.5
81
178.435
73.14177
37.8
96.4
95.4
99.3
1.056
18.8
66
175.895
77.67769
37.4
102.7
98.6
100.2
1.0283
31.4
67
172.085
74.27575
38.4
97.7
95.8
97.1
1.0382
26.8
64
170.815
68.15225
38.1
97.1
89
96.9
1.0568
18.4
64
184.785
86.29595
39.3
103.1
97.8
99.6
1.0377
27
70
177.8
77.4509
38.7
101.8
94.9
95
1.0378
27
72
175.895
76.20352
38.5
101.4
99.8
96.2
1.0386
26.6
67
171.45
75.74993
36.5
98.9
89.7
96.2
1.0648
14.9
72
170.815
71.5542
37.7
97.5
88.1
96.9
1.0462
23.1
64
167.005
72.57478
36.5
104.3
90.9
93.8
1.08
8.3
46
184.15
80.17245
38
97.3
86
99.3
1.0666
14.1
48
185.42
79.83226
36.7
96.7
86.5
98.3
1.052
20.5
46
177.8
80.28585
37.2
99.7
95.6
102.2
1.0573
18.2
44
176.53
81.53323
39.2
101.9
93.2
100.6
1.0795
8.5
47
179.07
74.95614
37.5
97.2
83.1
95.4
1.0424
24.9
46
182.245
87.31653
38
106.6
97.5
100.6
1.0785
9
47
189.23
83.57439
37.3
99.6
88.8
101.4
1.0991
17.4
53
197.485
101.8315
41.1
113.2
99.2
107.5
1.077
9.6
38
186.055
85.61556
37.5
99.1
91.6
102.4
1.073
11.3
50
168.91
73.70876
38.7
99.4
86.7
96.2
1.0582
17.8
46
173.355
70.98721
35.9
95.1
88.2
92.8
1.0484
22.2
47
182.88
89.3577
40
107.5
94
103.7
1.0506
21.2
49
186.69
90.03809
40.1
106.5
95
101.7
1.0524
20.4
48
182.88
78.81167
37
99.1
92
98.3
1.053
20.1
41
180.975
78.35808
36.3
96.7
89.2
98.3
1.048
22.3
49
187.325
89.2443
40.7
103.5
95.5
101.6
1.0412
25.4
43
175.895
80.28585
39.6
104
98.6
99.5
1.0578
18
43
173.99
75.06954
31.1
93.1
87.3
96.6
1.0547
19.3
43
186.69
90.83187
38.6
105.2
102.8
103.6
1.0569
18.3
52
188.595
92.19265
42
110
101.6
100.7
1.0593
17.3
43
191.77
87.99692
38.5
110.1
88.7
102.1
1.05
21.4
40
175.895
76.43031
34.2
97.8
92.3
100.6
1.0538
19.7
43
173.99
77.4509
37.2
96.3
90.6
99.3
1.0355
28
43
177.8
83.1208
37.1
108
105
103
1.0486
22.1
47
177.8
80.85284
40.2
99.7
95
98.6
1.0503
21.3
42
178.435
73.93556
35.3
93.5
89.6
99.8
1.0384
26.7
48
182.245
79.49206
38
100.7
92.4
97.5
1.0607
16.7
40
175.895
71.66759
36.3
97
86.6
92.6
1.0529
20.1
48
184.785
80.39925
36.8
96
90
99.7
1.0671
13.9
51
182.88
81.19303
41
99.2
90
96.4
1.0404
25.8
40
187.96
86.63614
38.3
95.4
92.4
104.3
1.0575
18.1
44
183.515
85.04857
38
101.8
87.5
101
1.0358
27.9
52
189.23
93.66682
40.8
104.3
99.2
104.1
1.0414
25.3
44
181.61
84.02799
39.5
99.2
98.1
101.4
1.0652
14.7
40
174.625
72.68818
36.9
99.3
83.3
97.5
1.0623
16
47
169.545
68.71924
36.9
94
86.1
95.2
1.0674
13.8
50
168.91
73.02837
37.7
98.9
84.1
94
1.0587
17.5
46
170.18
75.74993
36.6
101
89.9
100
1.0373
27.2
42
174.625
80.51265
38.9
98.7
92.1
98.5
1.059
17.4
43
172.085
69.05944
37.5
95.9
78
93.2
1.0515
20.8
40
186.055
87.20313
39.8
103.9
93.5
99.5
1.0648
14.9
42
177.165
74.95614
38.3
96.2
87
97.8
1.0575
18.1
49
181.61
77.90449
35.5
97.8
90.1
95.8
1.0472
22.7
40
179.07
77.67769
36.3
94.6
90.3
99.1
1.0452
23.6
47
186.055
89.3577
37.8
103.6
99.8
103.2
1.0398
26.1
50
169.545
71.214
37.8
100.4
89.4
92.3
1.0435
24.4
41
176.53
76.31692
36.5
98.4
87.2
98.4
1.0374
27.1
44
177.165
84.36818
37.8
104.6
101.1
102.1
1.0491
21.8
39
179.705
75.63653
37
92.9
86.1
95.6
1.0325
29.4
43
187.96
85.16197
37.7
97.8
98.6
100.6
1.0481
22.4
40
180.975
76.31692
34.3
98.3
88.5
98.3
1.0522
20.4
49
190.5
96.50178
40.8
104.7
106.6
107.7
1.0422
24.9
40
180.34
80.17245
37.4
98.6
93.1
101.6
1.0571
18.3
40
176.53
78.58488
36.5
99.5
93
99.3
1.0459
23.3
52
172.085
75.74993
37.5
102.7
91
98.9
1.0775
9.4
23
183.515
72.46138
35.5
92.1
77.1
93.9
1.0754
10.3
23
196.85
85.3434
38
96.6
85.3
102.5
1.0664
14.2
24
179.705
70.76041
35.7
92.7
81.9
95.3
1.055
19.2
24
184.785
94.57401
39.2
102
99.1
110.1
1.0322
29.6
25
177.165
93.66682
40.9
110.9
100.5
106.2
1.0873
5.3
25
184.15
65.2039
35.2
92.3
76.5
92.1
1.0416
25.2
26
178.435
101.1511
40.6
114.1
106.8
113.9
1.0776
9.4
26
175.26
69.05944
35.4
92.9
77.6
93.5
1.0542
19.6
26
189.23
109.656
41.8
108.3
102.9
114.4
1.0758
10.1
27
183.515
66.22449
34.1
88.5
72.8
91.1
1.061
16.5
27
170.815
71.1006
37.9
94
88.2
95.2
1.051
21
27
186.69
90.83187
38.2
101.1
100.1
105
1.0594
17.3
28
191.135
77.79109
35.6
92.1
83.5
98.3
1.0287
31.2
28
175.26
93.32663
38.5
105.6
105
106.4
1.0761
10
28
183.515
82.78061
37
98.5
90.8
102.5
1.0704
12.5
30
174.625
61.91536
35.9
88.7
76.6
89.8
1.0477
22.5
31
181.61
80.39925
36.2
101.1
92.4
99.3
1.0775
9.4
31
183.515
68.60585
35
94
81.2
91.5
1.0653
14.6
33
185.42
88.9041
38.5
103.8
95.6
105.1
1.069
13
33
174.625
83.57439
40.7
98.9
92.1
103.5
1.0644
15.1
34
179.07
63.50293
36
89.2
83.4
89.6
1.037
27.3
34
182.88
99.22333
39.5
111.4
106
108.8
1.0549
19.2
35
187.325
98.42954
40.5
107.5
95.1
104.5
1.0492
21.8
35
172.72
75.40973
38.5
99.1
90.4
95.6
1.0525
20.3
35
183.515
101.9449
43.9
108.2
100.4
106.8
1.018
34.3
35
176.53
103.5325
40.4
114.9
115.9
111.9
1.061
16.5
35
176.53
78.35808
37.6
99.1
90.8
98.1
1.0926
3
35
172.085
69.05944
37
92.2
81.9
92.8
1.0983
0.7
35
166.37
57.03924
34
90.8
75
89.2
1.0521
20.5
35
180.34
80.39925
38.4
100.5
90.3
98.7
1.0603
16.9
36
181.61
79.94566
38.7
98.2
90.3
99.9
1.0414
25.3
36
182.245
102.8521
41.5
115.3
108.8
114.4
1.0763
9.9
37
175.895
65.88429
36
96.8
79.4
89.2
1.0689
13.1
37
170.18
68.49245
35.3
92.6
83.2
96.4
1.0316
29.9
37
181.61
109.4292
42.1
119.2
110.3
113.9
1.0477
22.5
38
175.895
84.93517
38
102.7
92.7
101.9
1.0603
16.9
39
189.23
106.4808
42.8
109.5
104.5
109.9
1.0387
26.6
39
188.595
99.45013
40
108.5
104.6
109.8
1.1089
0
40
172.72
53.7507
33.8
79.3
69.4
85
1.0725
11.5
40
170.815
66.11109
35.5
95.5
83.6
91.6
1.0713
12.1
40
177.165
72.23458
35.3
92.3
86.8
96.1
1.0587
17.5
40
188.595
77.3375
37.7
98.9
90.4
95.5
1.0794
8.6
40
181.61
75.97672
39.4
89.5
83.7
98.1
1.0453
23.6
41
188.595
105.5736
41.9
117.5
109.3
108.8
1.0524
20.4
41
182.88
95.48119
38.5
107.4
98.9
104.1
1.052
20.5
41
184.15
91.73906
40.8
109.2
98
101.8
1.0434
24.4
41
173.355
83.91459
38
103.4
101.2
103.1
1.0728
11.4
41
175.895
69.39963
36.4
91.4
80.6
92.3
1.014
38.1
42
193.04
110.7899
41.8
115.2
113.7
112.4
1.0624
15.9
42
179.07
87.77012
40.7
104.9
94.1
102.7
1.0429
24.7
42
189.865
101.9449
38.5
106.7
105.7
111.8
1.047
22.8
42
184.785
73.82216
35.4
92.2
85.6
96.5
1.0411
25.5
42
173.355
81.64663
38.5
101.6
96.6
100.6
1.0488
22
42
175.26
70.87381
35.5
97.8
86
96.2
1.0583
17.7
42
181.61
76.20352
36.5
92
89.7
101
1.0841
6.6
42
184.785
75.86332
37.6
94
78
99
1.0462
23.6
43
171.45
77.4509
37.4
103.7
89.7
94.2
1.0709
12.2
43
178.435
80.85284
37.8
102.7
89.2
99.2
1.0484
22.1
43
175.895
68.03886
35.2
91.1
85.7
96.9
1.034
28.7
43
181.61
90.94527
37.9
107.2
103.1
105.5
1.0854
6
44
187.96
83.461
37.9
100.8
89.1
102.6
1.0209
34.8
44
177.165
101.1511
40.9
121.6
113.9
107.1
1.061
16.6
44
185.42
94.68741
41.9
105.6
96.3
102
1.025
32.9
44
166.37
75.29633
39.1
100.6
93.9
100.1
1.0254
32.8
47
184.15
88.45051
40.2
102.7
101.3
101.7
1.0771
9.6
47
178.435
72.80158
36
99.8
83.9
91.8
1.0742
10.8
47
179.705
72.46138
34.5
92.9
84.4
94
1.0829
7.1
49
172.72
63.72973
35.8
91.2
79.4
89
1.0373
27.2
49
189.23
98.08935
40.2
115.6
104
109
1.0543
19.5
49
182.245
76.31692
38.3
98.3
89.7
99.1
1.0561
18.7
50
179.705
88.33711
39
103.7
97.6
104.2
1.0543
19.5
50
185.42
78.35808
37.4
98.7
87.6
96.1
0.995
47.5
51
162.56
99.33673
41.2
119.8
122.1
112.8
1.0678
13.6
51
177.165
67.69866
34.8
92.8
81.1
96.3
1.0819
7.5
51
177.8
70.08002
36.9
93.3
81.5
94.4
1.0433
24.5
52
182.245
90.37828
39.4
106.8
100
105
1.0646
15
53
175.895
70.08002
37.6
93.9
88.7
94.5
1.0706
12.4
54
179.07
69.51303
38.5
99
91.8
96.2
1.0399
26
54
183.515
104.3262
42.5
119.9
110.4
105.5
1.0726
11.5
54
171.45
73.36857
37.4
94.2
87.6
95.6
1.0874
5.2
55
170.815
64.52351
35.2
92.7
82.8
91.9
1.074
10.9
55
174.625
81.53323
41.1
106.9
95.3
98.2
1.0703
12.5
55
169.545
57.37943
33.4
88.8
78.2
87.5
1.065
14.8
55
173.355
76.88391
37.2
101.7
91.1
97.1
1.0418
25.2
55
188.595
90.03809
38.3
105.3
96.7
106.6
1.0647
14.9
56
176.53
79.15187
38.1
104
89.4
98.4
1.0601
17
56
173.99
76.09012
37.4
98.6
93
97
1.0745
10.6
57
167.005
67.01827
35.2
99.6
86.4
90.1
1.062
16.1
57
182.245
82.66721
39.4
103.4
96.7
100.7
1.0636
15.4
58
181.61
79.60546
38
100.2
88.1
97.8
1.0384
26.7
58
170.815
73.36857
35.1
94.9
94.9
100.2
1.0403
25.8
60
171.45
71.5542
40.4
97.2
93.3
94
1.0563
18.6
62
171.45
76.54371
38.3
104.7
95.6
93.7
1.0424
24.8
62
183.515
86.86294
40.6
104
98.2
101.1
1.0372
27.3
63
176.53
99.40477
40.2
117.6
113.8
111.8
1.0705
12.4
64
176.53
70.42022
37.9
95.8
82.8
94.5
1.0316
29.9
65
167.005
86.06915
40.8
106.4
100.5
100.5
1.0599
17
65
167.005
57.83303
34.7
93
79.7
87.6
1.0207
35
65
173.355
101.8315
38.8
119.6
118
114.3
1.0304
30.4
66
182.88
106.254
41.4
119.7
109
109.1
1.0256
32.6
67
184.785
103.3057
41.3
115.8
113.4
109.8
1.0334
29
67
173.99
90.49168
40.7
118.3
106.1
101.6
1.0641
15.2
68
175.895
70.53361
36.3
97.4
84.3
94.4
1.0308
30.2
69
179.07
97.74916
40.8
113.7
107.6
110
1.0736
11
70
170.18
60.89478
34.9
89.2
83.6
88.8
1.0236
33.6
72
177.165
91.17207
40.9
108.5
105
104.5
1.0328
29.3
72
167.64
84.70838
38.9
111.1
111.5
101.7
1.0399
26
72
179.07
86.52274
38.9
108.3
101.3
97.8
1.0271
31.9
74
177.8
94.12042
40.8
112.4
108.5
107.1
ThighCircumf
KneeCircumf
ExtendBicepsCir
ForearmCircumf WristCircumf
cumf
AnkleCircumf
59
37.3
21.9
32
27.4
17.1
58.7
37.3
23.4
30.5
28.9
18.2
59.6
38.9
24
28.8
25.2
16.6
60.1
37.3
22.8
32.4
29.4
18.2
63.2
42.2
24
32.2
27.7
17.7
66
42
25.6
35.7
30.6
18.8
58.4
38.3
22.9
31.9
27.8
17.7
60
39.4
23.2
30.5
29
18.8
62.9
38.3
23.8
35.9
31.1
18.2
63.1
41.7
25
35.6
30
19.2
59.7
39.7
25.2
32.8
29.4
18.5
66.2
39.2
25.9
37.2
30.2
19
63.4
38.3
21.5
32.5
28.6
17.7
66
41.5
23.7
36.9
31.6
18.8
69
39
23.1
36.1
30.5
18.2
63.1
38.7
21.7
31.1
26.4
16.9
64.8
40.8
23.1
36.2
30.8
17.3
66.9
40
24.4
38.2
31.6
19.3
64.2
38.7
22.9
37.2
30.5
18.5
65.8
40.6
24
37.1
30.1
18.2
63.5
38
22.1
32.5
30.3
18.4
63.4
40.6
24.6
33
32.8
19.9
57.4
35.3
22.2
27.9
25.9
16.7
54.9
36.2
22.1
29.8
26.7
17.1
58.4
35.5
22.9
31.1
28
17.6
55
36.7
22.5
29.9
28.2
17.7
51.7
34.7
21.4
28.7
27
16.5
57.5
36
21
29.2
26.6
17
50.1
34.5
21.3
30.5
27.9
17.2
58.9
35.3
22.6
30.1
26.7
17.6
57.5
38.7
33.9
32.5
27.7
18.4
58.5
38.8
21.5
30.1
26.4
17.9
57.3
36.2
24.5
29
30
18.8
67.1
44.2
25.2
37.5
31.5
18.7
71.2
43.3
26.3
37.3
31.7
19.7
61.9
38.3
21.9
32
29.8
17
63.5
39.9
22.6
35.1
30.6
19
66
41.5
24.7
33.2
30.5
19.4
87.3
49.1
29.6
45
29
21.4
61.3
41.1
24.7
34.1
31
18.3
72.5
39.6
26.6
36.4
32.7
21.4
70.6
42.5
23.7
33.6
28.7
17.4
67.7
40.9
25
36.7
29.8
18.4
65
40.2
23
35.8
31.5
18.8
50
34.7
21
26.1
23.1
16.1
58.4
38.2
23.4
29.7
27.4
18.3
53.3
34.5
22.5
27.9
26.2
17.3
52.7
37.5
21.9
28.8
26.8
17.9
52
35.8
20.6
28.8
25.5
16.3
50.6
34.4
21.9
26.8
25.8
16.8
52.6
37.2
22.4
26
25.8
17.3
51.4
34.9
21
26.7
26.1
17.2
49.3
33.7
21.4
29.6
26
16.9
52.6
37.6
22.6
38.5
27.4
18.5
51.9
34.9
22.5
27.7
27.5
18.5
57.2
38
22
35.9
30.2
18.9
62.1
39.6
22.5
33.1
28.3
18.5
61.8
39.8
22.7
37.7
30.9
19.2
59.1
38
22.5
31.6
28.8
18.2
60.6
37.7
22.9
34.5
29.6
18.5
61.6
40.9
23.1
36.2
31.8
20.2
60.9
38
22.1
32.5
29.8
18.3
61
39.4
23.6
32.7
29.9
19.1
60.8
40.1
22.7
33.6
29
18.8
65
41.2
24.7
35.3
31.1
18.4
64.8
40.2
22.7
34.8
30.1
18.7
55
36.1
21.7
29.6
27.4
17.4
54.3
35.4
21.5
32.8
27.4
18.7
56
37.4
22.4
32.6
28.1
18.1
51.2
37.4
21.6
27.3
27.1
17.3
56.6
38.6
22.4
31.5
27.3
18.6
58.9
37.6
21.6
30.3
27.3
18.3
52.9
37.5
23.1
29.7
27.3
18.2
50.9
35.4
19.1
29.3
25.7
16.9
55.5
35.2
20.9
29.4
27
16.8
54.5
37
21.4
29.3
27
18.3
56.7
39.7
24.2
30.2
29.2
18.1
55
38.3
21.8
30.8
25.7
18.8
53.5
37.5
21.5
31.4
26.8
18.3
56.5
39.3
22.7
30.3
28.7
19
54.8
38.2
23.7
29.4
27.2
19
54.8
38
22
29.9
25.2
17.7
58.9
39
23
34.3
29.6
19
56
36.5
24.1
31.2
27.3
19.2
56.3
36.6
22
29.7
26.3
18
54.7
37.8
33.7
32.4
27.7
18.2
57.2
37.7
21.8
32.6
28
18.8
57.8
39.5
23.3
29.2
28.4
18.1
61
38.4
23.8
30.2
29.3
18.8
60.4
39.9
24.4
28.8
29.6
18.7
58.3
38.2
22.5
29.1
27.7
17.7
58.9
39.7
23.1
31.4
28.4
18.8
56.9
38.3
22.1
30.1
28.2
18.4
58.9
40.5
24.5
33.3
29.6
19.1
57.4
39.6
24.6
30.3
27.9
17.8
61.7
42.3
23.2
32.9
30.8
20.4
60.6
39.4
22.9
31.6
30.1
18.5
62.1
39.3
23.3
30.6
27.8
18.2
54.7
37.3
21.9
31.6
27.5
18.2
62.7
39
22.3
35.3
30.9
18.3
59
39.4
22.3
32.2
31
18.6
59.3
38.4
22.4
27.9
26.2
17
60
38.4
23.2
31
29.2
18.4
59.1
39.8
25.4
31
30.3
19.7
59.5
36.1
22
30.1
27.2
17.7
54.7
39
24.8
31
29.4
18.8
61.2
39.3
23.5
30.5
28.5
18.1
55.8
38.7
23.4
35.1
29.6
19.1
57.5
40
24.8
35.1
30.7
19.2
57.5
36.8
22.8
32.1
26
17.3
61.9
38
22.3
33.3
28.2
18.1
63.7
40
23.6
33.5
27.8
17.4
62.3
38.1
23.9
35.3
31.1
19.8
61.5
37.8
21.9
30.7
27.6
17.4
59.3
38.1
21.8
31.8
27.3
17.5
55.9
36.3
22.1
29.8
26.3
17.3
58.8
38.4
22.8
29.9
28
18.1
56.8
38.8
23.3
33.4
29.8
19.5
64.6
41.1
24.8
33.6
29.5
18.5
58.5
39.2
24.5
32.1
28.6
18
58.5
39.3
24.6
33.9
31.2
19.5
57.1
40.5
23.2
33
29.6
18.4
60.5
38.7
22.6
34.4
28
17.6
58.1
36.5
22.1
30.6
27.5
17.6
58.5
36.6
23.5
34.4
29.2
18
60.7
36
21.9
35.6
30.2
17.6
60.7
36.8
22.2
33.8
30.3
17.2
53.5
35.8
20.8
33.9
28.2
17.4
61.7
39
21.8
33.3
29.6
18.1
57.4
36.9
22.2
31.6
27.8
17.7
57
38.7
23.2
27.5
26.5
17.6
60.3
38.5
23
31.2
28.4
17.1
61.2
38.1
22.6
33.5
28.6
17.9
56.1
35.6
20.5
33.6
29.3
17.3
56
36.9
23
34
29.8
18.1
58.9
37.9
22.7
30.9
28.8
17.6
58.8
36.1
22.4
32.7
28.3
17.1
63.6
39.2
23.8
34.3
28.4
17.7
58.1
38.4
22.5
31.7
27.4
17.6
66.5
42.5
24.5
35.5
29.8
18.7
59.1
39.6
21.6
30.8
27.9
16.6
60.4
38.2
22
32
28.5
17.8
57.1
36.7
22.3
31.6
27.5
17.9
56.1
36.1
22.7
30.5
27.2
18.2
59.1
37.6
23.2
31.8
29.7
18.3
56.4
36.5
22
33.5
28.3
17.3
71.2
43.5
25.2
36.1
30.3
18.7
68.4
40.8
24.6
33.3
29.7
18.4
51.9
35.7
22
25.8
25.2
16.9
67.6
42.7
24.7
36
30.4
18.4
56.9
35.9
20.4
31.6
29
17.8
72.9
43.5
25.1
38.5
33.8
19.6
53.6
36.8
23.8
27.8
26.3
17.4
56.8
37.4
22.8
30.6
28.3
17.9
62.1
40
24.9
33.7
29.2
19.4
57.3
37.8
21.7
32.2
27.7
17.7
68.6
40
25.2
35.2
30.7
19.1
60.8
38.5
25
31.6
28
18.6
50.1
34.8
21.8
27
34.9
16.9
59.4
39
24.6
30.1
28.2
18.2
52.5
36.6
21
27
26.3
16.5
61.4
40.6
25
31.3
29.2
19.1
64
37.3
23.5
33.5
30.6
19.7
52.4
35.6
20.4
28.3
26.2
16.5
63.8
42
23.4
34
31.2
18.5
64.8
41.3
25.6
36.4
33.7
19.4
55.5
34.2
21.9
30.2
28.7
17.7
63.3
41.7
24.6
37.2
33.1
19.8
74.4
40.6
24
36.1
31.8
18.8
60.1
39.1
23.4
32.5
29.8
17.4
54.7
36.2
22.1
30.4
27.4
17.7
50
34.8
22
24.8
25.9
16.9
57.8
37.3
22.4
31
28.7
17.7
59.2
37.7
21.5
32.4
28.4
17.8
69.2
42.4
24
35.4
21
20.1
50.3
34.8
22.2
31
26.9
16.9
60
38.1
22
31.5
26.6
16.7
69.8
42.6
24.8
34.4
29.5
18.4
64.7
39.5
24.7
34.8
30.3
18.1
69.5
43.1
25.8
39.1
32.5
19.9
68.1
42.8
24.1
35.6
29
19
47.2
33.5
20.2
27.7
24.6
16.5
54.1
36.2
21.8
31.4
28.3
17.2
58
39.4
22.7
30
26.4
17.4
55.4
38.9
22.4
30.5
28.9
17.7
57.3
39.7
22.6
32.9
29.3
18.2
67.7
41.3
24.7
37.2
31.8
20
63.5
39.8
23.5
36.4
30.4
19.1
62.8
41.3
24.8
36.6
32.4
18.8
61.5
40.4
22.9
33.4
29.2
18.5
54.3
36.3
21.8
29.6
27.3
17.9
68.5
45
25.5
37.1
31.2
19.9
60.6
38.6
24.7
34
30.1
18.7
65.3
43.3
26
33.7
29.9
18.5
60.2
38.9
22.4
31.7
27.1
17.1
61.1
38.4
24.1
32.9
29.8
18.8
57.7
38.6
24
31.2
27.3
17.4
62.3
38
22.3
30.8
27.8
16.9
57.5
40
22.5
30.6
30
18.5
58.5
39
24.1
33.8
28.8
18.8
60.2
39.2
23.8
31.7
28.4
18.6
55.5
35.7
22
29.4
26.6
17.4
68.8
38.3
23.7
32.1
28.9
18.7
60.6
39
24
32.9
29.2
18.4
63.5
40.3
21.8
34.8
30.7
17.4
63.3
39.8
24.1
37.3
23.1
19.4
58.9
37.6
21.4
33.1
29.5
17.3
60.7
39.4
23.3
36.7
31.6
18.4
53
36.2
22.5
31.4
27.5
17.7
56
38.2
22.6
29
26.2
17.6
51.1
35
21.7
30.9
28.8
17.4
63.7
40.3
23.2
36.8
31
18.9
56.3
38.8
23
29.5
27.9
18.6
60
40.9
25.5
32.7
30
19
57.1
38.1
21.8
28.6
26.7
18
62.5
36.9
23.6
34.7
29.1
18.4
53.8
36.5
21.5
31.3
26.3
17.8
54.7
39
22.6
27.5
25.9
18.6
63.9
39.2
22.9
35.7
30.4
19.2
53.7
36.2
22
28.5
25.7
17.1
57.7
38.1
23.9
31.4
29.9
18.9
64.2
42.7
27
38.4
32
19.6
59.7
40.2
23.4
27.9
27
17.8
54.4
35.2
22.5
29.4
26.8
17
57.4
37.1
21.8
34.1
31.1
19.2
50.8
33
19.7
25.3
22
15.8
56.6
38.5
22.6
33.4
29.3
18.8
64
42.6
23.4
33.2
30
18.4
58.4
37.4
22.5
34.6
30.1
18.8
55.4
38.8
23.2
32.4
29.7
19
53
35
21.3
31.7
27.3
16.9
59.3
38.6
22.8
31.8
29.1
19
57.1
38.9
23.6
30.9
29.6
18
56.8
35.9
21
27.8
26.1
17.6
54.3
35.7
21
31.3
28.7
18.3
54.4
37.1
22.7
30.3
26.3
18.3
59.3
40.3
23
32.6
28.5
19
63.4
41.1
22.3
35.1
29.6
18.5
61.2
39.1
22.3
29.8
28.9
18.3
59.2
38.1
24
35.9
30.5
19.1
50.7
33.4
20.1
28.5
24.8
16.5
61.3
42.1
23.4
34.9
30.1
19.4
63.7
42.4
24.6
35.6
30.7
19.5
65.6
46
25.4
35.3
29.8
19.5
58.2
38.8
24.1
32.1
29.3
18.5
54.3
37.5
22.6
29.2
27.3
18.5
63.3
44
22.6
37.5
32.6
18.8
49.6
34.8
21.5
25.6
25.7
18.5
59.6
40.8
23.2
35.2
28.6
20.1
60.3
37.3
21.5
31.3
27.2
18
56
41.6
22.7
30.5
29.4
19.8
59.3
42.2
24.6
33.7
30
20.9
Essay Writing Service Features
Our Experience
No matter how complex your assignment is, we can find the right professional for your specific task. Achiever Papers is an essay writing company that hires only the smartest minds to help you with your projects. Our expertise allows us to provide students with high-quality academic writing, editing & proofreading services.
Free Features
Free revision policy
$10Free bibliography & reference
$8Free title page
$8Free formatting
$8How Our Dissertation Writing Service Works
First, you will need to complete an order form. It's not difficult but, if anything is unclear, you may always chat with us so that we can guide you through it. On the order form, you will need to include some basic information concerning your order: subject, topic, number of pages, etc. We also encourage our clients to upload any relevant information or sources that will help.
Complete the order form
Once we have all the information and instructions that we need, we select the most suitable writer for your assignment. While everything seems to be clear, the writer, who has complete knowledge of the subject, may need clarification from you. It is at that point that you would receive a call or email from us.
Writer’s assignment
As soon as the writer has finished, it will be delivered both to the website and to your email address so that you will not miss it. If your deadline is close at hand, we will place a call to you to make sure that you receive the paper on time.
Completing the order and download