The Behavioral Risk Factor Surveillance System (BRFSS) is an annual telephone survey of 350,000 people in the United States collected by the Centers for Disease Control and Prevention (CDC). As its name implies, the BRFSS is designed to identify risk factors in the adult population and report emerging health trends. For example, respondents are asked about their diet and weekly physical activity, their HIV/AIDS status, possible tobacco use, and even their level of healthcare coverage.

The BRFSS Web site (http://www.cdc.gov/brfss) contains a complete description of the survey, the questions that were asked and even research results that have been derived from the data. This data set is a random sample of 20,000 people from the BRFSS survey conducted in 2000. While there are over 200 questions or variables in this dataset, this data set only includes 9 variables.

1. 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     9

str(cdc)

## 'data.frame':    20000 obs. of  9 variables:
##  $ genhlth : Factor w/ 5 levels "excellent","very good",..: 3 3 3 3 2 2 2 2 3 3 ...
##  $ exerany : num  0 0 1 1 0 1 1 0 0 1 ...
##  $ hlthplan: num  1 1 1 1 1 1 1 1 1 1 ...
##  $ smoke100: num  0 1 1 0 0 0 0 0 1 0 ...
##  $ height  : num  70 64 60 66 61 64 71 67 65 70 ...
##  $ weight  : int  175 125 105 132 150 114 194 170 150 180 ...
##  $ wtdesire: int  175 115 105 124 130 114 185 160 130 170 ...
##  $ age     : int  77 33 49 42 55 55 31 45 27 44 ...
##  $ gender  : Factor w/ 2 levels "m","f": 1 2 2 2 2 2 1 1 2 1 ...

There are 20,000 cases and 9 variables, as indicated by the dimensions function.

Below are the classification of the variables, formatting into tables via the pander package.

cdc_var <- data.frame(variable = c("genhlth", "exerany", "hlthplan", "smoke100","height","weight","wtdesire","age","gender"), datatype = c("factor","numeric","numeric","numeric","numeric","integer","integer","integer","factor"), cat_disc = c("categorical","categorical","categorical","categorical","continuous","continuous","continuous","discrete","categorical"))
pander(cdc_var,style = 'rmarkdown')

variable	datatype	cat_disc
genhlth	factor	categorical
exerany	numeric	categorical
hlthplan	numeric	categorical
smoke100	numeric	categorical
height	numeric	continuous
weight	integer	continuous
wtdesire	integer	continuous
age	integer	discrete
gender	factor	categorical

2a. Create a numerical summary for `height` and `age`, and compute the interquartile range for each.

A summary of the height data, with the IQR added as a column:

height_summary <- summary(cdc$height)
height_summary <- t(height_summary)
height_IQR <- height_summary[5] - height_summary[2]
height_info <- data.frame(cbind(height_summary,height_IQR))
height_info

##   Min. X1st.Qu. Median    Mean X3rd.Qu. Max. height_IQR
## 1   48       64     67 67.1829       70   93          6

A summary of the age data, with the IQR added as a column:

age_summary <- summary(cdc$age)
age_summary <- t(age_summary)
age_IQR <- age_summary[5] - age_summary[2]
age_info <- data.frame(cbind(age_summary,age_IQR))
age_info

##   Min. X1st.Qu. Median     Mean X3rd.Qu. Max. age_IQR
## 1   18       31     43 45.06825       57   99      26

2b. Compute the relative frequency distribution for`gender` and `exerany`. How many males are in the sample? What proportion ofthe sample reports being in excellent health?

freq_table <- prop.table(table(cdc$gender, cdc$exerany))
colnames(freq_table) <- c("non-exercisers","exercisers")
freq_table

##    
##     non-exercisers exercisers
##   m        0.10745    0.37100
##   f        0.14685    0.37470

males_total <- sum(cdc$gender == "m")
male_exc_health <- sum(cdc$gender == "m" & cdc$genhlth == "excellent")
males_prop_exc_health <- round(male_exc_health / males_total,4) * 100
  
print(paste0("Males in sample: ", males_total))

## [1] "Males in sample: 9569"

print(paste0("Males reporting excellent health: ", male_exc_health))

## [1] "Males reporting excellent health: 2298"

print(paste0("Proportion of Males reporting excellent health: ", males_prop_exc_health, "%"))

## [1] "Proportion of Males reporting excellent health: 24.02%"

3a. What does the mosaic plot reveal about smoking habits and gender?

mosiac <- mosaicplot(table(cdc$gender,cdc$smoke100), main = "Smokers vs. Gender", color = T)

#### On the y-axis, the value “0” indicates the subject has smoked less than 100 cigarettes in his or her lifetime. The mosiac plot reveals that a great percentage of females can be so classified. This percentage is 57.6%, as compared to that of males of 47.5%.

non_smoker <- c((sum(!cdc$smoke100[cdc$gender == "f"])/ sum(cdc$gender == "f")),
              (sum(!cdc$smoke100[cdc$gender == "m"])/ sum(cdc$gender == "m")))
non_smoker

## [1] 0.5763589 0.4751803

3b. 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, cdc$age < 23 & cdc$smoke100 == 1)
head(under23_and_smoke)

##       genhlth exerany hlthplan smoke100 height weight wtdesire age gender
## 13  excellent       1        0        1     66    185      220  21      m
## 37  very good       1        0        1     70    160      140  18      f
## 96  excellent       1        1        1     74    175      200  22      m
## 180      good       1        1        1     64    190      140  20      f
## 182 very good       1        1        1     62     92       92  21      f
## 240 very good       1        0        1     64    125      115  22      f

4. 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.

cdc$bmi <- (cdc$weight / cdc$height^2) * 703
boxplot(cdc$bmi ~ cdc$genhlth)

This boxplot shows that as subjects considered themselves of worsening ordinal general health, both median BMI increaed and IQR widened.

exercisers_bmi <- subset(cdc, cdc$exerany == 1)
non_exercisers_bmi <- subset(cdc, cdc$exerany == 0)

exercisers_summary <- summary(exercisers_bmi$bmi)
non_exercisers_summary <- summary(non_exercisers_bmi$bmi)
x3 <- rbind(exercisers_summary, non_exercisers_summary)
x3

##                            Min.  1st Qu.   Median     Mean  3rd Qu.
## exercisers_summary     12.40045 22.65527 25.10714 25.98012 28.33963
## non_exercisers_summary 12.74954 23.02595 26.49673 27.26525 30.26681
##                            Max.
## exercisers_summary     73.09074
## non_exercisers_summary 62.64201

boxplot(cdc$bmi ~ cdc$exerany)

#### In this case, one would expect that people who exercise (cdc$exerany == 1) have a lower BMI on average than those who do not.

From the boxplot, we observe that the exercisers have a slightly lower medium, and a 3rd Quartile that is much lower.

In this case, one would expect that people who exercise (cdc$exerany == 1) have a lower BMI on average than those who do not. The mean BMI is revealed to indeed by higher for non-exercisers, 27.3, versus 26.0 for exercisers.

On Your Own

Q1: Make a scatterplot of weight versus desired weight. Describe the relationship between these two variables.

plot(x = cdc$wtdesire, y = cdc$weight, xlim=c(50,350))

reg2 <- lm(wtdesire ~ weight,data=cdc) 
summary(reg2)

## 
## Call:
## lm(formula = wtdesire ~ weight, data = cdc)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -167.98   -9.32    0.08   11.51  518.31 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 46.664015   0.590782   78.99   <2e-16 ***
## weight       0.639014   0.003388  188.59   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 19.21 on 19998 degrees of freedom
## Multiple R-squared:  0.6401, Adjusted R-squared:  0.6401 
## F-statistic: 3.556e+04 on 1 and 19998 DF,  p-value: < 2.2e-16

The summary reveals a moderately strong positive correlation with the regression correlation coefficient of 0.639.

Q2a: 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`.

cdc$wdiff <- cdc$wtdesire - cdc$weight

reg1 <- lm(bmi ~ wdiff, data=cdc) 
    with(cdc,plot(bmi, wdiff))
    abline(h=0)

Q2b: 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?

If wdiff equals 0 then the subject’s desired weight matches his or her current weight. If it is negative, and current weight exceeds desired weight, they perceive themselves as overweight. If it is positive, they view themselves as underweight and desire to gain weight.

Q3: 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?

class(cdc$wdiff)

## [1] "integer"

summary(cdc$wdiff)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## -300.00  -21.00  -10.00  -14.59    0.00  500.00

Both standard measures of center, mean and median, are negative, reflecting that most people view themselves as overweight. That mean is more negative than median suggests that the data is skewed left, with some largely negative values of wdiff.

hist(cdc$wdiff, breaks = 80)

The shape is shown in the histogram above, with a large spike showing that about 8000 or 20000 subjects seeing themselves as slightly overweight. The distribution does not seem symmetric or normal with the scant number of positive wdiff results.

sd(cdc$wdiff)

## [1] 24.04586

As for spread, IQR is 21 (3rd Quartile - 1st Quartile ) with a standard deviation of 24.05. Clearly those people who regard themselves as severely obese are leading to a widenening of SD as compared to IQR.

Using numerical summaries and a side-by-side box plot, determine if men tend to view their weight differently than women.

men_wdiff_summary <- summary(cdc$wdiff[cdc$gender == "m"])
women_wdiff_summary <- summary(cdc$wdiff[cdc$gender == "f"])
wdiff_sum <- rbind(men_wdiff_summary,women_wdiff_summary)
wdiff_sum

##                     Min. 1st Qu. Median      Mean 3rd Qu. Max.
## men_wdiff_summary   -300     -20     -5 -10.70613       0  500
## women_wdiff_summary -300     -27    -10 -18.15118       0   83

From the summary, we can generalize that women generally view themselves to be more pounds overweight than men. For both, weight satisfaction (wdiff=0) is the 3rd Quartile. There is an outlier among the men, in which one man who reported desiring to be 500 pounds heavier is skewing the mean.

boxplot(cdc$wdiff ~ cdc$gender)

Q4: 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.

prop <- sum((cdc$weight > (mean(cdc$weight) - sd(cdc$weight))) & cdc$weight < (mean(cdc$weight) + sd(cdc$weight)))/20000
prop2 <- sum((cdc$weight > (mean(cdc$weight) - 2 * sd(cdc$weight))) & cdc$weight < (mean(cdc$weight) + 2 * sd(cdc$weight)))/20000
data2 <- list(c(mean(cdc$weight)),sd(cdc$weight), prop, prop2)
data3 <- t(data2)
colnames(data3) <- c("mean", "sd", "prop w/in 1SD", "prop w/in 2 SD")
data3

##      mean    sd       prop w/in 1SD prop w/in 2 SD
## [1,] 169.683 40.08097 0.7076        0.9563

CUNY DATA 606_Lab1_Herold

1. How many cases are there in this data set? How many variables? For each variable, identify its data type (e.g. categorical, discrete).

There are 20,000 cases and 9 variables, as indicated by the dimensions function.

Below are the classification of the variables, formatting into tables via the pander package.

2a. Create a numerical summary for `height` and `age`, and compute the interquartile range for each.

A summary of the height data, with the IQR added as a column:

A summary of the age data, with the IQR added as a column:

2b. Compute the relative frequency distribution for`gender` and `exerany`. How many males are in the sample? What proportion ofthe sample reports being in excellent health?

3a. What does the mosaic plot reveal about smoking habits and gender?

3b. 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.

4. 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.

This boxplot shows that as subjects considered themselves of worsening ordinal general health, both median BMI increaed and IQR widened.

From the boxplot, we observe that the exercisers have a slightly lower medium, and a 3rd Quartile that is much lower.

In this case, one would expect that people who exercise (cdc$exerany == 1) have a lower BMI on average than those who do not. The mean BMI is revealed to indeed by higher for non-exercisers, 27.3, versus 26.0 for exercisers.

On Your Own

Q1: Make a scatterplot of weight versus desired weight. Describe the relationship between these two variables.

The summary reveals a moderately strong positive correlation with the regression correlation coefficient of 0.639.

Q2a: 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`.

Q2b: 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?

If wdiff equals 0 then the subject’s desired weight matches his or her current weight. If it is negative, and current weight exceeds desired weight, they perceive themselves as overweight. If it is positive, they view themselves as underweight and desire to gain weight.

Q3: 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?

Both standard measures of center, mean and median, are negative, reflecting that most people view themselves as overweight. That mean is more negative than median suggests that the data is skewed left, with some largely negative values of wdiff.

The shape is shown in the histogram above, with a large spike showing that about 8000 or 20000 subjects seeing themselves as slightly overweight. The distribution does not seem symmetric or normal with the scant number of positive wdiff results.

As for spread, IQR is 21 (3rd Quartile - 1st Quartile ) with a standard deviation of 24.05. Clearly those people who regard themselves as severely obese are leading to a widenening of SD as compared to IQR.

Using numerical summaries and a side-by-side box plot, determine if men tend to view their weight differently than women.

From the summary, we can generalize that women generally view themselves to be more pounds overweight than men. For both, weight satisfaction (wdiff=0) is the 3rd Quartile. There is an outlier among the men, in which one man who reported desiring to be 500 pounds heavier is skewing the mean.

Q4: 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.

The mean is 169.7. The Standard Deviation is 40.1, with 70.76% of cases falling with 1 standard deviation of the mean.

CUNY DATA 606_Lab1_Herold

1. How many cases are there in this data set? How many variables? For each variable, identify its data type (e.g. categorical, discrete).

There are 20,000 cases and 9 variables, as indicated by the dimensions function.

Below are the classification of the variables, formatting into tables via the pander package.

2a. Create a numerical summary for height and age, and compute the interquartile range for each.

A summary of the height data, with the IQR added as a column:

A summary of the age data, with the IQR added as a column:

2b. Compute the relative frequency distribution forgender and exerany. How many males are in the sample? What proportion ofthe sample reports being in excellent health?

3a. What does the mosaic plot reveal about smoking habits and gender?

3b. 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.

4. 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.

This boxplot shows that as subjects considered themselves of worsening ordinal general health, both median BMI increaed and IQR widened.

From the boxplot, we observe that the exercisers have a slightly lower medium, and a 3rd Quartile that is much lower.

In this case, one would expect that people who exercise (cdc$exerany == 1) have a lower BMI on average than those who do not. The mean BMI is revealed to indeed by higher for non-exercisers, 27.3, versus 26.0 for exercisers.

On Your Own

Q1: Make a scatterplot of weight versus desired weight. Describe the relationship between these two variables.

The summary reveals a moderately strong positive correlation with the regression correlation coefficient of 0.639.

Q2a: 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.

Q2b: 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?

If wdiff equals 0 then the subject’s desired weight matches his or her current weight. If it is negative, and current weight exceeds desired weight, they perceive themselves as overweight. If it is positive, they view themselves as underweight and desire to gain weight.

Q3: 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?

Both standard measures of center, mean and median, are negative, reflecting that most people view themselves as overweight. That mean is more negative than median suggests that the data is skewed left, with some largely negative values of wdiff.

The shape is shown in the histogram above, with a large spike showing that about 8000 or 20000 subjects seeing themselves as slightly overweight. The distribution does not seem symmetric or normal with the scant number of positive wdiff results.

As for spread, IQR is 21 (3rd Quartile - 1st Quartile ) with a standard deviation of 24.05. Clearly those people who regard themselves as severely obese are leading to a widenening of SD as compared to IQR.

Using numerical summaries and a side-by-side box plot, determine if men tend to view their weight differently than women.

From the summary, we can generalize that women generally view themselves to be more pounds overweight than men. For both, weight satisfaction (wdiff=0) is the 3rd Quartile. There is an outlier among the men, in which one man who reported desiring to be 500 pounds heavier is skewing the mean.

Q4: 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.

The mean is 169.7. The Standard Deviation is 40.1, with 70.76% of cases falling with 1 standard deviation of the mean.

2a. Create a numerical summary for `height` and `age`, and compute the interquartile range for each.

2b. Compute the relative frequency distribution for`gender` and `exerany`. How many males are in the sample? What proportion ofthe sample reports being in excellent health?

3b. 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.

Q2a: 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`.

Q2b: 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?

Q3: 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?