1 Instructions

  • This is an individual assignment. Submit your .Rmd and “knitted”.html files through Collab.

  • Upload your html file on RPubs and include the link when you submit your submission files on Collab.

  • Please don’t use ggplot2 for this assignment. We’ll use ggplot2 almost all the times after this assignment.

2 Part 1

  • Use the occupational experience variable (“oexp”) of the income_example dataset and plot

    • a histogram,
    • a kernel density estimate,
    • a boxplot of “oexp”,
    • a set of boxplots showing the distribution of “oexp” by sex crossed with occupational status (“occ”).

  • You can either produce four separate but small plots, or you can use par(mfrow = c(2, 2)) to create a plotting region consisting of four subplots.

  • Briefly describe the distributions of occupational experience in words (also include your plots and the R syntax).

[“Play” with the hist() and density() functions; for instance, by choosing a different number of bins or different break points for the hist() function, or different bandwidths using the adjust argument in density(). See also the corresponding help files and the examples given there. Only include the histogram and density estimate you find most informative. Also, add useful axis-labels and a title using the following arguments inside the plotting functions: xlab, ylab, main. Use the help ?par() for the description of many more plotting parameter.]

[That’s how the plots could look like – but you have to do it with your group;-)]

library(foreign)
incex <- read.table("income_exmpl.dat", header = T, sep = "\t")
incex$occ <- factor(incex$occ, levels = c('low', 'med.', 'high'))
incex$edu <- factor(incex$edu, levels = c('low', 'med.', 'high'))
incex$sex <- factor(incex$sex, levels = c('m', 'f'), labels = c('male', 'female'))
attach(incex)
mfrow = c(2,2)
hist(oexp, seq(0, 48, 2), xlab = "Occ. Experience (in years)", main = "Histogram of Occ. Experience")

kden <- function(x, h, x.val = seq(min(x)-2*h, max(x)+2*h, length = 200)) {
  x.val <- sort(unique(x.val))
  n <- length(x)  
  dens.f <- function(x.v) {
    z <- (x.v - x) / h
    d <- ifelse(z > -1 & z < 1, .5, 0)
    sum(d) / n / h
  }
  dens <- sapply(x.val, dens.f)
  data.frame(x = x.val, y = dens)
}
den <- kden(incex$oexp, h = 1)
den$x <- den$x - 100
plot(den, type = "s", lwd = 3, xlab = "Occ. Experience (in years)", ylab = "Density", main = "Density Estimate of Occ. Experience")

boxplot(oexp, horizontal = T, xlab = "Occ. Experience (in years)", main = "Boxplot of Occ. Experience")

boxplot(oexp ~ sex + occ, col = rep(c("blue", "red"), each = 3), ylab = "Occ. Experience (in years)", names = c("male\nlow", "female\nlow", "male\nmed.", "female\nmed.", "male\nhigh", "female\nhigh"), main = "Occ. Experience by Sex and Occ. Status") 

levels(sex)
## [1] "male"   "female"

From the histogram and density estimates, it is evident through the plots’ even distribution that a uniform distribution is present for the variable Occupational Experience (oexp).

As already discussed, the histogram and kernel density plots show the frequency and density of the variable oexp, respectively. The boxplot reveals the spread of the variable and the plot with multiple boxplots show the spread of the variable subsetted by sex and occupational status.

3 Part 2

  • Download the SCS Data set from Collab (there you also find a separate file containing a brief description of variables). Then investigate the relationship between the mathematics achievement score (“mathpre”) and the math anxiety score (“mars”) by plotting the data and the path of means.
  1. Produce a scatterplot between “mathpre” and “mars”. You might consider using jitter() or alpha() for avoiding overlying points.
scs <- read.spss("SCS_QE.sav", to.data.frame = TRUE)
## re-encoding from CP1252
## Warning in read.spss("SCS_QE.sav", to.data.frame = TRUE): Undeclared level(s) 0
## added in variable: married
plot(jitter(scs$mathpre, factor = 3), jitter(scs$mars, factor = 3), xlab = "Mathematics Achievement Score", ylab = "Math Anxiety Score")

  1. Draw a conditioning plot for female and male students (variable “male”). Include “| male” in your first argument to create a conditioning plot.
coplot(mars ~ mathpre | male, data = scs)

scs2 <- scs[which(scs$male == "female"),]
scs3 <- scs[which(scs$male == "male"),]
mean(scs$mars)
## [1] 58.02679
mean(scs2$mars)
## [1] 61.55215
mean(scs3$mars)
## [1] 47.03595
  1. Describe in words the relation between math scores and math anxiety. Do you find evidence of Simpson’s Paradox?

There is a noticeable negative correlation between math scores and math anxiety. When subset by sex, both plots still demonstrate a negative correlation, meaning that the relationship between math scores and math anxiety is consistent and thus no evidence of Simpson’s Paradox is found.

describe your plots. As noted, above is a scatterplot showing the relationship between math scores and math anxiety as well as a conditioning plot demonstrating this relationship for male and female students.

4 Part 3

  • Use a dataset that is available in data repositories (e.g., kaggle)

  • Briefly describe the dataset you’re using (e.g., means to access data, context, sample, variables, etc…)

    • This data contains over 65,000 incidences of traffic-related violations and is categorized by time and date of violation, demographic information about the violator (age, race, gender, etc.), and details of the incident (whether the person was arrested, result of violation).

  • Re-do Part 2, i.e.,

    • produce a scatterplot between “A” and “B”. You might consider using jitter() or alpha() for avoiding overlying points.
    • draw a scatterplot plot conditioning on variable “C”. Include “| C” in your first argument to create a conditioning plot.
    • describe in words the relation between “A” and “B.” Do you find evidence of Simpson’s Paradox?
trafficViolations <- read.csv(file = "traffic_violaions.csv")
trafficViolations$stop_time <- as.integer(gsub(":", "", trafficViolations$stop_time))
plot(jitter(trafficViolations$driver_age, factor = 9), jitter(trafficViolations$stop_time, factor = 9), xlab = "Age of Driver", ylab = "Time of Stop")

coplot(stop_time ~ driver_age | driver_gender, data = trafficViolations)

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37294, 37295, 37321, 37349, 37355, 37361, 37383, 37408, 37446, 37448, 37456, 37460, 37480, 37482, 37492, 37502, 37509, 37515, 37517, 37525, 37526, 37539, 37552, 37559, 37567, 37586, 37593, 37628, 37630, 37637, 37646, 37655, 37660, 37662, 37667, 37668, 37673, 37674, 37677, 37679, 37682, 37683, 37713, 37718, 37726, 37739, 37740, 37757, 37768, 37771, 37780, 37792, 37797, 37799, 37801, 37803, 37819, 37829, 37831, 37837, 37889, 37897, 37899, 37900, 37902, 37915, 37918, 37926, 37927, 37935, 37936, 37943, 37960, 37973, 37977, 38003, 38052, 38063, 38066, 38069, 38073, 38074, 38081, 38082, 38088, 38090, 38092, 38094, 38098, 38140, 38153, 38168, 38170, 38179, 38180, 38182, 38185, 38195, 38203, 38204, 38207, 38216, 38220, 38225, 38226, 38232, 38233, 38237, 38238, 38262, 38285, 38291, 38305, 38307, 38322, 38325, 38343, 38348, 38350, 38376, 38386, 38387, 38392, 38395, 38407, 38415, 38429, 38448, 38453, 38458, 38465, 38472, 38475, 38477, 38490, 38495, 38499, 38507, 38508, 38509, 38515, 38519, 38526, 38527, 38547, 38553, 38556, 38570, 38574, 38578, 38580, 38581, 38615, 38629, 38631, 38637, 38643, 38664, 38674, 38689, 38706, 38707, 38720, 38724, 38727, 38734, 38739, 38753, 38759, 38760, 38769, 38776, 38779, 38786, 38806, 38814, 38824, 38827, 38845, 38850, 38855, 38862, 38886, 38905, 38909, 38925, 38935, 38948, 38995, 38999, 39028, 39048, 39052, 39056, 39078, 39079, 39097, 39105, 39108, 39114, 39115, 39116, 39121, 39123, 39126, 39127, 39133, 39135, 39136, 39141, 39144, 39149, 39157, 39159, 39166, 39167, 39178, 39183, 39205, 39206, 39208, 39219, 39255, 39293, 39296, 39301, 39326, 39346, 39350, 39385, 39390, 39402, 39432, 39438, 39444, 39459, 39464, 39511, 39539, 39553, 39575, 39587, 39588, 39600, 39609, 39624, 39653, 39668, 39677, 39690, 39702, 39709, 39716, 39724, 39732, 39734, 39745, 39750, 39751, 39754, 39759, 39764, 39777, 39787, 39807, 39819, 39820, 39835, 39847, 39881, 39884, 39885, 39894, 39902, 39917, 39918, 39934, 39936, 39959, 39961, 39964, 39994, 40035, 40038, 40039, 40048, 40049, 40050, 40060, 40078, 40091, 40109, 40122, 40151, 40158, 40167, 40175, 40177, 40181, 40200, 40203, 40228, 40240, 40251, 40252, 40261, 40268, 40273, 40281, 40282, 40293, 40295, 40313, 40324, 40326, 40327, 40342, 40343, 40349, 40356, 40384, 40385, 40456, 40458, 40462, 40468, 40475, 40493, 40507, 40514, 40568, 40594, 40606, 40625, 40629, 40633, 40644, 40647, 40652, 40670, 40671, 40688, 40701, 40719, 40736, 40744, 40748, 40751, 40801, 40806, 40807, 40816, 40820, 40821, 40828, 40852, 40892, 40916, 40917, 40918, 40925, 40959, 40968, 40972, 40977, 40991, 41041, 41053, 41054, 41061, 41081, 41094, 41127, 41131, 41133, 41135, 41146, 41166, 41182, 41194, 41195, 41213, 41217, 41222, 41223, 41235, 41254, 41259, 41315, 41322, 41330, 41342, 41348, 41353, 41357, 41376, 41381, 41382, 41397, 41401, 41404, 41413, 41416, 41440, 41451, 41457, 41464, 41482, 41483, 41484, 41492, 41493, 41497, 41506, 41515, 41546, 41550, 41552, 41572, 41574, 41598, 41602, 41629, 41639, 41652, 41654, 41657, 41666, 41668, 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43323, 43349, 43351, 43363, 43366, 43371, 43383, 43403, 43410, 43446, 43455, 43475, 43479, 43488, 43497, 43527, 43531, 43554, 43574, 43602, 43605, 43609, 43612, 43626, 43648, 43650, 43680, 43693, 43698, 43700, 43702, 43707, 43713, 43720, 43725, 43731, 43735, 43743, 43749, 43764, 43766, 43781, 43788, 43793, 43808, 43809, 43810, 43843, 43853, 43854, 43865, 43903, 43915, 43917, 43918, 43937, 43939, 43971, 43988, 44014, 44029, 44049, 44058, 44071, 44125, 44134, 44162, 44217, 44219, 44230, 44237, 44239, 44242, 44251, 44267, 44288, 44297, 44308, 44309, 44315, 44329, 44352, 44374, 44409, 44467, 44478, 44502, 44506, 44508, 44510, 44511, 44512, 44538, 44547, 44562, 44564, 44578, 44581, 44595, 44605, 44606, 44617, 44642, 44644, 44649, 44660, 44681, 44751, 44778, 44792, 44794, 44817, 44819, 44849, 44918, 44941, 44943, 44951, 44959, 44963, 45025, 45039, 45043, 45057, 45062, 45076, 45090, 45097, 45098, 45114, 45116, 45131, 45144, 45148, 45155, 45176, 45181, 45185, 45199, 45203, 45213, 45216, 45239, 45241, 45265, 45326, 45331, 45338, 45339, 45371, 45376, 45401, 45402, 45416, 45425, 45427, 45449, 45452, 45458, 45474, 45479, 45481, 45508, 45526, 45527, 45528, 45530, 45538, 45561, 45569, 45581, 45605, 45610, 45629, 45648, 45690, 45696, 45699, 45719, 45724, 45732, 45744, 45749, 45759, 45770, 45773, 45782, 45798, 45803, 45819, 45848, 45849, 45859, 45873, 45874, 45914, 45988, 46003, 46021, 46032, 46038, 46049, 46082, 46119, 46138, 46140, 46152, 46154, 46190, 46213, 46261, 46263, 46268, 46289, 46291, 46302, 46331, 46335, 46400, 46401, 46424, 46450, 46454, 46457, 46476, 46484, 46488, 46501, 46512, 46520, 46533, 46553, 46570, 46576, 46584, 46611, 46625, 46629, 46643, 46644, 46658, 46659, 46681, 46684, 46693, 46694, 46695, 46699, 46736, 46740, 46749, 46760, 46761, 46779, 46780, 46799, 46807, 46814, 46816, 46823, 46856, 46862, 46869, 46871, 46896, 46905, 46937, 46967, 46968, 46993, 47015, 47052, 47072, 47095, 47118, 47134, 47135, 47156, 47169, 47180, 47192, 47214, 47217, 47218, 47223, 47244, 47251, 47257, 47302, 47304, 47307, 47314, 47315, 47361, 47373, 47384, 47393, 47394, 47406, 47416, 47460, 47471, 47473, 47478, 47481, 47484, 47495, 47499, 47508, 47510, 47524, 47562, 47575, 47577, 47579, 47588, 47643, 47673, 47680, 47681, 47684, 47686, 47693, 47695, 47696, 47802, 47806, 47816, 47857, 47858, 47874, 47878, 47883, 47892, 47904, 47919, 47927, 47929, 47945, 47951, 48002, 48009, 48034, 48035, 48049, 48057, 48078, 48085, 48087, 48128, 48130, 48148, 48159, 48171, 48172, 48174, 48191, 48192, 48226, 48235, 48238, 48246, 48251, 48252, 48266, 48275, 48303, 48310, 48350, 48358, 48365, 48399, 48402, 48404, 48410, 48416, 48430, 48451, 48460, 48508, 48509, 48545, 48588, 48611, 48613, 48619, 48628, 48636, 48675, 48678, 48690, 48692, 48694, 48730, 48771, 48776, 48811, 48812, 48814, 48815, 48842, 48864, 48879, 48885, 48896, 48907, 48926, 48927, 48950, 48962, 48990, 49020, 49036, 49060, 49064, 49070, 49084, 49087, 49097, 49144, 49193, 49243, 49257, 49263, 49269, 49285, 49289, 49293, 49348, 49349, 49352, 49360, 49375, 49383, 49413, 49442, 49444, 49447, 49458, 49459, 49462, 49468, 49481, 49499, 49514, 49535, 49553, 49561, 49595, 49631, 49643, 49670, 49691, 49706, 49726, 49737, 49761, 49791, 49793, 49802, 49823, 49824, 49843, 49854, 49856, 49874, 49913, 49914, 49923, 49945, 49960, 49995, 49999, 50003, 50010, 50016, 50040, 50056, 50062, 50064, 50075, 50077, 50078, 50101, 50123, 50129, 50133, 50135, 50141, 50148, 50152, 50156, 50157, 50164, 50214, 50228, 50238, 50266, 50284, 50286, 50288, 50292, 50319, 50338, 50344, 50361, 50367, 50383, 50384, 50386, 50392, 50401, 50404, 50407, 50424, 50428, 50432, 50433, 50442, 50462, 50504, 50508, 50524, 50539, 50547, 50571, 50573, 50574, 50579, 50594, 50626, 50635, 50677, 50686, 50706, 50715, 50733, 50747, 50748, 50759, 50761, 50762, 50766, 50798, 50837, 50843, 50859, 50866, 50884, 50885, 50898, 50910, 50917, 50922, 50935, 50938, 50941, 50944, 50951, 50963, 50986, 50989, 50999, 51000, 51004, 51012, 51021, 51044, 51057, 51067, 51068, 51091, 51175, 51178, 51205, 51262, 51267, 51295, 51299, 51300, 51330, 51354, 51364, 51372, 51376, 51384, 51398, 51409, 51422, 51440, 51448, 51451, 51461, 51469, 51472, 51474, 51524, 51527, 51535, 51539, 51550, 51552, 51558, 51567, 51568, 51576, 51590, 51595, 51654, 51667, 51669, 51674, 51686, 51716, 51725, 51756, 51762, 51773, 51775, 51811, 51838, 51840, 51883, 51890, 51911, 51916, 51968, 51972, 51993, 52014, 52043, 52045, 52065, 52076, 52102, 52106, 52133, 52143, 52155, 52176, 52199, 52202, 52203, 52231, 52240, 52243, 52260, 52270, 52314, 52341, 52362, 52367, 52377, 52423, 52432, 52445, 52448, 52453, 52463, 52471, 52472, 52480, 52481, 52482, 52495, 52550, 52584, 52585, 52629, 52672, 52674, 52682, 52690, 52696, 52697, 52700, 52726, 52733, 52752, 52755, 52769, 52772, 52773, 52810, 52814, 52824, 52832, 52864, 52872, 52885, 52940, 52958, 52961, 52962, 52964, 52966

There is no clear relationship between the age of the driver and the time of stop. Therefore, no evidence of Simpson’s Paradox was found.

  • You will present results of Part 3 to your neighbor(s) in class of Jan. 7 (Mon).