Data 606 Homework Lab 1
Uliana Plotnikova
February 10, 2019
Getting started
source("more/cdc.R")head (cdc)## genhlth exerany hlthplan smoke100 height weight wtdesire age gender
## 1 good 0 1 0 70 175 175 77 m
## 2 good 0 1 1 64 125 115 33 f
## 3 good 1 1 1 60 105 105 49 f
## 4 good 1 1 0 66 132 124 42 f
## 5 very good 0 1 0 61 150 130 55 f
## 6 very good 1 1 0 64 114 114 55 ftail (cdc)## genhlth exerany hlthplan smoke100 height weight wtdesire age
## 19995 good 0 1 1 69 224 224 73
## 19996 good 1 1 0 66 215 140 23
## 19997 excellent 0 1 0 73 200 185 35
## 19998 poor 0 1 0 65 216 150 57
## 19999 good 1 1 0 67 165 165 81
## 20000 good 1 1 1 69 170 165 83
## gender
## 19995 m
## 19996 f
## 19997 m
## 19998 f
## 19999 f
## 20000 mnames(cdc)## [1] "genhlth" "exerany" "hlthplan" "smoke100" "height" "weight"
## [7] "wtdesire" "age" "gender"How many cases are there in this data set? How many variables? For each variable, identify its data type (e.g. categorical, discrete).
dim (cdc)## [1] 20000 9For each variable, identify its data type (e.g. categorical, discrete)
genhlth - categorical
exerany - categorical
hlthplan - categorical
smoke100 - categorical
height - descrete
weight- descrete
wtdesire - descrete
age - descrete
gender - categorical
2. Create a numerical summary for height and age, and compute the interquartile range for each. Compute the relative frequency distribution for gender and exerany. How many males are in the sample? What proportion of the sample reports being in excellent health?
## numerical summary for height
summary(cdc$height)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 48.00 64.00 67.00 67.18 70.00 93.00##interquartile range for height
IQR (cdc$height)## [1] 6## numerical summary for age
summary(cdc$age)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 18.00 31.00 43.00 45.07 57.00 99.00##interquartile range for age
IQR(cdc$age)## [1] 26Relative frequency distribution for gender
Gdr<- cdc$gender
gend.freq <- table(Gdr)
gend.relfreq <- gend.freq/nrow(cdc)
gend.relfreq## Gdr
## m f
## 0.47845 0.52155Relative frequency distribution for exerany
Exerany<-cdc$exerany
v_exerany.freq <- table(Exerany)
v_exerany.relfreq<-v_exerany.freq/nrow(cdc)
v_exerany.relfreq## Exerany
## 0 1
## 0.2543 0.7457How many males are in the sample?
table(cdc$gender) [1]## m
## 9569What proportion of the sample reports being in excellent health?
table(cdc$genhlth) [1]/nrow(cdc)## excellent
## 0.232853. What does the mosaic plot reveal about smoking habits and gender?
mosaicplot(table(cdc$gender,cdc$smoke100), main="Smoking Habits")
The mosaic plot reveals that there are more males has smoked at least 100 cigarrettes a day than females.
4. Create a new object called under23_and_smoke that contains all observations of respondents under the age of 23 that have smoked 100 cigarettes in their lifetime. Write the command you used to create the new object as the answer to this exercise.
under23_and_smoke<-subset(cdc, smoke100==1 & age < 23)
under23_and_smoke## genhlth exerany hlthplan smoke100 height weight wtdesire age
## 13 excellent 1 0 1 66 185 220 21
## 37 very good 1 0 1 70 160 140 18
## 96 excellent 1 1 1 74 175 200 22
## 180 good 1 1 1 64 190 140 20
## 182 very good 1 1 1 62 92 92 21
## 240 very good 1 0 1 64 125 115 22
## 262 fair 0 1 1 71 185 185 20
## 296 fair 1 1 1 72 185 170 19
## 297 excellent 1 0 1 63 105 100 19
## 300 fair 1 1 1 71 185 150 18
## 306 excellent 0 1 1 66 138 138 21
## 325 fair 1 1 1 63 110 110 20
## 355 very good 1 1 1 64 150 135 20
## 370 good 1 0 1 64 200 120 21
## 414 excellent 1 1 1 63 130 130 22
## 416 very good 1 1 1 75 220 220 18
## 421 good 0 1 1 62 160 130 20
## 439 good 1 1 1 62 102 110 19
## 446 excellent 1 1 1 62 130 120 22
## 484 good 1 1 1 67 165 148 22
## 492 very good 1 1 1 76 253 226 19
## 521 very good 1 1 1 63 100 100 20
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## 588 excellent 1 1 1 69 164 135 21
## 628 excellent 1 1 1 72 165 175 21
## 674 excellent 1 1 1 69 175 175 21
## 693 excellent 1 0 1 77 208 200 21
## 698 excellent 1 0 1 67 140 150 22
## 699 good 1 0 1 69 238 170 18
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## 958 good 0 0 1 71 120 120 19
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## 17188 very good 1 1 1 70 160 200 18
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## 17311 fair 1 1 1 66 180 180 21
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## 17358 very good 1 1 1 64 100 80 20
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## 18547 good 1 1 1 71 140 140 19
## 18590 fair 1 1 1 71 180 180 19
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## 18727 good 1 1 1 61 98 98 18
## 18818 good 0 0 1 65 250 150 20
## 18868 good 1 1 1 69 135 160 21
## 18871 very good 0 1 1 63 115 115 20
## 18910 very good 1 1 1 63 104 104 18
## 18924 good 1 1 1 70 163 165 21
## 18931 very good 1 1 1 71 190 180 22
## 18936 good 1 0 1 72 180 195 22
## 19107 very good 1 1 1 70 165 180 21
## 19217 good 1 1 1 67 275 175 21
## 19230 excellent 0 0 1 71 225 190 22
## 19326 very good 1 1 1 60 95 95 18
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## 19392 very good 1 1 1 67 115 115 19
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## 19500 poor 0 0 1 74 350 220 19
## 19513 very good 1 1 1 68 216 180 18
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## 19634 fair 1 1 1 64 140 125 20
## 19637 fair 1 0 1 68 165 175 22
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## 19751 very good 1 1 1 64 190 135 20
## 19824 very good 1 0 1 73 195 205 21
## 19853 good 1 0 1 71 168 200 21
## 19860 good 1 1 1 72 170 200 18
## 19864 good 0 0 1 61 107 100 19
## 19890 fair 1 0 1 71 195 200 21
## 19903 very good 1 0 1 70 140 140 20
## 19919 excellent 1 0 1 69 150 170 20
## gender
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## 19864 f
## 19890 m
## 19903 m
## 19919 mNext let’s consider a new variable that doesn’t show up directly in this data set: Body Mass Index (BMI) (http://en.wikipedia.org/wiki/Body_mass_index). BMI is a weight to height ratio and can be calculated as:
\[ BMI = \frac{weight~(lb)}{height~(in)^2} * 703 \]
703 is the approximate conversion factor to change units from metric (meters and kilograms) to imperial (inches and pounds).
The following two lines first make a new object called bmi and then creates box plots of these values, defining groups by the variable cdc$genhlth.
bmi <- (cdc$weight / cdc$height^2) * 703
boxplot(bmi ~ cdc$genhlth, ylab="BMI")
5. What does this box plot show? Pick another categorical variable from the data set and see how it relates to BMI. List the variable you chose, why you might think it would have a relationship to BMI, and indicate what the figure seems to suggest.
BMI is simply one measure of health as it relates to the body weight. The box plot above shows that the
people with lower BMI are in the better health condition.
We can choose a gender as another variable from the data set and see how it relates to BMI.
bmi <- (cdc$weight / cdc$height^2) * 703
boxplot((bmi ~ cdc$gender), col=c("blue","red"), ylab="BMI")
The box plot above shows that females have lower median and BMI than males, however higher range and IQR.
On Your Own
1. Make a scatterplot of weight versus desired weight. Describe the relationship between these two variables.
plot (cdc$weight, cdc$wtdesire, xlab="Weight", ylab= "Desired Weight", main="Weight vs Desired Weight", col=c("red", "green"))
There is a positive correlation between weight and desired weight. The Desired weight slightly goes up when weight is increasing.
2. Let’s consider a new variable: the difference between desired weight (wtdesire) and current weight (weight). Create this new variable by subtracting the two columns in the data frame and assigning them to a new object called wdiff
wdiff <- (cdc$weight -cdc$wtdesire)summary(wdiff)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -500.00 0.00 10.00 14.59 21.00 300.003. What type of data is wdiff? If an observation wdiff is 0, what does this mean about the person’s weight and desired weight. What if wdiff is positive or negative?
typeof(wdiff)## [1] "integer"The weights are integer values, therefore wdiff can only take integer values itself.
If an observation wdiff is 0 - person’s weight is the same as desired weight.
If an observation wdiff is positive - person’s weigh is more than desired.
If an observation wdiff is negative - person’s weight is less than desired.
4. Describe the distribution of wdiff in terms of its center, shape, and spread, including any plots you use. What does this tell us about how people feel about their current weight?
mean(wdiff)## [1] 14.5891boxplot(wdiff, col="green")
plot(wdiff, col="blue")
hist(wdiff, col="green")
Data is very closed to 0 and we can conclude that for most people wight is the same as desired.
5. Using numerical summaries and a side-by-side box plot, determine if men tend to view their weight differently than women.
newdiff <- data.frame(wdiff, cdc$gender)
summary(subset(newdiff, cdc.gender == "m"))## wdiff cdc.gender
## Min. :-500.00 m:9569
## 1st Qu.: 0.00 f: 0
## Median : 5.00
## Mean : 10.71
## 3rd Qu.: 20.00
## Max. : 300.00summary(subset(newdiff, cdc.gender == "f"))## wdiff cdc.gender
## Min. :-83.00 m: 0
## 1st Qu.: 0.00 f:10431
## Median : 10.00
## Mean : 18.15
## 3rd Qu.: 27.00
## Max. :300.00boxplot((cdc$weight-cdc$wtdesire ~ cdc$gender), main="Man Vs Women weigh view", col=c("blue","red"))
Based on the plots above there is not a big difference between man and woman weight view. However, there is a little difference that shows us that women’s weight is a bit more than desired.
6. Now it’s time to get creative. Find the mean and standard deviation of weight and determine what proportion of the weights are within one standard deviation of the mean.
# Mean of Weight
mean(cdc$weight)## [1] 169.683avgwt <- mean(cdc$weight)# Standard Deviation of Weight
sd (cdc$weight)## [1] 40.08097sdwt <- sd(cdc$weight)# Proportion of the weights are within one standard deviation of the mean
withinstdev <- subset(cdc, weight < (avgwt + sdwt) & weight > (avgwt - sdwt))
dim(withinstdev)[1]/dim(cdc)[1]## [1] 0.7076