(Solution Manual) Modern Data Science with R

Baumer,Kaplan,Horton, 2

Math & Statistics

Solution Manual

2nd Edition

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Solution Manual for Modern Data Science with R, The downloadable file consists of 300 pages, and the total size of the file is 9.11 MB. Purchase now only for highly discounted price.

Author(s): Baumer, Kaplan, Horton

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Solutions Manual for Modern Data Science with R, 2e by Benjamin Baumer, Daniel Kaplan, Nicholas Horton (All Chapters) Chapter 1 Preface This document includes sample solutions for exercises in the second edition of Modern Data Science with R. Please do not share these solutions online. Note that the R environment is changing quickly and packages are frequently updated. Instructors should verify that their code works with their setup. We have marked the exercises as Easy, Medium, or Hard to help distinguish the degree of difficulty. The exercises have been ordered by difficulty level. These are quite arbitrary designations that may be appropriate or not depending on audience. Additional instructor materials (including freely downloadable sample chapters and related resources) can be found at http://mdsr-book.github.io. We welcome suggestions and improvements in these solutions. To be informed about updates please reach out to Nicholas Horton (nicholasjhor ton@gmail.com). 78 CHAPTER 1. PREFACE chapter EasyHardMedium N data-I 61 815 appR 11NA 213 reproducible 10NA 212 text 61 512 data-II 3NA 811 sqlI 41 611 dataviz-II 21 710 dataviz-III 12 710 ethics 11 810 simulation NANA 99 algorithmic 11 68 sqlII 15 28 foundations 2NA 57 learning-II NA 3 47 dataviz-I 1NA 56 iteration 21 36 join 11 46 learning-I 11 46 modeling 21 36 regression 1NA 45 spatial-I 13 15 spatial-II NA 2 24 netsci NA 2 13 not working NANA 11 Here is the summary of the online only exercises:9 chapter EasyMedium HardN data-I 6 NANA6 dataviz-I 3 2NA5 dataviz-II 4 NA 15 join 3 NA 14 algorithmic 2 1NA3 data-II 3 NANA3 text NA 213 dataI 1 NA 12 foundations NA 2NA2 simulation NA 112 sqlII 1 NA 12 dataviz-III NA 1NA1 ethics NA 1NA1 not-working NA NA 11 regression NA 1NA1 spatial NA NA 11 sqlI 1 NANA110 CHAPTER 1. PREFACEChapter 2 Data visualization 2.1 Exercises Problem 1 (Easy) : Consider the following data graphic. ggplot(mtcars, aes(x = disp, y = mpg)) + geom_point() 101520253035 100 200 300 400 disp Theamvariable takes the value 0if the car has automatic transmission and 1if the car has manual transmission. How could you differentiate the cars in the graphic based on their transmission type? SOLUTION: Map the coloraesthetic to the amvariable. Problem 2 (Medium) : Pick one of the Science Notebook entries at https: //www.edwardtufte.com/tufte (e.g., “Making better inferences from statistical graphics”). Write a brief reflection on the graphical principles that are illustrated by this entry. 1112 CHAPTER 2. DATA VISUALIZATION SOLUTION: Answers will vary. Problem 3 (Medium) : Find two graphs published in a newspaper or on the internet in the last two years. a.Identify a graphical display that you find compelling. What aspects of the display work well, and how do these relate to the principles established in this chapter? Include a screen shot of the display along with your solution. b.Identify a graphical display that you find less than compelling. What aspects of the display don’t work well? Are there ways that the display might be improved? Include a screen shot of the display along with your solution. SOLUTION: Answers will vary. Problem 4 (Medium) : Find two scientific papers from the last two years in a peer-reviewed journal ( NatureandScienceare good choices). a.Identify a graphical display that you find compelling. What aspects of the display work well, and how do these relate to the principles established in this chapter? Include a screen shot of the display along with your solution. b.Identify a graphical display that you find less than compelling. What aspects of the display don’t work well? Are there ways that the display might be improved? Include a screen shot of the display along with your solution. SOLUTION: Answers will vary. Problem 5 (Medium) : Consider the two graphics related to The New York Times“Taxmageddon” article at http://www.nytimes.com/2012/04/15/sunday- review/coming-soon-taxmageddon.html. The first is “Whose Tax Rates Rose or Fell” and the second is “Who Gains Most From Tax Breaks.” a.Examine the two graphics carefully. Discuss what you think they convey. What story do the graphics tell? b.Evaluate both graphics in terms of the taxonomy described in this chapter. Are the scales appropriate? Consistent? Clearly labeled? Do variable dimensions exceed data dimensions? c. What, if anything, is misleading about these graphics?2.1. EXERCISES 13 SOLUTION: a.Answers will vary. The main take-aways are that tax rates on the rich have fallen, while tax rates on the poor have not. Moreover, in terms of the “cost" to the US Treasury, most tax breaks go to those in the top 20% in income. b.Answers will vary. In the first graphic, the y-scale is the tax rate, but there is no axis. The labels about the segment of the income distribution are not reflected in any quantity. The color scheme is not immediately helpful. The change in real pre-tax income figures to not have a corresponding quantitative representation. In the second graphic, the y-scale is very confusing, and possibly misleading. The scale is a percentage, and yet the income amounts on the left are noton a linear scale. c. Answers will vary. Most obviously, the y-scales in either data graphic. Problem 6 (Medium) : Consider the data graphic http://tinyurl.com/nytimes- unplanned about birth control methods. a. What quantity is being shown on the y-axis of each plot? b.List the variables displayed in the data graphic, along with the units and a few typical values for each. c.List the visual cues used in the data graphic and explain how each visual cue is linked to each variable. d.Examine the graphic carefully. Describe, in words, what information you think the data graphic conveys. Do not just summarize the data—interpret the data in the context of the problem and tell us what it means. (Note: information is meaningful to human beings—it is not the same thing as data.) SOLUTION: •The number of women out of 100 who will have an unplanned preganancy. •Variables: –years: units of years: 1, 2, 3, ... –number_of_women : units of people: 1, 2, 3, ... –method: categorical: spermicides, etc. –use_type : categorical: typical, perfect •Mappings: –horizontal position is mapped to year –vertical position is mapped to number_of_women –facets are mapped to method –lines/shapes are mapped to use_type –color/shade is mapped to number_of_women •Most any birth control methods will likely fail at least once with typical use over a 10 year period. However, Depo-Provera and the pill are the most effective, especially with perfect use.14 CHAPTER 2. DATA VISUALIZATION 2.2 Supplementary Exercises Problem 1 (Easy) : Consider the following data-driven image, available for purchase at NBA Playoff Rings: https://cdn.shopify.com/s/files/1/0144/6552/p roducts/NBA-Basketball-2013-_6_1024x1024.jpg a. Identify the visual cues, coordinate system, and scale(s). b.How many variables are depicted in the graphic? Explicitly link each variable to a visual cue that you listed above. c. Critique this data graphic using the taxonomy described in this chapter. SOLUTION: a. Visual cues: Color, angle. Coordinate system: radial. Scale: categorical b.There are (at least) three variables: team, playoff round, and number of games won. c.Color evokes the team, as each team’s uniform colors are used to distinguish one team from another. Normally, tournaments such this are depicted as binary trees, in which each playoff round would be on its own level. Here, the author has chosen to wrap the tree structure into a circle. I don’t see any reason to think that this aids in our understanding. If anything, it probably confuses most readers. Another possible choice would be to decrease the saturation of teams that only won a few games. Note that each team that won a series, by necessity, won 4 games. But some of the losing teams won 3 games, while others won 0. One could argue that fading out the losing teams that won fewer games would help show a more accurate picture. Problem 2 (Easy) : 2016 ELECTION: Consider the following data graphic about results from the 2016 presidential election in Massachusetts. What type of color palette is used in this graphic? SOLUTION: Diverging2.2. SUPPLEMENTARY EXERCISES 15 Problem 3 (Easy) : Choose oneof the data graphics listed at http://mdsr- book.github.io/exercises.html#exercise_23 and answer the following questions. Be sure to indicate which graphical display you picked. 2. World’s Top 10 Best Selling Cigarette Brands, 2004-2007 3.GNPD Usage by Food Categories 4. UK University Rankings 5. Childhood Obesity in the US 6. Relationship between ages and psychosocial maturity a. Identify the visual cues, coordinate system, and scale(s). b.How many variables are depicted in the graphic? Explicitly link each variable to a visual cue that you listed above. c. Critique this data graphic using the taxonomy described in this chapter. SOLUTION: We critique this graphic from the Tax Policy Center. •Color is a visual cue that is mapped to the categorical variable of taxpayer status. Angle is the visual cue that is mapped to the numeric variable of the percentage of people. This exploding pie chart uses a radial coordinate system, and the scale is percentage. •There are two variables: percentage of taxpayers, and reason taxpayer status. •Aside from the common criticisms of pie charts in general, this pie chart makes two strange choices. First, the exploding nature of the pie chart (having pieces of the pie fall out of it) is pointless and distracting. Second, the use of color is odd. By using multiple shades of red, it implies an ordinal scale to the categorical variable of taxpayer status. But there is no logical ordering of this variable. Thus, a qualitative color scale would have been more appropriate. Problem 4 (Medium) : Answer the following questions for each of the following collections of data graphics listed at (http://mdsr-book.github.io/exercises.htm l#exercise_24). 1. What is a Data Scientist? 2. Charts that explain food in America Briefly (one paragraph) critique the designer’s choices. Would you have made different choices? Why or why not? Note: Each link contains a collection of many data graphics, and we don’t expect (or want) you to write a full report on each individual graphic. But each collection shares some common stylistic elements.16 CHAPTER 2. DATA VISUALIZATION You should comment on a few things that you notice about the design of the collection. SOLUTION: In theWhat is a data scientist? infographic, the designers make many illogical choices. For example, in several places they use angle instead of length to show differentiate between several quantities. They also use area in two places (squares and circles) to illustrate a single numeric variable. But we know that human beings are better at perceiving differences in length than they are either angle or area, so neither choice is a good one. The last data graphic is perhaps the worst. Although the labels show a single numeric variable (percentages), the square tiles are equally sized. Moreover, they are colored in seemingly random shades of blue and gray. The tiles do not appear to be in any kind of order (e.g., alphabetical, descending, etc.). It is not at all clear what the designed was trying to convey. Problem 5 (Medium) : Consider one of the more complicated data graphics listed at (http://mdsr-book.github.io/exercises.html#exercise_25): a.What story does the data graphic tell? What is the main message that you take away from it? b.Can the data graphic be described in terms of the taxonomy presented in this chapter? If so, list the visual cues, coordinate system, and scales(s) as you did in Problem 2(a). If not, describe the feature of this data graphic that lies outside of that taxonomy. c.Critique and/or praise the visualization choices made by the designer. Do they work? Are they misleading? Thought-provoking? Brilliant? Are there things that you would have done differently? Justify your response. SOLUTION: We discuss the New York Times graphic on Obama’s budget(link). •It seems clear that a large percentage of the federal budget is due to mandatoryentitlementprogramslikeMedicare, SocialSecurity, andinterest on the national debt. Military spending is by far the largest discretionary area •This is an interactive graphic comprised of four individual graphics. Each of those can be described in this taxonomy, but the interactive elements of switching between them and mousing-over to see contextual information is outside of the taxonomy. •This is a nice data graphic. One could question the mapping of area to a one-dimensional quantity, but in this case it motivates the interactive elements.Chapter 3 A grammar for graphics 3.1 Exercises Problem 1 (Easy) : Angelica Schuyler Church (1756–1814) was the daughter of New York Governer Philip Schuyler and sister of Elizabeth Schuyler Hamilton. Angelica, New York was named after her. Using the babynames package generate a plot of the reported proportion of babies born with the name Angelica over time and interpret the figure. SOLUTION: library(babynames) angelica <- filter(babynames, name == "Angelica") ggplot(data = angelica, aes(x = year, y = prop, color = sex)) + geom_line() 1718 CHAPTER 3. A GRAMMAR FOR GRAPHICS 0.00000.00050.00100.0015 1920 1960 2000 yearsex F M We see that there is a big jump in the number of babies named Angelica starting in the mid 1970’s. Problem 2 (Easy) : Using data from the nasaweather package, create a scatterplot between windandpressure , with color being used to distinguish thetypeof storm. SOLUTION: library(nasaweather) ggplot(data = storms, aes(x = pressure, y = wind, color = type)) + geom_point(alpha = 0.5)3.1. EXERCISES 19 4080120160 900 925 950 975 1000 pressuretype Extratropical Hurricane Tropical Depression Tropical Storm Problem 3 (Medium) : The following questions use the Marriage data set from the mosaicData package. library(mosaicData) a. Create an informative and meaningful data graphic. b.Identify each of the visual cues that you are using, and describe how they are related to each variable. c.Create a data graphic with at least fivevariables (either quantitative or categorical). For the purposes of this exercise, do not worry about making your visualization meaningful—just try to encode five variables into one plot. SOLUTION: Answers will vary. We will illustrate one potential solution. ggplot(data = Marriage, aes(x = age, y = prevcount, color = person)) + labs(y = "Previous marriages") + geom_point(alpha = 0.5) + geom_smooth()20 CHAPTER 3. A GRAMMAR FOR GRAPHICS 012345 20 40 60 ageperson Bride Groom Position in the x-direction is mapped to age, position in the y-direction is mapped to the number of previous marriages, color is mapped to the status as bride or groom. Each point represents one person. The smoother line indicates a positive trend between age and number of previous marriages, up to about age 45. That is, not surprisingly, people who marry later in life tend to have had more previous marriages. Marriage <- Marriage %>% mutate( /grave.ts1Grades completed /grave.ts1= factor(hs)) ggplot(data = Marriage, aes( x = age, y = prevcount, color = /grave.ts1Grades completed /grave.ts1, size = dayOfBirth )) + labs(y = "Previous marriages") + geom_point(alpha = 0.5) + facet_wrap(~person)3.1. EXERCISES 21 Bride Groom 20 40 60 20 40 60012345 ageGrades completed 8 9 10 11 12 dayOfBirth 100 200 300 Problem 4 (Medium) : Themacleish package contains weather data collected every 10 minutes in 2015 from two weather stations in Whately, MA. library(tidyverse) library(macleish) glimpse(whately_2015) ## Rows: 52,560 ## Columns: 8 ## $ when <dttm> 2015-01-01 00:00:00, 2015-01-01 00:10:00, 2015-01-01 ~ ## $ temperature <dbl> -9.32, -9.46, -9.44, -9.30, -9.32, -9.34, -9.30, -9.10~ ## $ wind_speed <dbl> 1.399, 1.506, 1.620, 1.141, 1.223, 1.090, 1.168, 1.307~ ## $ wind_dir <dbl> 225.4, 248.2, 258.3, 243.8, 238.4, 241.7, 242.3, 244.2~ ## $ rel_humidity <dbl> 54.55, 55.38, 56.18, 56.41, 56.87, 57.25, 57.71, 58.16~ ## $ pressure <int> 985, 985, 985, 985, 984, 984, 984, 984, 984, 984, 984,~ ## $ solar_radiation <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ~ ## $ rainfall <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ~ Usingggplot2, create a data graphic that displays the average temperature over each 10-minute interval ( temperature ) as a function of time ( when). SOLUTION: whately_2015 <- whately_2015 %>% mutate(Date = as.Date(when)) ggplot(data = whately_2015, aes(x = Date, y = temperature)) +22 CHAPTER 3. A GRAMMAR FOR GRAPHICS geom_line(size = 0.3, color = "darkgray") + labs( y = "Temperature (degrees C)", title = "Temperature measurements at Macleish Field Station" ) + geom_smooth() + scale_x_date() −20020 Jan 2015 Apr 2015 Jul 2015 Oct 2015 Jan 2016 DateTemperature measurements at Macleish Field Station Problem 5 (Medium) : Use the MLB_teams data in the mdsrpackage to create an informative data graphic that illustrates the relationship between winning percentage and payroll in context. SOLUTION: library(mdsr) ggplot(data = MLB_teams, aes( x = payroll / 1000000, y = WPct, alpha = yearID, color = lgID, size = metroPop )) + geom_point() + geom_smooth() + xlab("Payroll (Millions of USD)") + ylab("Team Winning Percentage")3.1. EXERCISES 23 0.30.40.50.6 50 100 150 200 Payroll (Millions of USD)2008 2009 2010 2011 2012 2013 2014 metroPop 5.0e+06 1.0e+07 1.5e+07 2.0e+07 lgID AL NL Problem 6 (Medium) : TheMLB_teams data set in the mdsrpackage contains information about Major League Baseball teams from 2008–2014. There are several quantitative and a few categorical variables present. See how many variables you can illustrate on a single plot in R. The current record is 7. (Note: This is notgood graphical practice—it is merely an exercise to help you understand how to use visual cues and aesthetics!) SOLUTION: library(mdsr) ggplot(MLB_teams) + geom_point(aes( x = payroll / 1000000, y = WPct, color = teamID, size = metroPop, shape = lgID, alpha = normAttend )) + facet_wrap(~yearID, ncol = 1) + xlab("Payroll (Millions of USD)") + ylab("Team Winning Percentage")24 CHAPTER 3. A GRAMMAR FOR GRAPHICS 2014201320122011201020092008 50 100 150 2000.30.40.50.6 0.30.40.50.6 0.30.40.50.6 0.30.40.50.6 0.30.40.50.6 0.30.40.50.6 0.30.40.50.6 Payroll (Millions of USD)teamID ARI ATL BAL BOS CHA CHN CIN CLE COL DET FLO HOU KCA LAA LAN MIAMIL MIN NYA NYN OAK PHI PIT SDN SEA SFN SLN TBA TEX TOR WAS normAttend 0.4 0.6 0.8 1.0 metroPop 5.0e+06 1.0e+07 1.5e+07 2.0e+07 lgID AL NL3.1. EXERCISES 25 Problem 7 (Medium) : TheRailTrail data set from the mosaicData package describes the usage of a rail trail in Western Massachusetts. Use these data to answer the following questions. a.Create a scatterplot of the number of crossings per day volumeagainst the high temperature that day b.Separate your plot into facets by weekday (an indicator of weekend/holiday vs. weekday) c. Add regression lines to the two facets SOLUTION: library(mosaicData) ggplot(RailTrail, aes(x = hightemp, y = volume)) + geom_point() 200400600 40 60 80 hightemp ggplot(RailTrail, aes(x = hightemp, y = volume)) + geom_point() + facet_wrap(~weekday)26 CHAPTER 3. A GRAMMAR FOR GRAPHICS FALSE TRUE 40 60 80 40 60 80200400600 hightemp ggplot(RailTrail, aes(x = hightemp, y = volume)) + geom_point() + facet_wrap(~weekday) + geom_smooth(method = "lm") FALSE TRUE 40 60 80 40 60 80200400600 hightemp3.1. EXERCISES 27 Problem 8 (Medium) : Using data from the nasaweather package, use the geom_path function to plot the path of each tropical storm in the stormsdata table. Use color to distinguish the storms from one another, and use faceting to plot each yearin its own panel. SOLUTION: library(nasaweather) library(ggplot2) bbox <- storms %>% select(lat, long) %>% map(range) %>% bind_rows() base_map <- ggplot(data = map_data("world"), aes(x = long, y = lat)) + geom_path(aes(group = group), color = "black", size = 0.1) + lims(x = pull(bbox, long), y = pull(bbox, lat)) storms <- storms %>% mutate(the_date = lubridate::ymd(paste(year, month, day))) base_map + geom_path( data = storms, aes(color = name, alpha = 0.1, size = wind), arrow = arrow(length = unit(0.1, "inches")) ) + facet_wrap(~year) + theme(legend.position = "none")28 CHAPTER 3. A GRAMMAR FOR GRAPHICS 1998 1999 20001995 1996 1997 −90 −60 −30 0 −90 −60 −30 0 −90 −60 −30 0204060 204060 long3.1. EXERCISES 29 Problem9(Medium) : Usingthe penguins datasetfromthe palmerpenguins package: a.Create a scatterplot of bill_length_mm againstbill_depth_mm where individual species are colored and a regression line is added to each species. Add regression lines to all of your facets. What do you observe about the association of bill depth and bill length? SOLUTION: library(palmerpenguins) ggplot(data = penguins, aes(x = bill_depth_mm, y = bill_length_mm)) + labs(x = "Bill depth (mm)", y = "Bill length (mm)") + geom_point() + facet_grid(~sex) + geom_smooth(method = "lm") female male NA 15.0 17.5 20.0 15.0 17.5 20.0 15.0 17.5 20.030405060 Bill depth (mm) b.Repeat the same scatterplot but now separate your plot into facets by species. How would you summarize the association between bill depth and bill length. SOLUTION: ggplot( data = penguins, aes(x = bill_depth_mm, y = bill_length_mm, colour = sex)30 CHAPTER 3. A GRAMMAR FOR GRAPHICS ) + labs(x = "Bill depth (mm)", y = "Bill length (mm)") + geom_point() + facet_grid(~species) + geom_smooth(method = "lm") Adelie Chinstrap Gentoo 15.017.520.0 15.017.520.0 15.017.520.030405060 Bill depth (mm)sex female male NA Problem 10 (Hard) : Use the make_babynames_dist() function in the mdsr package to recreate the “Deadest Names” graphic from FiveThirtyEight (https: //fivethirtyeight.com/features/how-to-tell-someones-age-when-all-you-know- is-her-name). library(tidyverse) library(mdsr) babynames_dist <- make_babynames_dist() SOLUTION: babynames_dist %>% filter(year >= 1900) %>% group_by(name, sex) %>% summarize( N = n(), total_est_alive_today = sum(est_alive_today), total = sum(n)3.1. EXERCISES 31 ) %>% mutate(pct_dead = 1 - (total_est_alive_today / total)) %>% filter(total > 50000) %>% arrange(desc(pct_dead)) %>% head(20) %>% ggplot(aes(x = reorder(name, pct_dead), y = pct_dead, fill = sex)) + geom_bar(stat = "identity") + geom_text( aes( y = pct_dead + 0.05, label = paste(round(pct_dead * 100, 1), "%") ) ) + coord_flip() + ggtitle("Deadest Names", subtitle = "Estimated % of Americans with a given name\nborn since 1900 who were dead as of Jan. 1, 2014" ) + scale_x_discrete(NULL) + scale_y_continuous(NULL) + scale_fill_manual(values = c("#f6b900", "#008fd5")) 78.9 % 78.5 % 76.6 % 76.3 % 75.3 % 73.5 % 72.7 % 72.1 % 71.7 % 71.7 % 71.5 % 71.4 % 71.3 % 69.6 % 69.6 % 69.3 % 68.8 % 68.8 % 68.4 % 68.3 % HazelMamieNellieGladysElsieElmerMinnieMildredPearlEthelBessieViolaAgnesFlorenceOpalBeulahBlancheMyrtleGertrudeMabel 0.0 0.2 0.4 0.6 0.8sex F MEstimated % of Americans with a given name born since 1900 who were dead as of Jan. 1, 2014Deadest Names