my_dt <- read.delim(textConnection(dt), header = TRUE, sep = "\t", stringsAsFactors = FALSE)

library(tidyverse)

my_dt <- my_dt %>% 
  mutate(Weight = as.numeric(Weight), 
         Height = as.numeric(Height), 
         Abdomen = as.numeric(Abdomen)) 
## Warning: NAs introduced by coercion
  1. Averages
my_dt %>% 
  summarise_all(.funs = c("mean", "sd"), na.rm = TRUE)
##   Weight_mean Height_mean Abdomen_mean Weight_sd  Height_sd Abdomen_sd
## 1    36.90441    1.408476     65.34031  11.15982 0.09828225   10.44111
library(ggplot2)
  1. Histograms
ggplot(my_dt) +
  geom_histogram(aes(x = Height))
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 1 rows containing non-finite values (stat_bin).

ggplot(my_dt) +
  geom_histogram(aes(x = Weight))
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

  1. Prob 1. Individual over 160 cm
my_dt %>% 
  filter(Height >= 1.6)
##   Weight Height Abdomen
## 1  51.70   1.65   70.33
## 2  94.60   1.60  112.83
## 3  63.45   1.61   83.33
## 4  37.75   1.60   67.00
## 5  46.30   1.61   66.00
## 6  54.10   1.64   75.00
## 7  88.10   1.76   96.33
## 8  49.85   1.62   64.50
## 9  47.75   1.65   66.33
my_dt %>% 
  mutate(ct_above16 = if_else(Height >= 1.6, 1, 0)) %>% 
  summarise(
    n = n(), 
    prob = sum(ct_above16, na.rm = TRUE),
    prob_above16 = prob / n * 100
  )
##     n prob prob_above16
## 1 247    9     3.643725
  1. Prob 2. Individual over 59 kg
my_dt %>% 
  mutate(ct_above59 = if_else(Weight > 59, 1, 0)) %>% 
  summarise(
    n = n(), 
    prob = sum(ct_above59, na.rm = TRUE),
    prob_above59 = prob / n * 100
  )
##     n prob prob_above59
## 1 247   10     4.048583
  1. Linear regression height
mylm1 <- lm(formula = Weight ~ Height, data = my_dt)
summary(mylm1)
## 
## Call:
## lm(formula = Weight ~ Height, data = my_dt)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -15.657  -4.586  -1.542   3.283  41.193 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -84.671      6.692  -12.65   <2e-16 ***
## Height        86.299      4.740   18.21   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.291 on 244 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.576,  Adjusted R-squared:  0.5743 
## F-statistic: 331.5 on 1 and 244 DF,  p-value: < 2.2e-16

Group 6: abdomen vs weight

mylm2 <- lm(formula = Weight ~ Abdomen, data = my_dt)

summary(mylm2)
## 
## Call:
## lm(formula = Weight ~ Abdomen, data = my_dt)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -12.8999  -3.1363  -0.3356   2.1786  20.6240 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -27.65741    1.98709  -13.92   <2e-16 ***
## Abdomen       0.98758    0.03003   32.88   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.693 on 223 degrees of freedom
##   (22 observations deleted due to missingness)
## Multiple R-squared:  0.829,  Adjusted R-squared:  0.8283 
## F-statistic:  1081 on 1 and 223 DF,  p-value: < 2.2e-16
residuals(mylm2) %>% 
  enframe() %>% 
  kable()
name value
1 -2.1544180
2 -3.3912515
3 -2.4480150
4 -0.1280130
5 0.6474554
6 -2.4159033
7 -2.0907472
8 -3.5530489
9 -1.8090678
10 -4.0089477
11 -1.4783252
12 -4.2162155
13 1.2898753
14 -5.2462135
15 -1.6283252
16 -6.5275806
17 -0.9286374
18 -3.3907472
19 8.7904279
20 0.2534743
21 -2.5480150
22 0.0027296
23 -0.7974624
24 -0.8355931
25 -0.5968380
26 1.3906199
27 0.5775735
28 0.9530419
29 -1.3831671
30 -5.8472704
31 1.2389386
32 0.8519850
33 -0.8592599
34 -5.5223063
35 3.1913646
36 -1.7850405
37 -6.0103168
38 2.5289426
39 4.5642149
40 -3.4159033
41 -9.1730510
42 -3.9475826
43 -5.6734834
44 -2.1968380
45 -3.2089477
46 2.6092528
47 -0.6788295
48 -1.8148464
49 2.1085082
50 -12.8998884
51 -2.5989517
52 -1.9165277
53 -0.7727387
54 1.2537865
55 2.0522253
56 4.5722993
57 3.5526095
58 0.1530419
59 -6.1486395
60 4.6778858
61 -0.1859053
62 -3.6353527
63 -2.3037936
64 0.9034743
65 -6.3723063
66 2.8034743
67 -0.2965257
68 1.3913646
69 0.6278858
70 -0.0965257
71 4.5392508
72 -0.2859053
73 -6.0873463
74 1.7406199
75 -8.2266057
76 -5.8234834
77 4.2389386
78 1.2413646
79 -1.2362175
80 4.0151516
81 0.9534743
82 4.0407401
83 -1.4847283
84 -0.9234834
85 -2.9355931
86 -5.7968380
87 1.2778858
88 0.9030419
89 -0.3983272
90 -2.5775806
91 -0.6348484
92 -1.4548504
93 -0.2780130
94 -1.4596923
95 -2.9903147
96 0.3903077
97 -10.4364096
98 2.3198014
99 -4.9089477
100 3.9645271
101 -3.6719941
102 10.7831600
103 3.6466388
104 -9.3980869
105 -5.7862894
106 -3.4730510
107 -5.0353527
108 0.0040988
110 -0.4266459
111 -3.5919893
112 -0.2352808
113 0.7157761
114 -6.7529838
115 -6.1230510
117 5.7037865
119 3.8016728
120 -4.0844160
121 2.4499330
122 -2.9093801
123 -4.5244785
124 5.1530419
125 -0.1468380
127 -3.4092599
128 -5.8719941
129 5.7634743
130 0.9158962
131 1.0022972
133 -8.2995762
134 7.2763381
135 -4.4116859
136 2.6799377
137 -3.1362759
138 -3.7872126
139 11.3252812
140 -3.0986395
141 -5.9474624
142 1.4268289
143 0.7640228
145 2.9158962
147 -3.2129348
148 -0.1105089
149 -2.8247323
150 8.3651516
151 1.6395631
152 -1.8724265
153 0.2413646
154 -1.6228589
155 -4.7842239
156 -6.6227387
157 -4.4604369
158 -3.8482071
159 -4.6595721
160 -1.2459012
161 1.8789426
162 -5.0231711
163 -1.7475826
164 -0.7469581
165 -0.3355931
166 -2.5352808
167 -2.2713696
168 0.2416768
169 3.8337845
170 5.5093730
171 4.2957021
172 5.8155840
173 1.8896832
174 2.3907401
175 9.9010483
176 5.0625335
177 10.8289808
178 -1.1421882
179 15.8935884
180 5.6086284
181 0.3826557
182 4.9513605
183 7.7966388
184 8.8125335
185 -1.8921163
186 6.1903077
187 -0.3559792
188 5.2534743
189 0.0524174
190 -1.3729308
191 -0.7603168
192 -4.2295742
193 1.9083161
194 0.1578118
195 2.5203057
196 8.7772613
197 -3.5485193
198 -3.2841038
199 1.8817909
200 7.6890587
201 1.3448373
202 5.5204258
203 20.6240187
204 -0.6424285
205 -7.7053548
206 -0.2539856
207 13.8086284
208 0.0827276
209 -3.8737956
210 2.8148393
211 12.8625335
212 10.0958942
213 2.1786304
214 -0.8983272
215 5.0221072
216 2.7637825
217 4.4870652
218 -1.5795742
219 1.2403077
220 2.8581960
221 -2.3721142
222 9.9013605
223 1.4413646
224 2.1395631
225 1.7403077
226 -1.0334793
227 -4.8735553
228 -5.2472704
229 -1.3962135
230 -4.2462135
231 1.2031620
232 -1.2086354 
my_dt %>% 
  filter(!is.na(Abdomen)) %>% 
  nrow()
## [1] 225
confint(mylm2, level = 0.95)
##                   2.5 %     97.5 %
## (Intercept) -31.5732820 -23.741544
## Abdomen       0.9283952   1.046761
plot(mylm2)

dt2 <- "
20 0.3 0.385
40 0.3 0.621
60 0.3 0.777
80 0.3 0.873
100 0.3 0.930
20 0.5 0.799
40 0.5 0.973
60 0.5 0.997
80 0.5 0.999
100 0.5 0.999
"
my_dt2 <- read.delim(textConnection(dt2), stringsAsFactors = FALSE, header = FALSE, sep = " ")

gg <- my_dt2 %>% 
  rename(sample_size = V1, 
         effect_size = V2, 
         power = V3) %>% 
  mutate(effect_size = factor(effect_size))
ggplot(gg) +
  geom_line(aes(x = sample_size,
                 y = power,
                 color = effect_size))