Reading data
Gender and age
Height and weight
Inference
Viˇsina, teˇza in BMI Primer analize Andrej Blejec
20. oktober 2011
What about the BMI?
Reading data
Gender and age
Height and weight
Inference
What about the BMI?
Data analysis: BMI To show the flavor of R data analysis, we will analyze a small dataset of people’s height and weight. People try to care about their body weight. It is a common knowledge, that weight is increasing with height. To compensate for the influence of height on weight, Body Mass Index (BMI) was introduced that can be calculated as: weight BMI = height 2 where weight is measured in kilograms and height is measured in meters. Our analysis will try to investigate the weights of different gender and age groups and the influence of height on weight and calculated BMI.
Reading data
Gender and age
Height and weight
Data file: bmiall.txt
gender age weight height M 17 73.6 1.730 M 17 71.0 1.765 M 17 62.4 1.770 M 17 71.0 1.870 M 17 72.4 1.765 ... F F F F F F
18 18 18 18 18 18
52.6 46.2 52.4 54.0 55.2 55.4
1.626 1.624 1.638 1.630 1.690 1.677
Inference
What about the BMI?
Reading data
Gender and age
Height and weight
Reading data
1 2 3 4 5 6
gender age weight height M 17 73.6 1.730 M 17 71.0 1.765 M 17 62.4 1.770 M 17 71.0 1.870 M 17 72.4 1.765 M 17 104.0 1.825
Inference
What about the BMI?
Reading data
Gender and age
Height and weight
Inference
What about the BMI?
Get info about the data
'data.frame': 419 obs. of 4 variables: $ gender: Factor w/ 2 levels "F","M": 2 2 2 2 2 2 2 2 2 $ age : int 17 17 17 17 17 17 17 17 17 17 ... $ weight: num 73.6 71 62.4 71 72.4 104 70.4 79.8 63.4 $ height: num 1.73 1.76 1.77 1.87 1.76 ... [1] 419
4
Reading data
Gender and age
Height and weight
Inference
What about the BMI?
Data summary
gender F:205 M:214
age Min. :17.00 1st Qu.:17.00 Median :17.00 Mean :17.49 3rd Qu.:18.00 Max. :18.00
weight Min. : 44.80 1st Qu.: 57.20 Median : 63.20 Mean : 64.59 3rd Qu.: 71.00 Max. :104.00
height Min. :1.502 1st Qu.:1.652 Median :1.720 Mean :1.720 3rd Qu.:1.780 Max. :1.970
Reading data
Gender and age
Gender and age tables
gender F M 205 214 age gender 17 18 F 101 104 M 112 102
Height and weight
Inference
What about the BMI?
Reading data
Gender and age
Height and weight
Inference
Flat contingency table
> highWeight <- weight > mean(weight) > ftable(gender, age, highWeight) highWeight FALSE TRUE gender age F 17 18 M 17 18
80 80 40 29
21 24 72 73
What about the BMI?
Reading data
Gender and age
Contingency tables ...
, , age = 17 gender highWeight F M FALSE 80 40 TRUE 21 72 , , age = 18 gender highWeight F M FALSE 80 29 TRUE 24 73
Height and weight
Inference
What about the BMI?
Reading data
Gender and age
Height and weight
Inference
What about the BMI?
... and independence test
Call: xtabs(formula = ~highWeight + gender + age) Number of cases in table: 419 Number of factors: 3 Test for independence of all factors: Chisq = 89.81, df = 4, p-value = 1.448e-18 1 5 3 7 2 6 4 8
highWeight gender age Freq FALSE F 17 80 FALSE F 18 80 FALSE M 17 40 FALSE M 18 29 TRUE F 17 21 TRUE F 18 24 TRUE M 17 72 TRUE M 18 73
Reading data
Gender and age
Height and weight
Inference
What about the BMI?
Total, row, and column proportions: prop.table()
age gender 17 18 F 0.24 0.25 M 0.27 0.24 age gender 17 18 F 0.49 0.51 M 0.52 0.48 age gender 17 18 F 47.4 50.5 M 52.6 49.5
Reading data
Gender and age
Height and weight
Plot table - weight above Q3
17 18 F 4 8 M 43 49
Inference
What about the BMI?
Reading data
Gender and age
Height and weight
Mosaic plot Weight above Q3 = 71
M
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18
Inference
What about the BMI?
Reading data
Gender and age
Height and weight
Inference
Barplot
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What about the BMI?
Reading data
Gender and age
Height and weight
Inference
What about the BMI?
Numerical variables and summary statistics > mean(weight) [1] 64.5883 > mean(height) [1] 1.719964 > c(sd(weight), sd(height)) [1] 10.53051077 0.08752747 > (V <- var(cbind(weight, height))) weight height weight 110.8916572 0.601565848 height 0.6015658 0.007661059 > cor(weight, height) [1] 0.6526635 > my.cor <- V[1, 2]/(sd(weight) * sd(height)) > cat("Correlation r =", my.cor, "\n") Correlation r = 0.6526635
Reading data
Gender and age
Height and weight
Inference
What about the BMI?
Are there differences in weight and height in gender age classes?
1 2 3 4
Group.1 Group.2 weight height 17 F 58.51881 1.650644 18 F 59.42500 1.656644 17 M 69.12500 1.775857 18 M 70.88137 1.791794
Reading data
Gender and age
Height and weight
Inference
Grand tour: height Data, histogram, boxplot, and quantile plot
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Normal Q−Q Plot
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What about the BMI?
Reading data
Gender and age
Height and weight
Inference
Grand tour: weight Histogram of x
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What about the BMI?
Reading data
Gender and age
Height and weight
Inference
I am heavy because I am tall :) 1
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M F MM MM M M M MMMM MM MMM MM M M M F MM MM M M M M MM F M M M M M M M MM FF F M MMM M M M M M F M M F M M M M M M M M M M M M FM M M M F M FM MM M M M MMM MFFM M MMM M MM F F M M F F M M M FM F FMM F M MMM M M FFFF FFFFFFF M M FF M M M F M F M F M M F M M F M F F M M MM MMM M M FF M M M FM FFFM F M M FFFFFF M M F M M F M M M M F FFM F M F M FF M M M F FF M F FFFFFF M F M M F M FF M F FM FM F M F FF M M F F M M F FF FFFM FFF F M FF M FF M F M FFF F FF FM FF F FM FF FF MM M FFFF FF FFFF M M F F F FFFFFF F F F F F F F F F F F FF F
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What about the BMI?
Reading data
Gender and age
Height and weight
I am heavy because I am tall :) Gender: F Call: lm(formula = y ~ x) Coefficients: (Intercept) -29.63
x 53.58
Gender: M Call: lm(formula = y ~ x) Coefficients: (Intercept) -81.98
x 85.20
Inference
What about the BMI?
Reading data
Gender and age
Height and weight
Inference
I am heavy because I am tall :) 1
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1.7
1.8
90
1.5
1.8
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1.9
1.9
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100 weight
90 weight
70 50
1.7
height
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1.6
1.6
height
●
1.5
70
weight
1.9
●
80
1.6
60
1.5
M F MM MM M M M MMMM MM MMM MM M M M F MM MM M M M M MM F M M M M M M M MM FF F M MMM M M M M M F M M F M M M M M M M M M M M M FM M M M F M FM MM M M M MMM MFFM M MMM M MM F F M M F F M M M FM F FMM F M MMM M M FFFF FFFFFFF M M FF M M M F M F M F M M F M M F M F F M M MM MMM M M FF M M M FM FFFM F M M FFFFFF M M F M M F M M M M F FFM F M F M FF M M M F FF M F FFFFFF M F M M F M FF M F FM FM F M F FF M M F F M M F FF FFFM FFF F M FF M FF M F M FFF F FF FM FF F FM FF FF MM M FFFF FF FFFF M M F F F FFFFFF F F F F F F F F F F F FF F
50
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40
70 50
weight
90
●
1.4
1.6
1.8
2.0
What about the BMI?
Reading data
Gender and age
Height and weight
Inference
110
Regression
● ●
40 50 60 70 80 90
weight
●
● ● ● ● ● ●●
●
● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ●●● ● ●● ●● ●● ● ●● ●● ●● ● ●● ● ●● ● ● ●● ●●●● ●●●●● ● ●● ● ● ● ●●● ● ●●● ● ●● ● ●● ● ● ● ● ●●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ●●● ● ● ●●● ● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●●● ●● ● ● ●● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●●● ●●● ● ● ● ● ●●● ● ● ● ●● ● ●● ●● ●●●●●●●● ● ● ● ●● ●●● ● ● ●● ● ● ●● ●● ●● ●●● ●● ●●● ● ● ●● ● ●● ●● ● ● ●●●● ● ● ● ● ● ● ● ●● ● ● ● ●●● ● ●●●●● ●●●●● ● ●● ● ●● ● ● ●● ● ● ● ● ● ●● ●● ● ●●● ● ● ●●● ●●●●●● ● ●● ●● ● ● ●●● ● ● ●●●●● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ●●●● ● ● ● ● ●●● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●
1.4
1.5
1.6
1.7 height
1.8
1.9
2.0
What about the BMI?
Reading data
Gender and age
Height and weight
Extract coefficients from all models
F M (Intercept) -29.62659 -81.98327 height 53.58033 85.19731
Inference
What about the BMI?
Reading data
Gender and age
Height and weight
Inference
What about the BMI?
Gender and age effects on height and weight
Df gender 1 age 1 Residuals 416 --Signif. codes:
Sum Sq 1.76308 0.01282 1.42642
Mean Sq F value Pr(>F) 1.76308 514.1828 < 2e-16 *** 0.01282 3.7395 0.05382 . 0.00343
0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1
Df Sum Sq Mean Sq F value gender 1 12631 12631.2 156.6954 age 1 188 187.9 2.3305 Residuals 416 33534 80.6 --Signif. codes: 0 '***' 0.001 '**' 0.01
Pr(>F) <2e-16 *** 0.1276
'*' 0.05 '.' 0.1
Reading data
Gender and age
Height and weight
Inference
What about the BMI?
Gender and height effects on weight Call: lm(formula = weight ~ 0 + gender * height) Residuals: Min 1Q -15.8396 -5.1961
Median -0.9167
3Q 4.2347
Max 38.5225
Coefficients: genderF genderM height genderM:height --Signif. codes:
Estimate Std. Error t value Pr(>|t|) -29.627 16.339 -1.813 0.0705 . -81.983 15.882 -5.162 3.80e-07 *** 53.580 9.875 5.426 9.82e-08 *** 31.617 13.294 2.378 0.0178 *
0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1
Residual standard error: 7.931 on 415 degrees of freedom
Reading data
Gender and age
Height and weight
Inference
Plot of predicted values shows interaction
100
● ●
● ● ● ● ● ●●
90
●
80
●
● ●
●
● ●
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● ● ● ●
●●
60
70
● ●
50
weight
●
●
●
● ●●
1.5
1.6
1.7 height
1.8
1.9
●
What about the BMI?
Reading data
Gender and age
Height and weight
Inference
What about the BMI?
Student t-test
Welch Two Sample t-test data: height by gender t = -22.6415, df = 416.359, p-value < 2.2e-16 alternative hypothesis: true difference in means is not 95 percent confidence interval: -0.1410314 -0.1184996 sample estimates: mean in group F mean in group M 1.653688 1.783453
Reading data
Gender and age
Height and weight
Inference
Distribution of BMI Histogram of x
0
100
200
300
100 40
Frequency
0
20
x
30
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400
20
25
Index
30
35
x
30
●
20
30 20
● ● ● ●
Sample Quantiles
Normal Q−Q Plot ●
●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●●●
−3
−2
−1
0
1
2
Theoretical Quantiles
3
What about the BMI?
Reading data
Gender and age
Height and weight
Inference
Make a new data frame and show correlations
weight height BMI
weight height BMI 1.000 0.653 0.768 0.653 1.000 0.022 0.768 0.022 1.000
What about the BMI?
Reading data
Gender and age
Height and weight
Inference
Plot scattergrams 1.8
1.9
●
● ●●● ●● ● ● ● ●● ●● ● ●● ● ● ●● ● ● ● ● ● ● ●● ●●●●●●● ● ● ●● ●●●●●● ●● ● ● ● ● ●● ● ● ●● ● ●● ●● ●● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ●● ● ● ●● ●● ●● ●● ●●●● ● ● ● ● ● ● ● ●●● ● ● ● ●● ● ● ● ●●●● ● ●● ● ● ● ● ● ●● ● ●● ● ● ● ● ●● ●● ●● ● ● ●● ● ● ● ● ● ● ●●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●●● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●●●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ●● ● ●● ●● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ●● ● ●●●●
height
● ● ● ●●●●● ● ● ●●● ●● ● ● ● ● ● ●● ●● ● ● ●● ● ● ● ●●● ● ● ● ● ● ● ● ●● ●●●● ● ●●●● ●●● ●● ● ●● ● ● ●● ● ●●● ●● ● ●● ● ●● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●●●● ● ●● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ●●● ● ●● ● ●● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ●●●● ●● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ●●● ● ●● ●●● ● ●● ●● ● ● ●● ● ●● ●●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●●●●●●● ●●●● ● ● ● ● ● ●●●●● ● ●● ● ●●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ●● ●● ● ●●● ● ●● ●●● ● ● ●●● ● ● ● ●●● ●●●●● ● ● ● ●● ●● ●● ●● ● ●● ● ● ●● ●● ● ●
● ●
●● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ●● ●● ● ● ●● ● ●● ●● ● ● ● ● ●● ● ●●●● ● ● ● ● ● ● ● ●● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●●● ● ● ●● ● ●● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ●●● ● ● ● ●●● ● ● ● ●● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●●● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ●●● ●●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ●
50
60
70
80
90
●
●
●
● ●
●
30
●
●
●
35
●
●
● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●●● ● ● ● ●● ● ● ●●●● ●●● ● ● ●● ● ● ● ●●● ●● ● ●●● ●● ●● ● ●● ● ● ● ● ● ● ● ●● ●●● ● ● ● ● ●● ● ●● ● ● ●● ● ●● ● ● ●● ● ●● ● ● ● ●● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ●● ● ● ●● ● ● ●● ●● ●●● ● ● ●●● ●●●●● ● ●●●● ● ●● ● ●● ● ● ● ●● ● ●● ● ●● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ●●●● ● ● ● ●●●● ● ● ●● ●● ●●● ● ●● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ●● ●●● ● ● ● ● ● ●● ●●●●●●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●●● ● ●●● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ●● ● ●● ●● ● ● ● ● ●●● ●● ● ● ●●●●● ●●● ● ● ●●● ●
BMI
25
● ● ● ●● ● ● ●● ● ● ●● ●● ● ● ● ●● ● ● ●● ●●●● ● ● ● ●●● ●● ● ● ●● ● ●●● ● ● ● ● ● ●● ●● ●● ●●●● ● ●●● ●●● ●● ● ● ●●●● ● ● ●● ●●● ●● ●● ● ● ● ● ● ●● ● ● ●● ● ●● ●● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ●● ●● ● ● ● ●● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ●●● ● ● ●● ● ● ● ● ● ● ●●● ●● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●●●●● ● ● ● ● ● ●●● ● ● ●● ● ● ●● ● ● ●● ● ●●● ●●● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ●● ● ●● ● ● ● ● ●●● ● ● ●●● ●● ●● ●●● ●● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ●● ●● ●● ● ● ● ●● ● ● ● ●● ●●● ● ● ● ● ●●● ● ● ●● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ●● ● ●
●
● ●● ● ●● ●● ● ●● ● ●● ● ●● ●● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ●● ●●● ●●●● ●● ● ● ● ● ● ● ●● ● ●● ●● ●● ●● ● ●● ● ●● ● ● ●● ●● ● ● ● ●●● ●● ● ● ● ●●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ●●●●●● ● ● ●●● ● ●●● ● ● ●● ●● ● ● ● ● ●● ● ● ●● ● ●●● ● ● ●● ●● ● ● ● ●● ● ● ●● ●● ● ●● ● ● ●● ● ● ● ●●● ●● ● ● ● ● ● ● ●● ●● ●● ● ●● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ●● ● ● ●● ● ●● ● ● ●● ● ●● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ●●● ● ●●●●● ●● ● ● ● ● ● ●● ● ●● ●●● ● ● ● ● ● ● ● ● ● ●●●● ● ● ● ●● ● ●● ●● ● ● ●● ●● ● ● ●●● ● ●● ● ●● ●● ● ● ● ● ● ● ● ● ●● ●● ●● ●●● ● ● ●● ● ● ● ●●● ● ● ● ●●●● ● ●● ● ● ● ● ● ●● ●● ● ●
20
1.5
1.7
1.9
weight
●
90
1.7 ●
70
1.6
50
1.5
20
25
30
35
What about the BMI?
Reading data
Gender and age
Height and weight
Inference
What about the BMI?
Distributions of numerical variables height
weight
●
●
100
35
● ●
BMI
● ●
1.9
● ● ● ● ● ●
30
90
● ●
●
●
●
1.8
● ●
●
1.5
50
20
1.6
●
60
70
1.7
25
80
● ●
●
F
M
F
M
F
M
Reading data
Gender and age
Height and weight
Inference
What about the BMI?
Calculated sizes of symbols 1.8
1.9
●
●
●
● ●● ●●
● ● ● ● ●● ●●●●●● ●● ● ● ● ●● ●●● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ●●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ●●● ● ● ●●●●● ● ●● ● ● ● ●●
● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ●●●● ●● ● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ●● ● ●● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ●● ●
●
● ● ● ●● ● ●●●● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ●● ●● ● ● ●●● ●●● ● ● ●● ● ● ●● ●● ● ● ● ●
● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ●●● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ●●● ● ● ● ●● ●● ● ● ●● ● ● ● ● ● ●● ● ● ●● ●●● ● ● ● ● ● ●● ●● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ●● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ●●● ● ●● ●● ● ●● ● ● ●● ● ● ● ●
● ● ● ● ● ●● ● ●
●● ●●● ●● ● ●● ● ●●●●
●
● ● ●●
height
●●
● ●● ●●●● ●●●●● ●
● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●
● ●
●
●●●● ● ● ●● ●● ●● ● ●● ●●
50
60
●
● ●
35
●● ● ● ●●●
● ● ●● ●●● ● ●● ● ● ● ● ● ●● ●● ●● ● ● ● ● ●● ● ● ● ●● ● ●● ● ●● ● ● ● ●● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ●●● ● ●
BMI
● ● ●●●● ● ● ● ●● ● ● ●● ● ●● ● ● ●● ●●●● ●● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ●● ● ●● ●● ●● ● ●● ● ● ● ●● ● ● ● ● ● ● ●● ● ●● ● ●● ●● ●● ●● ● ● ●● ● ●● ● ● ● ●● ●●● ● ●● ●●●
●●
●
●
●●
●
●●● ●●● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●●● ●● ● ● ● ●● ● ● ● ● ●● ●
● ● ● ●● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●●● ● ● ● ● ● ●
●
30
● ● ●
●● ●
●
●● ●
● ●● ● ● ● ● ●● ● ● ●● ● ● ● ●● ● ●● ● ● ● ● ● ● ●● ● ●● ●● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ●●● ●●●● ● ● ● ● ● ●● ● ● ● ● ● ● ●
●
●●
● ● ● ● ●●● ● ●
● ● ●
● ● ● ● ●●●●● ●● ● ● ● ● ●●●● ●●● ●● ● ● ● ●●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●●●● ● ●● ● ● ● ● ●●● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ●● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ●● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ●● ● ● ● ● ● ●● ●●● ● ●● ●● ●● ●●● ● ●● ●
●
● ●
●
●
25
1.5
1.7
1.9
●
●
20
weight
● ● ●●● ●
●● ● ●●● ●● ● ●● ●● ●● ● ●● ● ● ●● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●●● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ●● ● ● ●
90
1.7
70
1.6
50
1.5
●
● ●●
70
80
90
20
25
30
35
Reading data
Gender and age
Height and weight
Inference
What about the BMI?
BMI classes
> bmic <- cut(BMI, c(0, 13, 18, 25, 30, Inf)) > levels(bmic) [1] "(0,13]"
"(13,18]"
"(18,25]"
"(25,30]"
"(30,Inf
> levels(bmic) <- c("S", "s", "N", "h", "H") > bmic <- factor(bmic, levels = c("S", "s", "N", "h", "H + ordered = T) > is.ordered(bmic) [1] TRUE
Reading data
Gender and age
Height and weight
Inference
What about the BMI?
Color coded BMI classes 1.8
1.9
●
●
●
● ●● ●●
● ● ● ● ●● ●●●●●● ●● ● ● ● ●● ●●● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ●●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●●● ● ● ●●●●● ●●● ● ● ●●
● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ●●●● ●● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ●● ● ●● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ●● ●
●
● ● ● ●● ● ●●●● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ●● ●● ● ● ●●● ●●● ● ● ●● ● ● ●● ●● ● ● ● ●
● ●
●
●
● ● ●● ● ● ● ●● ● ● ● ● ● ● ●●● ● ● ●● ● ● ● ● ● ●● ● ● ●● ●● ● ● ●● ● ● ●●● ● ● ● ● ● ●●● ● ● ● ●● ●● ● ● ●● ● ● ● ● ● ●● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ●● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ●●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ●● ● ● ● ●●
● ● ●●
●
●
●●
●
● ● ● ● ●●● ● ●
● ● ●
● ●● ● ● ● ● ●● ● ● ●● ● ● ● ●● ● ●● ● ● ● ● ●● ● ● ●● ●● ● ● ● ● ●● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ●●●● ● ● ● ● ●● ● ● ● ● ● ● ●
● ● ●● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●●●
● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ●● ● ● ● ●
● ●● ● ●●● ●● ● ●● ● ●
50
60
●
● ●
●● ● ● ●●●
● ● ●● ●●● ● ●● ● ● ● ● ● ●● ●● ●● ● ● ● ● ●● ● ● ● ●● ● ●● ● ●● ● ● ● ●● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●●● ● ● ●●
80
90
●
●
BMI
● ● ●●●● ● ● ● ●● ● ● ●● ● ●● ● ● ●● ●●●● ●● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ●● ●●● ● ● ● ● ● ● ●● ● ● ●● ●● ●● ● ● ●● ● ●● ● ●● ● ●● ● ● ● ●● ●● ●●● ●
●● ● ● ● ● ● ● ● ●● ●● ● ●● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ●● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ●● ● ● ●●
70
●
●●
●
● ●● ● ● ●● ● ● ● ● ●●● ●● ●
●●●● ● ● ●● ●● ●● ● ●● ●●
●● ●
●
●● ●
● ●
●
●●
35
1.5
● ●●
height
30
1.7
●
● ●
● ● ●
● ● ● ● ●●●●● ●● ● ● ● ● ●●●● ●●● ●● ● ● ● ●●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●●●● ● ●● ● ● ● ● ●●● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ●● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ●● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ●● ● ● ● ● ● ●● ●●● ● ●● ●● ●● ●●● ● ●● ●
● ● ● ●
●
●
●●
20
1.9
●
● ● ● ● ● ●● ● ●
●● ●●● ●● ● ●● ● ●●●●
●
25
weight
● ● ●●● ●
●● ● ●●● ●● ● ●● ●● ●● ● ●● ● ● ●● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ●● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ●● ● ● ●
90
1.7
70
1.6
50
1.5
●
20
25
30
35
Reading data
Gender and age
Height and weight
Inference
What about the BMI?
150
Barplots are easy to understand ...
0
50
100
F M
S
s
N
h
H