bmi-2011s
DESCRIPTION
http://ablejec.nib.si/seminar2011/BMI-2011S.pdfTRANSCRIPT
Reading data Gender and age Height and weight Inference What about the BMI?
Visina, teza in BMIPrimer analize
Andrej Blejec
20. oktober 2011
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 smalldataset of people’s height and weight. People try to care abouttheir body weight. It is a common knowledge, that weight isincreasing with height. To compensate for the influence of heighton weight, Body Mass Index (BMI) was introduced that can becalculated as:
BMI =weight
height2
where weight is measured in kilograms and height is measured inmeters.Our analysis will try to investigate the weights of different genderand age groups and the influence of height on weight andcalculated BMI.
Reading data Gender and age Height and weight Inference What about the BMI?
Data file: bmiall.txt
gender age weight heightM 17 73.6 1.730M 17 71.0 1.765M 17 62.4 1.770M 17 71.0 1.870M 17 72.4 1.765
...
F 18 52.6 1.626F 18 46.2 1.624F 18 52.4 1.638F 18 54.0 1.630F 18 55.2 1.690F 18 55.4 1.677
Reading data Gender and age Height and weight Inference What about the BMI?
Reading data
gender age weight height1 M 17 73.6 1.7302 M 17 71.0 1.7653 M 17 62.4 1.7704 M 17 71.0 1.8705 M 17 72.4 1.7656 M 17 104.0 1.825
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 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 75.8 ...$ 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 age weight heightF:205 Min. :17.00 Min. : 44.80 Min. :1.502M:214 1st Qu.:17.00 1st Qu.: 57.20 1st Qu.:1.652
Median :17.00 Median : 63.20 Median :1.720Mean :17.49 Mean : 64.59 Mean :1.7203rd Qu.:18.00 3rd Qu.: 71.00 3rd Qu.:1.780Max. :18.00 Max. :104.00 Max. :1.970
Reading data Gender and age Height and weight Inference What about the BMI?
Gender and age tables
genderF M
205 214
agegender 17 18
F 101 104M 112 102
Reading data Gender and age Height and weight Inference What about the BMI?
Flat contingency table
> highWeight <- weight > mean(weight)> ftable(gender, age, highWeight)
highWeight FALSE TRUEgender ageF 17 80 21
18 80 24M 17 40 72
18 29 73
Reading data Gender and age Height and weight Inference What about the BMI?
Contingency tables ...
, , age = 17
genderhighWeight F M
FALSE 80 40TRUE 21 72
, , age = 18
genderhighWeight F M
FALSE 80 29TRUE 24 73
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: 419Number of factors: 3Test for independence of all factors:Chisq = 89.81, df = 4, p-value = 1.448e-18
highWeight gender age Freq1 FALSE F 17 805 FALSE F 18 803 FALSE M 17 407 FALSE M 18 292 TRUE F 17 216 TRUE F 18 244 TRUE M 17 728 TRUE M 18 73
Reading data Gender and age Height and weight Inference What about the BMI?
Total, row, and column proportions: prop.table()
agegender 17 18
F 0.24 0.25M 0.27 0.24
agegender 17 18
F 0.49 0.51M 0.52 0.48
agegender 17 18
F 47.4 50.5M 52.6 49.5
Reading data Gender and age Height and weight Inference What about the BMI?
Plot table - weight above Q3
17 18F 4 8M 43 49
Reading data Gender and age Height and weight Inference What about the BMI?
Mosaic plot
Weight above Q3 = 71
17 18
FM
Reading data Gender and age Height and weight Inference What about the BMI?
Barplot
17 18
Weight above Q3 = 71
010
2030
40
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 heightweight 110.8916572 0.601565848height 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 ageclasses?
Group.1 Group.2 weight height1 17 F 58.51881 1.6506442 18 F 59.42500 1.6566443 17 M 69.12500 1.7758574 18 M 70.88137 1.791794
Reading data Gender and age Height and weight Inference What about the BMI?
Grand tour: heightData, histogram, boxplot, and quantile plot
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−3 −2 −1 0 1 2 3
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Normal Q−Q Plot
Theoretical Quantiles
Sam
ple
Qua
ntile
s
Reading data Gender and age Height and weight Inference What about the BMI?
Grand tour: weight
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−3 −2 −1 0 1 2 3
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Normal Q−Q Plot
Theoretical Quantiles
Sam
ple
Qua
ntile
s
Reading data Gender and age Height and weight Inference What about the BMI?
I am heavy because I am tall :)
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1.4 1.6 1.8 2.0
4060
8010
0
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ght
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Reading data Gender and age Height and weight Inference What about the BMI?
I am heavy because I am tall :)
Gender: F
Call:lm(formula = y ~ x)
Coefficients:(Intercept) x
-29.63 53.58
Gender: M
Call:lm(formula = y ~ x)
Coefficients:(Intercept) x
-81.98 85.20
Reading data Gender and age Height and weight Inference What about the BMI?
I am heavy because I am tall :)
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Reading data Gender and age Height and weight Inference What about the BMI?
Regression
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Reading data Gender and age Height and weight Inference What about the BMI?
Extract coefficients from all models
F M(Intercept) -29.62659 -81.98327height 53.58033 85.19731
Reading data Gender and age Height and weight Inference What about the BMI?
Gender and age effects on height and weight
Df Sum Sq Mean Sq F value Pr(>F)gender 1 1.76308 1.76308 514.1828 < 2e-16 ***age 1 0.01282 0.01282 3.7395 0.05382 .Residuals 416 1.42642 0.00343---Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Df Sum Sq Mean Sq F value Pr(>F)gender 1 12631 12631.2 156.6954 <2e-16 ***age 1 188 187.9 2.3305 0.1276Residuals 416 33534 80.6---Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 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 Median 3Q Max
-15.8396 -5.1961 -0.9167 4.2347 38.5225
Coefficients:Estimate Std. Error t value Pr(>|t|)
genderF -29.627 16.339 -1.813 0.0705 .genderM -81.983 15.882 -5.162 3.80e-07 ***height 53.580 9.875 5.426 9.82e-08 ***genderM:height 31.617 13.294 2.378 0.0178 *---Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 7.931 on 415 degrees of freedomMultiple R-squared: 0.9855, Adjusted R-squared: 0.9853F-statistic: 7027 on 4 and 415 DF, p-value: < 2.2e-16
Reading data Gender and age Height and weight Inference What about the BMI?
Plot of predicted values shows interaction
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Reading data Gender and age Height and weight Inference What about the BMI?
Student t-test
Welch Two Sample t-test
data: height by gendert = -22.6415, df = 416.359, p-value < 2.2e-16alternative hypothesis: true difference in means is not equal to 095 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 What about the BMI?
Distribution of BMI
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Index
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Normal Q−Q Plot
Theoretical Quantiles
Sam
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Reading data Gender and age Height and weight Inference What about the BMI?
Make a new data frame and show correlations
weight height BMIweight 1.000 0.653 0.768height 0.653 1.000 0.022BMI 0.768 0.022 1.000
Reading data Gender and age Height and weight Inference What about the BMI?
Plot scattergrams
weight
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20 25 30 35
2025
3035
BMI
Reading data Gender and age Height and weight Inference What about the BMI?
Distributions of numerical variables
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F M
1.5
1.6
1.7
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height
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F M
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2025
3035
BMI
Reading data Gender and age Height and weight Inference What about the BMI?
Calculated sizes of symbols
weight
1.5 1.6 1.7 1.8 1.9
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20 25 30 35
2025
3035
BMI
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
weight
1.5 1.6 1.7 1.8 1.9
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20 25 30 35
2025
3035
BMI
Reading data Gender and age Height and weight Inference What about the BMI?
Barplots are easy to understand ...
S s N h H
FM
050
100
150