Assignment 4
Ted Bond
6/27/2017
- Assignment 4 Exploratory Data Analysis
- Chapter 1 Exploring Categorical Data
- Chapter 2 Exploring Numerical Data
- 2.1 Faceted histogram
- 2.2 Boxplots and density plots
- 2.3 Compare distribution via plots
- 2.4 Marginal and conditional histograms
- 2.5 Marginal and conditional histograms interpretation
- 2.6 Three bindwidths
- 2.7 Three bindwiths interpretation
- 2.8 Box plots for outliers
- 2.9 Plot selection
- 2.10 3 variable plot
- 2.11 Interpret 3 var plot
- Chapter 3 Numerical Summaries
- Chapter 4 Case Study
- Quiz 4
- 1. Use the code below to create a new variable, rural takes the value of rural if it has less than 1,000 people per square mile and the value of urban otherwise.
- 2. Examine the living standard of the US counties, using
per_capita_incomeas a measure, and how it differs by whether the county is rural or urban. To that end, do the following and interpret the results: - 3. Use the box plot you created above and identify an outlier, a rural county that has a per_capita_income higher than $60,000 a year when a typical rural county’s per capita income is less than $23,000 a year.
Assignment 4 Exploratory Data Analysis
Chapter 1 Exploring Categorical Data
1.1 Bar chart expectations
Data can be summarized in a side-by-side barchart.
Which one of the barcharts shows no relationship between age and flavor? In other words, which shows that pie preference is the same for both young and old?
Plot 1
1.2 Contingency table review
Creating a contingency table is a useful way to represent the total counts of observations that fall into each combination of the levels of categorical variables.
# Import data
comics <- read.csv("comics.csv")
# Print the first rows of the data
head(comics, rows = 5)
## name id align eye
## 1 Spider-Man (Peter Parker) Secret Good Hazel Eyes
## 2 Captain America (Steven Rogers) Public Good Blue Eyes
## 3 Wolverine (James \\\\"Logan\\\\" Howlett) Public Neutral Blue Eyes
## 4 Iron Man (Anthony \\\\"Tony\\\\" Stark) Public Good Blue Eyes
## 5 Thor (Thor Odinson) No Dual Good Blue Eyes
## 6 Benjamin Grimm (Earth-616) Public Good Blue Eyes
## hair gender gsm alive appearances first_appear
## 1 Brown Hair Male <NA> Living Characters 4043 Aug-62
## 2 White Hair Male <NA> Living Characters 3360 Mar-41
## 3 Black Hair Male <NA> Living Characters 3061 Oct-74
## 4 Black Hair Male <NA> Living Characters 2961 Mar-63
## 5 Blond Hair Male <NA> Living Characters 2258 Nov-50
## 6 No Hair Male <NA> Living Characters 2255 Nov-61
## publisher
## 1 marvel
## 2 marvel
## 3 marvel
## 4 marvel
## 5 marvel
## 6 marvel
# Check levels of align
levels(comics$align)
## [1] "Bad" "Good" "Neutral"
## [4] "Reformed Criminals"
# Check the levels of gender
levels(comics$gender)
## [1] "Female" "Male" "Other"
# Create a 2-way contingency table
table(comics$align, comics$gender)
##
## Female Male Other
## Bad 1573 7561 32
## Good 2490 4809 17
## Neutral 836 1799 17
## Reformed Criminals 1 2 01.3 Dropping levels
To simplify an analysis, it often helps to drop levels with small amounts of data. In R, this requires two steps: first filtering out any rows with the levels that have very low counts, then removing these levels from the factor variable with droplevels(). This is because the droplevels() function would keep levels that have just 1 or 2 counts; it only drops levels that don’t exist in a dataset.
# Load dplyr
library(dplyr)
tab <- table(comics$align, comics$gender)
# Print tab
tab
##
## Female Male Other
## Bad 1573 7561 32
## Good 2490 4809 17
## Neutral 836 1799 17
## Reformed Criminals 1 2 0
# Remove align level
comics <- comics %>%
filter(align != "Reformed Criminals") %>%
droplevels()
1.4 Side-by-side barcharts
You can construct two side-by-side barcharts of the comics data. This shows that there can often be two or more options for presenting the same data. Passing the argument position = “dodge” to geom_bar() says that you want a side-by-side (i.e. not stacked) barchart.
# Load ggplot2
library(ggplot2)
# Create side-by-side barchart of gender by alignment
ggplot(comics, aes(x = align, fill = gender)) +
geom_bar(position = "dodge")
# Create side-by-side barchart of alignment by gender
ggplot(comics, aes(x = gender, fill = align)) +
geom_bar(position = "dodge") +
theme(axis.text.x = element_text(angle = 90))
1.5 Bar Chart Interpretation
Which of the following interpretations of the bar charts to you right is not valid?
Possible Answers
Across all genders, “Bad” is the most common alignment.
1.6 Conditional proportions
You can generate tables of joint and conditional proportions. This shows that approximately 51% of all female characters are good.
tab <- table(comics$align, comics$gender)
options(scipen = 999, digits = 3) # Print fewer digits
prop.table(tab) # Joint proportions
##
## Female Male Other
## Bad 0.082210 0.395160 0.001672
## Good 0.130135 0.251333 0.000888
## Neutral 0.043692 0.094021 0.000888
prop.table(tab, 2) # Conditional on columns
##
## Female Male Other
## Bad 0.321 0.534 0.485
## Good 0.508 0.339 0.258
## Neutral 0.171 0.127 0.2581.7 Counts vs. proportions (2)
Bar charts are different depending on whether they represent counts or proportions and, if proportions, what the proportions are conditioned on.
# Plot of gender by align
ggplot(comics, aes(x = align, fill = gender)) +
geom_bar()
# Plot proportion of gender, conditional on align
ggplot(comics, aes(x = align, fill = gender)) +
geom_bar(position = "fill")
1.8 Marginal barchart
You can construct a barchart to illustrate a single variable.
# Change the order of the levels in align
comics$align <- factor(comics$align,
levels = c("Bad", "Neutral", "Good"))
# Create plot of align
ggplot(comics, aes(x = align)) +
geom_bar()
1.9 Conditional barchart
You can break down the distribution of a variable by using conditional distributions. You could make these by creating multiple filtered datasets or by faceting the plot of your variable.
# Plot of alignment broken down by gender
ggplot(comics, aes(x = align)) +
geom_bar() +
facet_wrap(~ gender)
1.10 Improve piechart
The piechart is a very common way to represent the distribution of a single categorical variable, but they can be more difficult to interpret than barcharts.
# Import data
pies <- read.csv("pie.csv")
pies_tb <- table(pies$flavor)
pies_tb
##
## apple blueberry boston creme cherry key lime
## 17 14 15 13 16
## pumpkin strawberry
## 12 11
# Create a pie chart
pie(pies_tb)
# Put levels of flavor in decending order
lev <- c("apple", "key lime", "boston creme", "blueberry", "cherry", "pumpkin", "strawberry")
pies$flavor <- factor(pies$flavor, levels = lev)
# Create barchart of flavor
ggplot(pies, aes(x = flavor)) +
geom_bar(fill = "chartreuse") +
theme(axis.text.x = element_text(angle = 90))
Chapter 2 Exploring Numerical Data
2.1 Faceted histogram
You can use a faceted histogram to see the distribution of one variable spread across a categroical variable.
# Load data
cars <- read.csv("cars.csv")
# Load package
library(ggplot2)
# Learn data structure
str(cars)
## 'data.frame': 428 obs. of 19 variables:
## $ name : Factor w/ 425 levels "Acura 3.5 RL 4dr",..: 66 67 68 69 70 114 115 133 129 130 ...
## $ sports_car : logi FALSE FALSE FALSE FALSE FALSE FALSE ...
## $ suv : logi FALSE FALSE FALSE FALSE FALSE FALSE ...
## $ wagon : logi FALSE FALSE FALSE FALSE FALSE FALSE ...
## $ minivan : logi FALSE FALSE FALSE FALSE FALSE FALSE ...
## $ pickup : logi FALSE FALSE FALSE FALSE FALSE FALSE ...
## $ all_wheel : logi FALSE FALSE FALSE FALSE FALSE FALSE ...
## $ rear_wheel : logi FALSE FALSE FALSE FALSE FALSE FALSE ...
## $ msrp : int 11690 12585 14610 14810 16385 13670 15040 13270 13730 15460 ...
## $ dealer_cost: int 10965 11802 13697 13884 15357 12849 14086 12482 12906 14496 ...
## $ eng_size : num 1.6 1.6 2.2 2.2 2.2 2 2 2 2 2 ...
## $ ncyl : int 4 4 4 4 4 4 4 4 4 4 ...
## $ horsepwr : int 103 103 140 140 140 132 132 130 110 130 ...
## $ city_mpg : int 28 28 26 26 26 29 29 26 27 26 ...
## $ hwy_mpg : int 34 34 37 37 37 36 36 33 36 33 ...
## $ weight : int 2370 2348 2617 2676 2617 2581 2626 2612 2606 2606 ...
## $ wheel_base : int 98 98 104 104 104 105 105 103 103 103 ...
## $ length : int 167 153 183 183 183 174 174 168 168 168 ...
## $ width : int 66 66 69 68 69 67 67 67 67 67 ...
# Create faceted histogram
ggplot(cars, aes(x = city_mpg)) +
geom_histogram() +
facet_wrap(~ suv)
2.2 Boxplots and density plots
You can also use box plots and density plots to explore the relationship between two variables.
# Filter cars with 4, 6, 8 cylinders
common_cyl <- filter(cars, ncyl %in% c(4,6,8))
# Create box plots of city mpg by ncyl
ggplot(common_cyl, aes(x = as.factor(ncyl), y = city_mpg)) +
geom_boxplot()
# Create overlaid density plots for same data
ggplot(common_cyl, aes(x = city_mpg, fill = as.factor(ncyl))) +
geom_density(alpha = .3)
2.3 Compare distribution via plots
Which of the following interpretations of the plot is not valid?
The variability in mileage of 8 cylinder cars is similar to the variability in mileage of 4 cylinder cars.
2.4 Marginal and conditional histograms
I’ve made two plots using the “data pipeline” paradigm, where you start with the raw data and end with the plot.
# Create hist of horsepwr
cars %>%
ggplot(aes(x = horsepwr)) +
geom_histogram() +
ggtitle("Horsepower Distribution")
# Create hist of horsepwr for affordable cars
cars %>%
filter(msrp < 25000) %>%
ggplot(aes(x = horsepwr)) +
geom_histogram() +
xlim(c(90, 550)) +
ggtitle("Horsepower for Affordable Cars")
2.5 Marginal and conditional histograms interpretation
Observe the two histograms in the plotting window and decide which of the following is a valid interpretation.
The highest horsepower car in the less expensive range has just under 250 horsepower.
2.6 Three bindwidths
The binwidth determines how smooth your distribution will appear: the smaller the binwidth, the more jagged your distribution becomes.
# Create hist of horsepwr with binwidth of 3
cars %>%
ggplot(aes(x = horsepwr)) +
geom_histogram(binwidth = 3) +
ggtitle("Horsepower with binwidth = 3")
# Create hist of horsepwr with binwidth of 30
cars %>%
ggplot(aes(x = horsepwr)) +
geom_histogram(binwidth = 30) +
ggtitle("Horsepower with binwidth = 30")
# Create hist of horsepwr with binwidth of 60
cars %>%
ggplot(aes(x = horsepwr)) +
geom_histogram(binwidth = 60) +
ggtitle("Horsepower with binwidth = 60")
2.7 Three bindwiths interpretation
What feature is present in Plot A that’s not found in B or C?
There is a tendency for cars to have horsepower right at 200 or 300 horsepower.
2.8 Box plots for outliers
A box plot provides a graphical means to detect outliers.
# Construct box plot of msrp
cars %>%
ggplot(aes(x = 1, y = msrp)) +
geom_boxplot()
# Exclude outliers from data
cars_no_out <- cars %>%
filter(msrp < 100000)
# Construct box plot of msrp using the reduced dataset
cars_no_out %>%
ggplot(aes(x = 1, y = msrp)) +
geom_boxplot()
2.9 Plot selection
Both density plots and box plots display the central tendency and spread of the data, but the box plot is more robust to outliers.
# Create plot of city_mpg
cars %>%
ggplot(aes(x = 1, y = city_mpg)) +
geom_boxplot()
# Create plot of width
cars %>%
ggplot(aes(x = width)) +
geom_density()
2.10 3 variable plot
Faceting is a valuable technique for looking at several conditional distributions at the same time. If the faceted distributions are laid out in a grid, you can consider the association between a variable and two others, one on the rows of the grid and the other on the columns.
# Facet hists using hwy mileage and ncyl
common_cyl %>%
ggplot(aes(x = hwy_mpg)) +
geom_histogram() +
facet_grid(ncyl ~ suv) +
ggtitle("MPG for 4,6 and 8 cyl vehicles vs. SUVs")
2.11 Interpret 3 var plot
Which of the following interpretations of the plot is valid?
Across both SUVs and non-SUVs, mileage tends to decrease as the number of cylinders increases.
Chapter 3 Numerical Summaries
3.1 Choice of center measure
When chosing the measure for center of a data set you should consider the shape of the distribution before deciding on the measure.
Which set of measures of central tendency would be worst for describing the two distributions shown here?
A: mean, B: mode
3.2 Calculate center measure
The commands group_by() and summarize(), allow you to carry out an analysis on different subsets of a full dataset.
# Load data
library(gapminder)
# Create dataset of 2007 data
gap2007 <- filter(gapminder, year ==2007)
# Compute groupwise mean and median lifeExp
gap2007 %>%
group_by(continent) %>%
summarize(mean(lifeExp),
median(lifeExp))
## # A tibble: 5 x 3
## continent `mean(lifeExp)` `median(lifeExp)`
## <fctr> <dbl> <dbl>
## 1 Africa 54.8 52.9
## 2 Americas 73.6 72.9
## 3 Asia 70.7 72.4
## 4 Europe 77.6 78.6
## 5 Oceania 80.7 80.7
# Generate box plots of lifeExp for each continent
gap2007 %>%
ggplot(aes(x = continent, y = lifeExp)) +
geom_boxplot()
3.3 Choice of spread measure
When chosing the measure for spread of a data set it is important that you consider the shape of the distribution before deciding on the measure.
Which set of measures of spread would be worst for describing the two distributions shown here?
A: Variance, B: Range
3.4 Calculate spread measures
You can use the group_by() and summarize() commands to compute the measures of spread.
# Compute groupwise measures of spread
gap2007 %>%
group_by(continent) %>%
summarize(sd(lifeExp),
IQR(lifeExp),
n())
## # A tibble: 5 x 4
## continent `sd(lifeExp)` `IQR(lifeExp)` `n()`
## <fctr> <dbl> <dbl> <int>
## 1 Africa 9.631 11.610 52
## 2 Americas 4.441 4.632 25
## 3 Asia 7.964 10.152 33
## 4 Europe 2.980 4.782 30
## 5 Oceania 0.729 0.516 2
# Generate overlaid density plots
gap2007 %>%
ggplot(aes(x = lifeExp, fill = continent)) +
geom_density(alpha = 0.3)
3.5 Choose measures for center and spread
In this exercise, you’ll select the most appropriate measures to describe the centers and spreads of the data and then calculate them.
# Compute stats for lifeExp in Americas
gap2007 %>%
filter(continent == "Americas") %>%
summarize(mean(lifeExp),
sd(lifeExp))
## # A tibble: 1 x 2
## `mean(lifeExp)` `sd(lifeExp)`
## <dbl> <dbl>
## 1 73.6 4.44
# Compute stats for population
gap2007 %>%
summarize(median(pop),
IQR(pop))
## # A tibble: 1 x 2
## `median(pop)` `IQR(pop)`
## <dbl> <dbl>
## 1 10517531 267020083.6 Describe the shape
Which of the following options does the best job of describing their shape in terms of modality and skew/symmetry?
Possible Answers
- A: unimodal left-skewed; B: unimodal symmetric; C: unimodal right-skewed, D: bimodal symmetric.
3.7 Transformations
Transformations can be helpful in revealing the more subtle structure.
Here you’ll focus on the population variable, which exhibits strong right skew, and transform it with the natural logarithm function (log() in R).
# Create density plot of old variable
gap2007 %>%
ggplot(aes(x = pop)) +
geom_density()
# Transform the skewed pop variable
gap2007 <- gap2007 %>%
mutate(log_pop = log(pop))
# Create density plot of new variable
gap2007 %>%
ggplot(aes(x = log_pop)) +
geom_density()
3.8 Identify outliers
Consider the distribution, shown here, of the life expectancies of the countries in Asia. The box plot identifies one clear outlier: a country with a notably low life expectancy. Do you have a guess as to which country this might be? Test your guess in the console using either min() or filter(), then proceed to building a plot with that country removed.
# Filter for Asia, add column indicating outliers
gap_asia <- gap2007 %>%
filter(continent == "Asia") %>%
mutate(is_outlier = lifeExp < 50)
# Remove outliers, create box plot of lifeExp
gap_asia %>%
filter(!is_outlier) %>%
ggplot(aes(x = 1, y = lifeExp)) +
geom_boxplot()
Chapter 4 Case Study
4.1 Spam and num_char
Here, you’ll use the email dataset to settle the question of whether or not there is an association between spam and the number of characters in an email. You can explore this association by linking a dplyr chain with the layers in a ggplot2 object.
# Load packages
library(openintro)
library(ggplot2)
library(dplyr)
# Compute summary statistics
email %>%
group_by(spam) %>%
summarize(median(num_char),
IQR(num_char))
## # A tibble: 2 x 3
## spam `median(num_char)` `IQR(num_char)`
## <dbl> <dbl> <dbl>
## 1 0 6.83 13.58
## 2 1 1.05 2.82
# Create plot
email %>%
mutate(log_num_char = log(num_char)) %>%
ggplot(aes(x = spam, y = log_num_char)) +
geom_boxplot()
4.2 Spam and num_char
Which of the following interpretations of the plot is valid?
- The median length of not-spam emails is greater than that of spam emails.
4.3 Spam and !!!
The variable exclaim_mess contains the number of exclamation marks in each message. Using summary statistics and visualization, see if there is a relationship between this variable and whether or not a message is spam.
# Compute center and spread for exclaim_mess by spam
email %>%
group_by(spam) %>%
summarize(median(exclaim_mess),
IQR(exclaim_mess))
## # A tibble: 2 x 3
## spam `median(exclaim_mess)` `IQR(exclaim_mess)`
## <dbl> <dbl> <dbl>
## 1 0 1 5
## 2 1 0 1
# Create plot for spam and exclaim_mess
email %>%
mutate(log_exclaim_mess = log(exclaim_mess + .01)) %>%
ggplot(aes(x = log_exclaim_mess)) +
geom_histogram() +
facet_wrap(~ spam)
4.4 Spam !!! and interpretation
Which interpretation of these faceted histograms is not correct?
- There are more cases of spam in this dataset than not-spam.
4.5 Collapsing levels
In this data set there were 3811 emails with 0 images. You can collapse image into a categorical variable that indicates whether or not the email had at least one image. In this exercise, you’ll create this new variable and explore its association with spam.
# Create plot of proportion of spam by image
email %>%
mutate(has_image = image > 0) %>%
ggplot(aes(x = has_image, fill = spam)) +
geom_bar(position = "fill")
4.6 Image and spam interpretation
Which of the following interpretations of the plot is valid?
- An email without an image is more likely to be not-spam than spam.
4.7 Data integrity
The variable num_char contains the number of characters in the email, in thousands, so it could take decimal values, but it certainly shouldn’t take negative values. To verify that all of the cases indeed have non-negative values for num_char, we can take the sum of this vector: sum(email$num_char < 0).
# Test if images count as attachments
email$image < 0
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sum(email$image < 0)
## [1] 0
sum(email$attach < 0)
## [1] 04.8 Answering questions with chains
When you have a specific question about a dataset, you can find your way to an answer by carefully constructing the appropriate chain of R code.
# Question 1
email %>%
filter(dollar > 0) %>%
group_by(spam) %>%
summarize(median(dollar))
## # A tibble: 2 x 2
## spam `median(dollar)`
## <dbl> <dbl>
## 1 0 4
## 2 1 2
# Question 2
email %>%
filter(dollar > 10) %>%
ggplot(aes(x = spam)) +
geom_bar()
4.9 What’s in a number?
To explore the association between this variable and spam, select and construct an informative plot.
# Reorder levels
email$number <- factor(email$number, levels = c("none", "small", "big"))
# Construct plot of number
ggplot(email, aes(x = number)) +
geom_bar() +
facet_wrap(~ spam)
4.10 What’s in a number interpretation
Which of the following interpretations of the plot is not valid?
- Given that an email contains no number, it is more likely to be spam.
Quiz 4
How can we revitalize a region’s economy? Assume that you live in a rural community and are interested in helping your community develop its economy. So you want to identify a rural community in the U.S. that enjoys a high living standards and investigate what makes them different from the rest of the rural America. For this brief analysis, use the countyComplete data set in the openintro R package. Click the link to open the manual and find the definitions of the variables in the data set.
1. Use the code below to create a new variable, rural takes the value of rural if it has less than 1,000 people per square mile and the value of urban otherwise.
# Load data
data(countyComplete) # It comes from the openintro package
head(countyComplete, rows = 5)
## state name FIPS pop2010 pop2000 age_under_5 age_under_18
## 1 Alabama Autauga County 1001 54571 43671 6.6 26.8
## 2 Alabama Baldwin County 1003 182265 140415 6.1 23.0
## 3 Alabama Barbour County 1005 27457 29038 6.2 21.9
## 4 Alabama Bibb County 1007 22915 20826 6.0 22.7
## 5 Alabama Blount County 1009 57322 51024 6.3 24.6
## 6 Alabama Bullock County 1011 10914 11714 6.8 22.3
## age_over_65 female white black native asian pac_isl two_plus_races
## 1 12.0 51.3 78.5 17.7 0.4 0.9 NA 1.6
## 2 16.8 51.1 85.7 9.4 0.7 0.7 NA 1.5
## 3 14.2 46.9 48.0 46.9 0.4 0.4 NA 0.9
## 4 12.7 46.3 75.8 22.0 0.3 0.1 NA 0.9
## 5 14.7 50.5 92.6 1.3 0.5 0.2 NA 1.2
## 6 13.5 45.8 23.0 70.2 0.2 0.2 NA 0.8
## hispanic white_not_hispanic no_move_in_one_plus_year foreign_born
## 1 2.4 77.2 86.3 2.0
## 2 4.4 83.5 83.0 3.6
## 3 5.1 46.8 83.0 2.8
## 4 1.8 75.0 90.5 0.7
## 5 8.1 88.9 87.2 4.7
## 6 7.1 21.9 88.5 1.1
## foreign_spoken_at_home hs_grad bachelors veterans mean_work_travel
## 1 3.7 85.3 21.7 5817 25.1
## 2 5.5 87.6 26.8 20396 25.8
## 3 4.7 71.9 13.5 2327 23.8
## 4 1.5 74.5 10.0 1883 28.3
## 5 7.2 74.7 12.5 4072 33.2
## 6 3.8 74.7 12.0 943 28.1
## housing_units home_ownership housing_multi_unit
## 1 22135 77.5 7.2
## 2 104061 76.7 22.6
## 3 11829 68.0 11.1
## 4 8981 82.9 6.6
## 5 23887 82.0 3.7
## 6 4493 76.9 9.9
## median_val_owner_occupied households persons_per_household
## 1 133900 19718 2.70
## 2 177200 69476 2.50
## 3 88200 9795 2.52
## 4 81200 7441 3.02
## 5 113700 20605 2.73
## 6 66300 3732 2.85
## per_capita_income median_household_income poverty
## 1 24568 53255 10.6
## 2 26469 50147 12.2
## 3 15875 33219 25.0
## 4 19918 41770 12.6
## 5 21070 45549 13.4
## 6 20289 31602 25.3
## private_nonfarm_establishments private_nonfarm_employment
## 1 877 10628
## 2 4812 52233
## 3 522 7990
## 4 318 2927
## 5 749 6968
## 6 120 1919
## percent_change_private_nonfarm_employment nonemployment_establishments
## 1 16.6 2971
## 2 17.4 14175
## 3 -27.0 1527
## 4 -14.0 1192
## 5 -11.4 3501
## 6 -18.5 390
## firms black_owned_firms native_owned_firms asian_owned_firms
## 1 4067 15.2 NA 1.3
## 2 19035 2.7 0.4 1.0
## 3 1667 NA NA NA
## 4 1385 14.9 NA NA
## 5 4458 NA NA NA
## 6 417 NA NA NA
## pac_isl_owned_firms hispanic_owned_firms women_owned_firms
## 1 NA 0.7 31.7
## 2 NA 1.3 27.3
## 3 NA NA 27.0
## 4 NA NA NA
## 5 NA NA 23.2
## 6 NA NA 38.8
## manufacturer_shipments_2007 mercent_whole_sales_2007 sales
## 1 NA NA 598175
## 2 1410273 NA 2966489
## 3 NA NA 188337
## 4 0 NA 124707
## 5 341544 NA 319700
## 6 NA NA 43810
## sales_per_capita accommodation_food_service building_permits
## 1 12003 88157 191
## 2 17166 436955 696
## 3 6334 NA 10
## 4 5804 10757 8
## 5 5622 20941 18
## 6 3995 3670 1
## fed_spending area density
## 1 331142 594 91.8
## 2 1119082 1590 114.6
## 3 240308 885 31.0
## 4 163201 623 36.8
## 5 294114 645 88.9
## 6 108846 623 17.5
# Create a new variable, rural
countyComplete$rural <- ifelse(countyComplete$density < 1000, "rural", "urban")
countyComplete$rural <- factor(countyComplete$rural)2. Examine the living standard of the US counties, using per_capita_income as a measure, and how it differs by whether the county is rural or urban. To that end, do the following and interpret the results:
Compute groupwise mean and median per_capita_income by rural
countyComplete %>%
group_by(rural) %>%
summarize(mean(per_capita_income),
median(per_capita_income))
## # A tibble: 2 x 3
## rural `mean(per_capita_income)` `median(per_capita_income)`
## <fctr> <dbl> <dbl>
## 1 rural 22117 21598
## 2 urban 30576 28522Compute groupwise measures of spread for per_capita_income by rural
countyComplete %>%
group_by(rural) %>%
summarize(sd(per_capita_income),
IQR(per_capita_income))
## # A tibble: 2 x 3
## rural `sd(per_capita_income)` `IQR(per_capita_income)`
## <fctr> <dbl> <dbl>
## 1 rural 4884 5498
## 2 urban 8598 9594Create faceted histogram for per_capita_income by rural
countyComplete %>%
ggplot(aes(x = per_capita_income)) +
geom_histogram() +
facet_wrap(~rural)
Create overlaid density plots for per_capita_income by rural
countyComplete %>%
ggplot(aes(x = per_capita_income, fill = rural)) +
geom_density(alpha = 0.3)
Create box plots of per_capita_income by rural
countyComplete %>%
ggplot(aes(x = 1, y = per_capita_income)) +
geom_boxplot()+ facet_wrap(~rural)
3. Use the box plot you created above and identify an outlier, a rural county that has a per_capita_income higher than $60,000 a year when a typical rural county’s per capita income is less than $23,000 a year.
countyComplete %>%
filter(per_capita_income > 60000) %>%
group_by(rural) %>%
summarize(mean(white), mean(black), mean(hs_grad), mean(bachelors))
## # A tibble: 1 x 5
## rural `mean(white)` `mean(black)` `mean(hs_grad)` `mean(bachelors)`
## <fctr> <dbl> <dbl> <dbl> <dbl>
## 1 rural 93.5 0.5 96.1 59.7
countyComplete %>%
filter(per_capita_income < 23000) %>%
group_by(rural) %>%
summarize(mean(white), mean(black), mean(hs_grad), mean(bachelors))
## # A tibble: 2 x 5
## rural `mean(white)` `mean(black)` `mean(hs_grad)` `mean(bachelors)`
## <fctr> <dbl> <dbl> <dbl> <dbl>
## 1 rural 81.5 NA 80.0 14.8
## 2 urban 56.7 34 79.8 23.0What makes this rural county successful? Compare it with a typical rural county in the country (compare the county’s data with means of that of the rest of the rural counties)
To see what may be responsible for the higher income rate in the outlier county I looked at four factors: percentage of white residents, percentage of black residents, high school graduation rates and college graduation rates. There was a significant difference in college graduation rates. 59.7% of residents in the high income county had bachelor’s degrees while only 14.8% of residents in the typical rural county had bachelors degrees. It is likely that education level has an effect on income levels.