Introduction to R and RStudio

Recap:

Last week

  • Intro to R/Rstudio: Data types and structures
  • Subsetting structures
  • Choice statements and for-loops
  • Reproducibility (renv)
  • Best practices (e.g., naming conventions)
  • Reading and writing files in several formats

Today

  • Functions
  • Inferential statistics: A 5-min primer of linear regression
  • Principles of tidy data and short comparison of base R and the tidyverse
  • Data wrangling with the tidyverse
  • Speeding up queries in large datasets

Writing your own functions

What are functions?

Functions are reusable pieces of code that

  1. take some standard input (e.g. a vector of numbers)
  2. do some computation (e.g. calculate the mean)
  3. return some standard output (e.g. one number with the mean)

We have been using a lot of functions: code of the form something() is usually a function.

mean(1:6)
## [1] 3.5

Our own function

We can make our own functions as follows:

squared <- function(x){
  x_square <- x * x
  return(x_square) 
}

squared(4)
## [1] 16

x, the input, is called the (formal) argument of the function. x_square is called the return value.

Our own function

If there is no return(), the last line is automatically returned, so we can also just write:

square <- function(x){
  x * x
}

square(-2)
## [1] 4

I do not recommend this, please always specify what you return unless you have a one-line function.

Anonymous/Lambda expressions

df <- data.frame("V1" = rnorm(5),
                 "V2" = rnorm(5, mean = 5, sd = 2), 
                 "V3" = rnorm(5, mean = 6, sd = 1))

head(df)
##           V1       V2       V3
## 1 -0.1690818 3.717684 6.652676
## 2  0.2344541 3.463449 8.123901
## 3  2.7007013 6.737512 5.970811
## 4  0.1939332 1.765620 4.846595
## 5  0.9380132 3.009092 5.697954
#Python
df.apply(lambda x: np.percentile(x, .42))
#R
sapply(df, {function(x) quantile(x, .42)})
##    V1.42%    V2.42%    V3.42% 
## 0.2214875 3.3180544 5.8834969

Default options in functions

  • Default options for some arguments are provided in many functions.
  • They allow us to provide additional (optional) arguments
is_contained <- function(str_1, str_2, print_input = TRUE){
  if (print_input){
    cat("Testing if", str_1, "contained in", str_2, "\n")
  }
  return(str_1 %in% str_2)
}
is_contained("R", "rstudio")
is_contained("R", "rstudio")
## Testing if R contained in rstudio
## [1] FALSE
is_contained("R", "rstudio", print_input = TRUE)
## Testing if R contained in rstudio
## [1] FALSE
is_contained("R", "rstudio", print_input = FALSE)
## [1] FALSE

Create documentation of functions

##Python
def square(x):
  """
  Squares a number

  Parameters:
  x (float): Number (or vector)

  Returns:
  float: Squared numbers
  """
  return(x**2)
##R more info at https://r-pkgs.org/man.html

#' Squares a number
#' 
#' @param x A number.
#' @returns A numeric vector.
#' @examples
#' square(3)
square <- function(x){
  return(x * x)
}

Troubleshooting

  • Your first self-written for-loop, or function, will probably not work.

  • Don’t panic! Just go line-by-line, keeping track of what is currently inside each variable.

  • Stackoverflow and LLMs are your friends.

Scoping rules in R

Global environemnt (workspace)

When you write the name of a variable, R needs to find the value.

In the interactive computation (outside of functions, e.g., your console), this happens in the following order:

  • First, search the global environment (i.e., your workspace)
  • If it cannot be found, search each of the loaded packages
search()
## [1] ".GlobalEnv"        "package:stats"     "package:graphics" 
## [4] "package:grDevices" "package:utils"     "package:datasets" 
## [7] "package:methods"   "Autoloads"         "package:base"

The order of packages is important.

Scoping rules in R: Functions

Inside a function, this happens in the following order:

  • First, search within the function.
  • If it cannot be found, search in the global environment (i.e., your workspace)
  • If it cannot be found, search each of the loaded packages
y <- 3
test_t <- function() {
  print(y)
}
test_t()
## [1] 3
y <- 3
test_t <- function() {
  y <- 2
  print(y)
}
test_t()
## [1] 2

Scoping rules in R: Functions

What happens inside a function, stays within a function (unless you specify it differently)

y <- 3
test_t <- function() {
  y <- 2
  print(y)
}
test_t()
## [1] 2
y
## [1] 3

Scoping rules in R: Packages

Packages are neatly contained/isolated, so they are not affected by your code. They do so through namespaces:

  • Namespaces allow the package developer to hide functions and data.
  • Objects in the global environment that match objects in the function’s namespace are ignored when running functions from packages (prevent clashes)
  • Functions are executed within the namespace of the package and have access to the global environment
  • They provide a way to refer to an object, with the double colon ::
dplyr::n_distinct(c(1,2,3,4,2))
## [1] 4

Scoping rules in R: Packages (good practices)

  • Pass to the function (using arguments) everything that the function needs to use (i.e. don’t define something outside the function that is being used for the function)

BAD

shifted_mean <- function(numbers) {
   return(mean(numbers) + shift_by)
}

shift_by <- 3
shifted_mean(c(1,2,3))

GOOD

shifted_mean <- function(numbers, shift_by) {
   return(mean(numbers) + shift_by)
}

shift_by <- 3
shifted_mean(c(1,2,3), shift_by)

Modeling

Linear regression (model)

Linear regression. Source: R. Kukuh (medium)

Linear regression (visual interpretation)

Linear regression. Source: R. Kukuh (medium)

Linear regression (fitting)

Linear regression. Source: R. Kukuh (medium)

Modeling in R

To model objects based on other objects, we use ~ (tilde)

For example, to model the relationship between body mass index (bmi) and weight, we would type

bmi ~ weight

The ~ is used to separate the dependent variable (left side) from the independent variables (right side).

For functions within the formula we use I(). For example, to model body mass index (BMI) on its deterministic function of weight and height, we would type

bmi ~ I(weight / height^2)

We can then plug the formula into a model.

Let’s use the boys dataset.

lm(bmi ~ wgt, data = boys)
## 
## Call:
## lm(formula = bmi ~ wgt, data = boys)
## 
## Coefficients:
## (Intercept)          wgt  
##     14.5401       0.0935
lm(bmi ~ I(wgt / (hgt / 100)^2), data = boys)
## 
## Call:
## lm(formula = bmi ~ I(wgt/(hgt/100)^2), data = boys)
## 
## Coefficients:
##        (Intercept)  I(wgt/(hgt/100)^2)  
##          -0.005553            1.000034

Why we really need I()

lm(bmi ~ wgt + wgt^2, data = boys)
## 
## Call:
## lm(formula = bmi ~ wgt + wgt^2, data = boys)
## 
## Coefficients:
## (Intercept)          wgt  
##     14.5401       0.0935

lm(bmi ~ wgt + I(wgt^2), data = boys)
## 
## Call:
## lm(formula = bmi ~ wgt + I(wgt^2), data = boys)
## 
## Coefficients:
## (Intercept)          wgt     I(wgt^2)  
##   16.271466    -0.041715     0.001604

More efficient

It is better to store the output from the function in an object. The convention for regression models is an object called fit.

fit <- lm(bmi ~ I(wgt / (hgt / 100)^2), data = boys)

The object fit contains a lot more than just the regression weights. To inspect what is inside you can use attributes()

attributes(fit)
## $names
##  [1] "coefficients"  "residuals"     "effects"       "rank"         
##  [5] "fitted.values" "assign"        "qr"            "df.residual"  
##  [9] "na.action"     "xlevels"       "call"          "terms"        
## [13] "model"        
## 
## $class
## [1] "lm"

Finding the coefficients

summary(fit)
## 
## Call:
## lm(formula = bmi ~ I(wgt/(hgt/100)^2), data = boys)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.005195 -0.002381  0.000152  0.002322  0.005125 
## 
## Coefficients:
##                      Estimate Std. Error   t value Pr(>|t|)    
## (Intercept)        -5.553e-03  6.366e-04    -8.724   <2e-16 ***
## I(wgt/(hgt/100)^2)  1.000e+00  3.473e-05 28795.609   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.002857 on 725 degrees of freedom
##   (21 observations deleted due to missingness)
## Multiple R-squared:      1,  Adjusted R-squared:      1 
## F-statistic: 8.292e+08 on 1 and 725 DF,  p-value: < 2.2e-16

Classes in R

class(fit)
## [1] "lm"

Classes are used in object-oriented programming. It defines a set of properties and methods that are common to all objects of one type. For example, no matter what model you fit, you’ll always need some common attributes.

In R, objects are the instances of a class (i.e., all objects in R have a class).

When you apply a generic function to an object (e.g. class = “lm”), R first tries to find a function of the class of the object.

When a generic function function (e.g. plot()) is applied to an object with class attribute "lm", the system searches for a function called plot.lm() and, if it finds it, applies it to the object.

If R cannot find plot.lm() it then uses the default function (e.g. plot())—if it exists.

Classes example: plotting without class

plot(bmi ~ wgt, data = boys)

Classes example: plotting with class

plot(lm(bmi ~ wgt, data = boys), which = 1)

Classes example: plotting with class

plot(lm(bmi ~ wgt, data = boys), which = 2)

Classes example: plotting with class

plot(lm(bmi ~ wgt, data = boys), which = 3)

Classes example: plotting with class

plot(lm(bmi ~ wgt, data = boys), which = 4)

Classes example: plotting with class

plot(lm(bmi ~ wgt, data = boys), which = 5)

Classes example: plotting with class

plot(lm(bmi ~ wgt, data = boys), which = 6)

Reading and writing files in several formats

Reading and Writing

Reading files

#install.packages(c("readr","readxl","haven","foreign","Hmisc","feather"),
#repos = "http://cran.us.r-project.org")

readr::read_delim("here_path.csv", delim = ",") #CSV
readr::read_rds("here_path.Rds") #RDS (R format)
readxl::read_excel("here_path.xlsx") #Excel
haven::read_dta("here_path.dta") #Stata
haven::read_sav("here_path.sav") #SPSS
feather::read_feather("tmp/here_path.feather") #feather

Writing to files

#install.packages(c("writexl"),
#    repos = "http://cran.us.r-project.org")

## Writing
readr::write_delim(virginia,"tmp/here_path.csv", delim = ",") #CSV
readr::write_rds(virginia,"tmp/here_path.Rds") #RDS (R format)
writexl::write_xlsx(virginia,"tmp/here_path.xlsx") #Excel
haven::write_dta(virginia,"tmp/here_path.dta") #Stata
haven::write_sav(virginia,"tmp/here_path.sav") #SPSS
feather::write_feather(virginia, "tmp/here_path.feather") #feather

Reading and writing

  • CSV: Easy to use, share, open in excel or a text editor.
  • RDS: binary format, only for R. Your factors (categorical variables) will stay as factors. Small size and decent read time.
  • feather: binary format, efficient for large data files and to share.

Principles of tidy data

Library

library(tidyverse)
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr     1.1.2     ✔ readr     2.1.4
## ✔ forcats   1.0.0     ✔ stringr   1.5.0
## ✔ ggplot2   3.4.2     ✔ tibble    3.2.1
## ✔ lubridate 1.9.2     ✔ tidyr     1.3.0
## ✔ purrr     1.0.1     
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

Tidy data

Simple but extremely useful idea:

  1. Each variable has its own column.
  2. Each observation has its own row.
  3. Each value has its own cell.

Source: R for data science

Original paper of Tidy Data

Tidy vs non-tidy data

There are three variables in this data set. What are they?

## # A tibble: 2 × 3
##   ``     `2010` `2015`
##   <chr>   <dbl>  <dbl>
## 1 Male        0      5
## 2 Female      1      4
## # A tibble: 4 × 3
##    year gender count
##   <dbl> <chr>  <dbl>
## 1  2010 Female     1
## 2  2010 Female     0
## 3  2015 Male       4
## 4  2015 Male       5

What are the variables in the following dataset

#Death rates per 1000 in Virginia in 1940.
virginia <- readr::read_csv("../common_datasets/virginia.txt")
names(virginia) <- c("Age","Rural Male","Rural Female","Urban Male","Urban Female")
virginia
## # A tibble: 5 × 5
##   Age   `Rural Male` `Rural Female` `Urban Male` `Urban Female`
##   <chr>        <dbl>          <dbl>        <dbl>          <dbl>
## 1 50-54         11.7            8.7         15.4            8.4
## 2 55-59         18.1           11.7         24.3           13.6
## 3 60-64         26.9           20.3         37             19.3
## 4 65-69         41             30.9         54.6           35.1
## 5 70-74         66             54.3         71.1           50

Advantages of tidy data

  1. Consistent way of storing data = reuse of tools/code
  2. Facilitate manipulation, visualization and modelling
  • Combining tables (e.g., merging two tables by year)
  • Plotting: you’ll typically want to show how one variable depends on another (y ~ x)
  • Statistical models (y ~ x + year)
  1. Performance: R is fast applying functions to columns (vectorized)

e.g. merging dataset

How to fix datasets: Melting (pivot_longer)

df <- tibble::tribble(
  ~"gender", ~"2010", ~"2015",
  #--|--|----
  "Male", 0, 5,
  "Female", 1, 4
)
df
## # A tibble: 2 × 3
##   gender `2010` `2015`
##   <chr>   <dbl>  <dbl>
## 1 Male        0      5
## 2 Female      1      4
tidyr::pivot_longer(df, cols = c("2010","2015"), names_to = "year", values_to = "count")
## # A tibble: 4 × 3
##   gender year  count
##   <chr>  <chr> <dbl>
## 1 Male   2010      0
## 2 Male   2015      5
## 3 Female 2010      1
## 4 Female 2015      4

How to fix datasets: Pivot_wider

df <- tibble::tribble(
  ~"gender", ~"variable", ~"value",
  #--|--|----
  "Male", "happiness", 5,
  "Male", "count", 5,
)
df
## # A tibble: 2 × 3
##   gender variable  value
##   <chr>  <chr>     <dbl>
## 1 Male   happiness     5
## 2 Male   count         5
tidyr::pivot_wider(df, id_cols = c("gender"), names_from = "variable", values_from = "value")
## # A tibble: 1 × 3
##   gender happiness count
##   <chr>      <dbl> <dbl>
## 1 Male           5     5

Tidy vs base R

Reading the data

data <- readr::read_csv("../common_datasets/dataset_boys.csv", col_select = c("age","wgt","bmi","reg") )
data
## # A tibble: 748 × 4
##      age   wgt   bmi reg  
##    <dbl> <dbl> <dbl> <chr>
##  1 0.035  3.65  14.5 south
##  2 0.038  3.37  11.8 south
##  3 0.057  3.14  12.6 south
##  4 0.06   4.27  14.4 south
##  5 0.062  5.03  15.2 south
##  6 0.068  4.66  15.1 south
##  7 0.068  3.81  13.8 south
##  8 0.071  3.89  13.8 west 
##  9 0.071  3.88  12.8 west 
## 10 0.073  4.2   14.1 east 
## # ℹ 738 more rows

Subsetting (columns)

base R

data[, c("age","bmi")]
## # A tibble: 748 × 2
##      age   bmi
##    <dbl> <dbl>
##  1 0.035  14.5
##  2 0.038  11.8
##  3 0.057  12.6
##  4 0.06   14.4
##  5 0.062  15.2
##  6 0.068  15.1
##  7 0.068  13.8
##  8 0.071  13.8
##  9 0.071  12.8
## 10 0.073  14.1
## # ℹ 738 more rows

tidyverse

dplyr::select(data, age, bmi)
## # A tibble: 748 × 2
##      age   bmi
##    <dbl> <dbl>
##  1 0.035  14.5
##  2 0.038  11.8
##  3 0.057  12.6
##  4 0.06   14.4
##  5 0.062  15.2
##  6 0.068  15.1
##  7 0.068  13.8
##  8 0.071  13.8
##  9 0.071  12.8
## 10 0.073  14.1
## # ℹ 738 more rows

Subsetting (rows)

base R

data[data$age > 20, ]
## # A tibble: 12 × 4
##      age   wgt   bmi reg  
##    <dbl> <dbl> <dbl> <chr>
##  1  20.0  68.8  23.8 east 
##  2  20.0  71    22.2 city 
##  3  20.0  73    21.6 north
##  4  20.1  89.4  25.1 east 
##  5  20.3  81.1  23.7 south
##  6  20.3  69    20.7 north
##  7  20.4  59.8  16.8 west 
##  8  20.4  67.2  20.5 north
##  9  20.8  88    24.6 west 
## 10  20.8  75.4  20.1 west 
## 11  20.8  78    21.8 north
## 12  21.2  76.5  23.1 east

tidyverse

dplyr::filter(data, age > 20)
## # A tibble: 12 × 4
##      age   wgt   bmi reg  
##    <dbl> <dbl> <dbl> <chr>
##  1  20.0  68.8  23.8 east 
##  2  20.0  71    22.2 city 
##  3  20.0  73    21.6 north
##  4  20.1  89.4  25.1 east 
##  5  20.3  81.1  23.7 south
##  6  20.3  69    20.7 north
##  7  20.4  59.8  16.8 west 
##  8  20.4  67.2  20.5 north
##  9  20.8  88    24.6 west 
## 10  20.8  75.4  20.1 west 
## 11  20.8  78    21.8 north
## 12  21.2  76.5  23.1 east

Drop missing values

base R

nans <- rowSums(is.na(data[, c("bmi","reg")]))
data[!nans,]
## # A tibble: 724 × 4
##      age   wgt   bmi reg  
##    <dbl> <dbl> <dbl> <chr>
##  1 0.035  3.65  14.5 south
##  2 0.038  3.37  11.8 south
##  3 0.057  3.14  12.6 south
##  4 0.06   4.27  14.4 south
##  5 0.062  5.03  15.2 south
##  6 0.068  4.66  15.1 south
##  7 0.068  3.81  13.8 south
##  8 0.071  3.89  13.8 west 
##  9 0.071  3.88  12.8 west 
## 10 0.073  4.2   14.1 east 
## # ℹ 714 more rows

tidyverse

tidyr::drop_na(data, 
               bmi,  reg)
## # A tibble: 724 × 4
##      age   wgt   bmi reg  
##    <dbl> <dbl> <dbl> <chr>
##  1 0.035  3.65  14.5 south
##  2 0.038  3.37  11.8 south
##  3 0.057  3.14  12.6 south
##  4 0.06   4.27  14.4 south
##  5 0.062  5.03  15.2 south
##  6 0.068  4.66  15.1 south
##  7 0.068  3.81  13.8 south
##  8 0.071  3.89  13.8 west 
##  9 0.071  3.88  12.8 west 
## 10 0.073  4.2   14.1 east 
## # ℹ 714 more rows

Sort (by age (descending) and bmi (ascending)

base R

data[order(rev(data$age), data$bmi), ]
## # A tibble: 748 × 4
##      age   wgt   bmi reg  
##    <dbl> <dbl> <dbl> <chr>
##  1  21.2  76.5  23.1 east 
##  2  20.8  78    21.8 north
##  3  20.8  75.4  20.1 west 
##  4  20.8  88    24.6 west 
##  5  20.4  67.2  20.5 north
##  6  20.4  59.8  16.8 west 
##  7  20.3  69    20.7 north
##  8  20.3  81.1  23.7 south
##  9  20.1  89.4  25.1 east 
## 10  20.0  73    21.6 north
## # ℹ 738 more rows

tidyverse

dplyr::arrange(data, desc(age), bmi) 
## # A tibble: 748 × 4
##      age   wgt   bmi reg  
##    <dbl> <dbl> <dbl> <chr>
##  1  21.2  76.5  23.1 east 
##  2  20.8  78    21.8 north
##  3  20.8  75.4  20.1 west 
##  4  20.8  88    24.6 west 
##  5  20.4  67.2  20.5 north
##  6  20.4  59.8  16.8 west 
##  7  20.3  69    20.7 north
##  8  20.3  81.1  23.7 south
##  9  20.1  89.4  25.1 east 
## 10  20.0  73    21.6 north
## # ℹ 738 more rows

Creating new column in a new data frame

base R

new_data <- data
new_data$age_sqrt <- sqrt(new_data$age)
new_data
## # A tibble: 748 × 5
##      age   wgt   bmi reg   age_sqrt
##    <dbl> <dbl> <dbl> <chr>    <dbl>
##  1 0.035  3.65  14.5 south    0.187
##  2 0.038  3.37  11.8 south    0.195
##  3 0.057  3.14  12.6 south    0.239
##  4 0.06   4.27  14.4 south    0.245
##  5 0.062  5.03  15.2 south    0.249
##  6 0.068  4.66  15.1 south    0.261
##  7 0.068  3.81  13.8 south    0.261
##  8 0.071  3.89  13.8 west     0.266
##  9 0.071  3.88  12.8 west     0.266
## 10 0.073  4.2   14.1 east     0.270
## # ℹ 738 more rows

tidyverse

new_data <- dplyr::mutate(data,
                          age_srt = sqrt(age))
new_data
## # A tibble: 748 × 5
##      age   wgt   bmi reg   age_srt
##    <dbl> <dbl> <dbl> <chr>   <dbl>
##  1 0.035  3.65  14.5 south   0.187
##  2 0.038  3.37  11.8 south   0.195
##  3 0.057  3.14  12.6 south   0.239
##  4 0.06   4.27  14.4 south   0.245
##  5 0.062  5.03  15.2 south   0.249
##  6 0.068  4.66  15.1 south   0.261
##  7 0.068  3.81  13.8 south   0.261
##  8 0.071  3.89  13.8 west    0.266
##  9 0.071  3.88  12.8 west    0.266
## 10 0.073  4.2   14.1 east    0.270
## # ℹ 738 more rows

Applying a function by columns (map is more consistent)

base R

sum_nans <- function(x) {sum(is.na(x))}
apply(data, MARGIN = 2, 
      FUN = sum_nans)
## age wgt bmi reg 
##   0   4  21   3
lapply(data, sum_nans)
## $age
## [1] 0
## 
## $wgt
## [1] 4
## 
## $bmi
## [1] 21
## 
## $reg
## [1] 3

tidyverse

sum_nans <- function(x) {sum(is.na(x))}
#Returns a vector of integer (map_xxx)
purrr::map_int(data, sum_nans)
## age wgt bmi reg 
##   0   4  21   3
purrr::map(data, sum_nans)
## $age
## [1] 0
## 
## $wgt
## [1] 4
## 
## $bmi
## [1] 21
## 
## $reg
## [1] 3

Merge

base R

#Decent syntax (sorts desc.)
system.time(
  merg <- merge(data, data, by = "reg")
  )
##    user  system elapsed 
##   0.143   0.003   0.146
merg[, c("reg", "age.x","age.y")]
##         reg  age.x  age.y
## 1      city 12.646 12.646
## 2      city 12.646 13.300
## 3      city 12.646  0.788
## 4      city 12.646  0.714
## 5      city 12.646  1.242
## 6      city 12.646  1.938
## 7      city 12.646  0.147
## 8      city 12.646  1.062
## 9      city 12.646 11.791
## 10     city 12.646 10.477
## 11     city 12.646  7.600
## 12     city 12.646  0.254
## 13     city 12.646 17.023
## 14     city 12.646 13.500
## 15     city 12.646 18.850
## 16     city 12.646  0.550
## 17     city 12.646  5.338
## 18     city 12.646 12.996
## 19     city 12.646 16.443
## 20     city 12.646  1.210
## 21     city 12.646  0.172
## 22     city 12.646  0.271
## 23     city 12.646  3.099
## 24     city 12.646 16.720
## 25     city 12.646  1.182
## 26     city 12.646  0.703
## 27     city 12.646  0.977
## 28     city 12.646 15.622
## 29     city 12.646  0.257
## 30     city 12.646  0.555
## 31     city 12.646  2.088
## 32     city 12.646 13.555
## 33     city 12.646  0.169
## 34     city 12.646 13.577
## 35     city 12.646 14.094
## 36     city 12.646  0.777
## 37     city 12.646  7.849
## 38     city 12.646  3.827
## 39     city 12.646  0.079
## 40     city 12.646 14.650
## 41     city 12.646  7.041
## 42     city 12.646  0.334
## 43     city 12.646  3.433
## 44     city 12.646 13.275
## 45     city 12.646  0.405
## 46     city 12.646 12.520
## 47     city 12.646 10.160
## 48     city 12.646 15.906
## 49     city 12.646  1.308
## 50     city 12.646 19.942
## 51     city 12.646  0.251
## 52     city 12.646 14.297
## 53     city 12.646 15.520
## 54     city 12.646  0.295
## 55     city 12.646 11.759
## 56     city 12.646 15.893
## 57     city 12.646 10.157
## 58     city 12.646 17.579
## 59     city 12.646 10.945
## 60     city 12.646 16.268
## 61     city 12.646 15.304
## 62     city 12.646 13.656
## 63     city 12.646 20.030
## 64     city 12.646 13.656
## 65     city 12.646 11.665
## 66     city 12.646 14.332
## 67     city 12.646  1.697
## 68     city 12.646 18.453
## 69     city 12.646  0.689
## 70     city 12.646  9.034
## 71     city 12.646  1.853
## 72     city 12.646 11.545
## 73     city 12.646 16.547
## 74     city 13.300 12.646
## 75     city 13.300 13.300
## 76     city 13.300  0.788
## 77     city 13.300  0.714
## 78     city 13.300  1.242
## 79     city 13.300  1.938
## 80     city 13.300  0.147
## 81     city 13.300  1.062
## 82     city 13.300 11.791
## 83     city 13.300 10.477
## 84     city 13.300  7.600
## 85     city 13.300  0.254
## 86     city 13.300 17.023
## 87     city 13.300 13.500
## 88     city 13.300 18.850
## 89     city 13.300  0.550
## 90     city 13.300  5.338
## 91     city 13.300 12.996
## 92     city 13.300 16.443
## 93     city 13.300  1.210
## 94     city 13.300  0.172
## 95     city 13.300  0.271
## 96     city 13.300  3.099
## 97     city 13.300 16.720
## 98     city 13.300  1.182
## 99     city 13.300  0.703
## 100    city 13.300  0.977
## 101    city 13.300 15.622
## 102    city 13.300  0.257
## 103    city 13.300  0.555
## 104    city 13.300  2.088
## 105    city 13.300 13.555
## 106    city 13.300  0.169
## 107    city 13.300 13.577
## 108    city 13.300 14.094
## 109    city 13.300  0.777
## 110    city 13.300  7.849
## 111    city 13.300  3.827
## 112    city 13.300  0.079
## 113    city 13.300 14.650
## 114    city 13.300  7.041
## 115    city 13.300  0.334
## 116    city 13.300  3.433
## 117    city 13.300 13.275
## 118    city 13.300  0.405
## 119    city 13.300 12.520
## 120    city 13.300 10.160
## 121    city 13.300 15.906
## 122    city 13.300  1.308
## 123    city 13.300 19.942
## 124    city 13.300  0.251
## 125    city 13.300 14.297
## 126    city 13.300 15.520
## 127    city 13.300  0.295
## 128    city 13.300 11.759
## 129    city 13.300 15.893
## 130    city 13.300 10.157
## 131    city 13.300 17.579
## 132    city 13.300 10.945
## 133    city 13.300 16.268
## 134    city 13.300 15.304
## 135    city 13.300 13.656
## 136    city 13.300 20.030
## 137    city 13.300 13.656
## 138    city 13.300 11.665
## 139    city 13.300 14.332
## 140    city 13.300  1.697
## 141    city 13.300 18.453
## 142    city 13.300  0.689
## 143    city 13.300  9.034
## 144    city 13.300  1.853
## 145    city 13.300 11.545
## 146    city 13.300 16.547
## 147    city  0.788 12.646
## 148    city  0.788 13.300
## 149    city  0.788  0.788
## 150    city  0.788  0.714
## 151    city  0.788  1.242
## 152    city  0.788  1.938
## 153    city  0.788  0.147
## 154    city  0.788  1.062
## 155    city  0.788 11.791
## 156    city  0.788 10.477
## 157    city  0.788  7.600
## 158    city  0.788  0.254
## 159    city  0.788 17.023
## 160    city  0.788 13.500
## 161    city  0.788 18.850
## 162    city  0.788  0.550
## 163    city  0.788  5.338
## 164    city  0.788 12.996
## 165    city  0.788 16.443
## 166    city  0.788  1.210
## 167    city  0.788  0.172
## 168    city  0.788  0.271
## 169    city  0.788  3.099
## 170    city  0.788 16.720
## 171    city  0.788  1.182
## 172    city  0.788  0.703
## 173    city  0.788  0.977
## 174    city  0.788 15.622
## 175    city  0.788  0.257
## 176    city  0.788  0.555
## 177    city  0.788  2.088
## 178    city  0.788 13.555
## 179    city  0.788  0.169
## 180    city  0.788 13.577
## 181    city  0.788 14.094
## 182    city  0.788  0.777
## 183    city  0.788  7.849
## 184    city  0.788  3.827
## 185    city  0.788  0.079
## 186    city  0.788 14.650
## 187    city  0.788  7.041
## 188    city  0.788  0.334
## 189    city  0.788  3.433
## 190    city  0.788 13.275
## 191    city  0.788  0.405
## 192    city  0.788 12.520
## 193    city  0.788 10.160
## 194    city  0.788 15.906
## 195    city  0.788  1.308
## 196    city  0.788 19.942
## 197    city  0.788  0.251
## 198    city  0.788 14.297
## 199    city  0.788 15.520
## 200    city  0.788  0.295
## 201    city  0.788 11.759
## 202    city  0.788 15.893
## 203    city  0.788 10.157
## 204    city  0.788 17.579
## 205    city  0.788 10.945
## 206    city  0.788 16.268
## 207    city  0.788 15.304
## 208    city  0.788 13.656
## 209    city  0.788 20.030
## 210    city  0.788 13.656
## 211    city  0.788 11.665
## 212    city  0.788 14.332
## 213    city  0.788  1.697
## 214    city  0.788 18.453
## 215    city  0.788  0.689
## 216    city  0.788  9.034
## 217    city  0.788  1.853
## 218    city  0.788 11.545
## 219    city  0.788 16.547
## 220    city  0.714 12.646
## 221    city  0.714 13.300
## 222    city  0.714  0.788
## 223    city  0.714  0.714
## 224    city  0.714  1.242
## 225    city  0.714  1.938
## 226    city  0.714  0.147
## 227    city  0.714  1.062
## 228    city  0.714 11.791
## 229    city  0.714 10.477
## 230    city  0.714  7.600
## 231    city  0.714  0.254
## 232    city  0.714 17.023
## 233    city  0.714 13.500
## 234    city  0.714 18.850
## 235    city  0.714  0.550
## 236    city  0.714  5.338
## 237    city  0.714 12.996
## 238    city  0.714 16.443
## 239    city  0.714  1.210
## 240    city  0.714  0.172
## 241    city  0.714  0.271
## 242    city  0.714  3.099
## 243    city  0.714 16.720
## 244    city  0.714  1.182
## 245    city  0.714  0.703
## 246    city  0.714  0.977
## 247    city  0.714 15.622
## 248    city  0.714  0.257
## 249    city  0.714  0.555
## 250    city  0.714  2.088
## 251    city  0.714 13.555
## 252    city  0.714  0.169
## 253    city  0.714 13.577
## 254    city  0.714 14.094
## 255    city  0.714  0.777
## 256    city  0.714  7.849
## 257    city  0.714  3.827
## 258    city  0.714  0.079
## 259    city  0.714 14.650
## 260    city  0.714  7.041
## 261    city  0.714  0.334
## 262    city  0.714  3.433
## 263    city  0.714 13.275
## 264    city  0.714  0.405
## 265    city  0.714 12.520
## 266    city  0.714 10.160
## 267    city  0.714 15.906
## 268    city  0.714  1.308
## 269    city  0.714 19.942
## 270    city  0.714  0.251
## 271    city  0.714 14.297
## 272    city  0.714 15.520
## 273    city  0.714  0.295
## 274    city  0.714 11.759
## 275    city  0.714 15.893
## 276    city  0.714 10.157
## 277    city  0.714 17.579
## 278    city  0.714 10.945
## 279    city  0.714 16.268
## 280    city  0.714 15.304
## 281    city  0.714 13.656
## 282    city  0.714 20.030
## 283    city  0.714 13.656
## 284    city  0.714 11.665
## 285    city  0.714 14.332
## 286    city  0.714  1.697
## 287    city  0.714 18.453
## 288    city  0.714  0.689
## 289    city  0.714  9.034
## 290    city  0.714  1.853
## 291    city  0.714 11.545
## 292    city  0.714 16.547
## 293    city  1.242 12.646
## 294    city  1.242 13.300
## 295    city  1.242  0.788
## 296    city  1.242  0.714
## 297    city  1.242  1.242
## 298    city  1.242  1.938
## 299    city  1.242  0.147
## 300    city  1.242  1.062
## 301    city  1.242 11.791
## 302    city  1.242 10.477
## 303    city  1.242  7.600
## 304    city  1.242  0.254
## 305    city  1.242 17.023
## 306    city  1.242 13.500
## 307    city  1.242 18.850
## 308    city  1.242  0.550
## 309    city  1.242  5.338
## 310    city  1.242 12.996
## 311    city  1.242 16.443
## 312    city  1.242  1.210
## 313    city  1.242  0.172
## 314    city  1.242  0.271
## 315    city  1.242  3.099
## 316    city  1.242 16.720
## 317    city  1.242  1.182
## 318    city  1.242  0.703
## 319    city  1.242  0.977
## 320    city  1.242 15.622
## 321    city  1.242  0.257
## 322    city  1.242  0.555
## 323    city  1.242  2.088
## 324    city  1.242 13.555
## 325    city  1.242  0.169
## 326    city  1.242 13.577
## 327    city  1.242 14.094
## 328    city  1.242  0.777
## 329    city  1.242  7.849
## 330    city  1.242  3.827
## 331    city  1.242  0.079
## 332    city  1.242 14.650
## 333    city  1.242  7.041
## 334    city  1.242  0.334
## 335    city  1.242  3.433
## 336    city  1.242 13.275
## 337    city  1.242  0.405
## 338    city  1.242 12.520
## 339    city  1.242 10.160
## 340    city  1.242 15.906
## 341    city  1.242  1.308
## 342    city  1.242 19.942
## 343    city  1.242  0.251
## 344    city  1.242 14.297
## 345    city  1.242 15.520
## 346    city  1.242  0.295
## 347    city  1.242 11.759
## 348    city  1.242 15.893
## 349    city  1.242 10.157
## 350    city  1.242 17.579
## 351    city  1.242 10.945
## 352    city  1.242 16.268
## 353    city  1.242 15.304
## 354    city  1.242 13.656
## 355    city  1.242 20.030
## 356    city  1.242 13.656
## 357    city  1.242 11.665
## 358    city  1.242 14.332
## 359    city  1.242  1.697
## 360    city  1.242 18.453
## 361    city  1.242  0.689
## 362    city  1.242  9.034
## 363    city  1.242  1.853
## 364    city  1.242 11.545
## 365    city  1.242 16.547
## 366    city  1.938 12.646
## 367    city  1.938 13.300
## 368    city  1.938  0.788
## 369    city  1.938  0.714
## 370    city  1.938  1.242
## 371    city  1.938  1.938
## 372    city  1.938  0.147
## 373    city  1.938  1.062
## 374    city  1.938 11.791
## 375    city  1.938 10.477
## 376    city  1.938  7.600
## 377    city  1.938  0.254
## 378    city  1.938 17.023
## 379    city  1.938 13.500
## 380    city  1.938 18.850
## 381    city  1.938  0.550
## 382    city  1.938  5.338
## 383    city  1.938 12.996
## 384    city  1.938 16.443
## 385    city  1.938  1.210
## 386    city  1.938  0.172
## 387    city  1.938  0.271
## 388    city  1.938  3.099
## 389    city  1.938 16.720
## 390    city  1.938  1.182
## 391    city  1.938  0.703
## 392    city  1.938  0.977
## 393    city  1.938 15.622
## 394    city  1.938  0.257
## 395    city  1.938  0.555
## 396    city  1.938  2.088
## 397    city  1.938 13.555
## 398    city  1.938  0.169
## 399    city  1.938 13.577
## 400    city  1.938 14.094
## 401    city  1.938  0.777
## 402    city  1.938  7.849
## 403    city  1.938  3.827
## 404    city  1.938  0.079
## 405    city  1.938 14.650
## 406    city  1.938  7.041
## 407    city  1.938  0.334
## 408    city  1.938  3.433
## 409    city  1.938 13.275
## 410    city  1.938  0.405
## 411    city  1.938 12.520
## 412    city  1.938 10.160
## 413    city  1.938 15.906
## 414    city  1.938  1.308
## 415    city  1.938 19.942
## 416    city  1.938  0.251
## 417    city  1.938 14.297
## 418    city  1.938 15.520
## 419    city  1.938  0.295
## 420    city  1.938 11.759
## 421    city  1.938 15.893
## 422    city  1.938 10.157
## 423    city  1.938 17.579
## 424    city  1.938 10.945
## 425    city  1.938 16.268
## 426    city  1.938 15.304
## 427    city  1.938 13.656
## 428    city  1.938 20.030
## 429    city  1.938 13.656
## 430    city  1.938 11.665
## 431    city  1.938 14.332
## 432    city  1.938  1.697
## 433    city  1.938 18.453
## 434    city  1.938  0.689
## 435    city  1.938  9.034
## 436    city  1.938  1.853
## 437    city  1.938 11.545
## 438    city  1.938 16.547
## 439    city  0.147 12.646
## 440    city  0.147 13.300
## 441    city  0.147  0.788
## 442    city  0.147  0.714
## 443    city  0.147  1.242
## 444    city  0.147  1.938
## 445    city  0.147  0.147
## 446    city  0.147  1.062
## 447    city  0.147 11.791
## 448    city  0.147 10.477
## 449    city  0.147  7.600
## 450    city  0.147  0.254
## 451    city  0.147 17.023
## 452    city  0.147 13.500
## 453    city  0.147 18.850
## 454    city  0.147  0.550
## 455    city  0.147  5.338
## 456    city  0.147 12.996
## 457    city  0.147 16.443
## 458    city  0.147  1.210
## 459    city  0.147  0.172
## 460    city  0.147  0.271
## 461    city  0.147  3.099
## 462    city  0.147 16.720
## 463    city  0.147  1.182
## 464    city  0.147  0.703
## 465    city  0.147  0.977
## 466    city  0.147 15.622
## 467    city  0.147  0.257
## 468    city  0.147  0.555
## 469    city  0.147  2.088
## 470    city  0.147 13.555
## 471    city  0.147  0.169
## 472    city  0.147 13.577
## 473    city  0.147 14.094
## 474    city  0.147  0.777
## 475    city  0.147  7.849
## 476    city  0.147  3.827
## 477    city  0.147  0.079
## 478    city  0.147 14.650
## 479    city  0.147  7.041
## 480    city  0.147  0.334
## 481    city  0.147  3.433
## 482    city  0.147 13.275
## 483    city  0.147  0.405
## 484    city  0.147 12.520
## 485    city  0.147 10.160
## 486    city  0.147 15.906
## 487    city  0.147  1.308
## 488    city  0.147 19.942
## 489    city  0.147  0.251
## 490    city  0.147 14.297
## 491    city  0.147 15.520
## 492    city  0.147  0.295
## 493    city  0.147 11.759
## 494    city  0.147 15.893
## 495    city  0.147 10.157
## 496    city  0.147 17.579
## 497    city  0.147 10.945
## 498    city  0.147 16.268
## 499    city  0.147 15.304
## 500    city  0.147 13.656
## 501    city  0.147 20.030
## 502    city  0.147 13.656
## 503    city  0.147 11.665
## 504    city  0.147 14.332
## 505    city  0.147  1.697
## 506    city  0.147 18.453
## 507    city  0.147  0.689
## 508    city  0.147  9.034
## 509    city  0.147  1.853
## 510    city  0.147 11.545
## 511    city  0.147 16.547
## 512    city  1.062 12.646
## 513    city  1.062 13.300
## 514    city  1.062  0.788
## 515    city  1.062  0.714
## 516    city  1.062  1.242
## 517    city  1.062  1.938
## 518    city  1.062  0.147
## 519    city  1.062  1.062
## 520    city  1.062 11.791
## 521    city  1.062 10.477
## 522    city  1.062  7.600
## 523    city  1.062  0.254
## 524    city  1.062 17.023
## 525    city  1.062 13.500
## 526    city  1.062 18.850
## 527    city  1.062  0.550
## 528    city  1.062  5.338
## 529    city  1.062 12.996
## 530    city  1.062 16.443
## 531    city  1.062  1.210
## 532    city  1.062  0.172
## 533    city  1.062  0.271
## 534    city  1.062  3.099
## 535    city  1.062 16.720
## 536    city  1.062  1.182
## 537    city  1.062  0.703
## 538    city  1.062  0.977
## 539    city  1.062 15.622
## 540    city  1.062  0.257
## 541    city  1.062  0.555
## 542    city  1.062  2.088
## 543    city  1.062 13.555
## 544    city  1.062  0.169
## 545    city  1.062 13.577
## 546    city  1.062 14.094
## 547    city  1.062  0.777
## 548    city  1.062  7.849
## 549    city  1.062  3.827
## 550    city  1.062  0.079
## 551    city  1.062 14.650
## 552    city  1.062  7.041
## 553    city  1.062  0.334
## 554    city  1.062  3.433
## 555    city  1.062 13.275
## 556    city  1.062  0.405
## 557    city  1.062 12.520
## 558    city  1.062 10.160
## 559    city  1.062 15.906
## 560    city  1.062  1.308
## 561    city  1.062 19.942
## 562    city  1.062  0.251
## 563    city  1.062 14.297
## 564    city  1.062 15.520
## 565    city  1.062  0.295
## 566    city  1.062 11.759
## 567    city  1.062 15.893
## 568    city  1.062 10.157
## 569    city  1.062 17.579
## 570    city  1.062 10.945
## 571    city  1.062 16.268
## 572    city  1.062 15.304
## 573    city  1.062 13.656
## 574    city  1.062 20.030
## 575    city  1.062 13.656
## 576    city  1.062 11.665
## 577    city  1.062 14.332
## 578    city  1.062  1.697
## 579    city  1.062 18.453
## 580    city  1.062  0.689
## 581    city  1.062  9.034
## 582    city  1.062  1.853
## 583    city  1.062 11.545
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## 1745   city 16.720 14.332
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## 1747   city 16.720 18.453
## 1748   city 16.720  0.689
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## 1752   city 16.720 16.547
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## 1754   city  1.182 13.300
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## 1756   city  1.182  0.714
## 1757   city  1.182  1.242
## 1758   city  1.182  1.938
## 1759   city  1.182  0.147
## 1760   city  1.182  1.062
## 1761   city  1.182 11.791
## 1762   city  1.182 10.477
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## 1775   city  1.182  3.099
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## 1780   city  1.182 15.622
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## 1783   city  1.182  2.088
## 1784   city  1.182 13.555
## 1785   city  1.182  0.169
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## 1787   city  1.182 14.094
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## 1789   city  1.182  7.849
## 1790   city  1.182  3.827
## 1791   city  1.182  0.079
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## 1793   city  1.182  7.041
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## 1795   city  1.182  3.433
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## 1797   city  1.182  0.405
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## 1799   city  1.182 10.160
## 1800   city  1.182 15.906
## 1801   city  1.182  1.308
## 1802   city  1.182 19.942
## 1803   city  1.182  0.251
## 1804   city  1.182 14.297
## 1805   city  1.182 15.520
## 1806   city  1.182  0.295
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## 1811   city  1.182 10.945
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## 1815   city  1.182 20.030
## 1816   city  1.182 13.656
## 1817   city  1.182 11.665
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## 1825   city  1.182 16.547
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## 1827   city  0.703 13.300
## 1828   city  0.703  0.788
## 1829   city  0.703  0.714
## 1830   city  0.703  1.242
## 1831   city  0.703  1.938
## 1832   city  0.703  0.147
## 1833   city  0.703  1.062
## 1834   city  0.703 11.791
## 1835   city  0.703 10.477
## 1836   city  0.703  7.600
## 1837   city  0.703  0.254
## 1838   city  0.703 17.023
## 1839   city  0.703 13.500
## 1840   city  0.703 18.850
## 1841   city  0.703  0.550
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## 1843   city  0.703 12.996
## 1844   city  0.703 16.443
## 1845   city  0.703  1.210
## 1846   city  0.703  0.172
## 1847   city  0.703  0.271
## 1848   city  0.703  3.099
## 1849   city  0.703 16.720
## 1850   city  0.703  1.182
## 1851   city  0.703  0.703
## 1852   city  0.703  0.977
## 1853   city  0.703 15.622
## 1854   city  0.703  0.257
## 1855   city  0.703  0.555
## 1856   city  0.703  2.088
## 1857   city  0.703 13.555
## 1858   city  0.703  0.169
## 1859   city  0.703 13.577
## 1860   city  0.703 14.094
## 1861   city  0.703  0.777
## 1862   city  0.703  7.849
## 1863   city  0.703  3.827
## 1864   city  0.703  0.079
## 1865   city  0.703 14.650
## 1866   city  0.703  7.041
## 1867   city  0.703  0.334
## 1868   city  0.703  3.433
## 1869   city  0.703 13.275
## 1870   city  0.703  0.405
## 1871   city  0.703 12.520
## 1872   city  0.703 10.160
## 1873   city  0.703 15.906
## 1874   city  0.703  1.308
## 1875   city  0.703 19.942
## 1876   city  0.703  0.251
## 1877   city  0.703 14.297
## 1878   city  0.703 15.520
## 1879   city  0.703  0.295
## 1880   city  0.703 11.759
## 1881   city  0.703 15.893
## 1882   city  0.703 10.157
## 1883   city  0.703 17.579
## 1884   city  0.703 10.945
## 1885   city  0.703 16.268
## 1886   city  0.703 15.304
## 1887   city  0.703 13.656
## 1888   city  0.703 20.030
## 1889   city  0.703 13.656
## 1890   city  0.703 11.665
## 1891   city  0.703 14.332
## 1892   city  0.703  1.697
## 1893   city  0.703 18.453
## 1894   city  0.703  0.689
## 1895   city  0.703  9.034
## 1896   city  0.703  1.853
## 1897   city  0.703 11.545
## 1898   city  0.703 16.547
## 1899   city  0.977 12.646
## 1900   city  0.977 13.300
## 1901   city  0.977  0.788
## 1902   city  0.977  0.714
## 1903   city  0.977  1.242
## 1904   city  0.977  1.938
## 1905   city  0.977  0.147
## 1906   city  0.977  1.062
## 1907   city  0.977 11.791
## 1908   city  0.977 10.477
## 1909   city  0.977  7.600
## 1910   city  0.977  0.254
## 1911   city  0.977 17.023
## 1912   city  0.977 13.500
## 1913   city  0.977 18.850
## 1914   city  0.977  0.550
## 1915   city  0.977  5.338
## 1916   city  0.977 12.996
## 1917   city  0.977 16.443
## 1918   city  0.977  1.210
## 1919   city  0.977  0.172
## 1920   city  0.977  0.271
## 1921   city  0.977  3.099
## 1922   city  0.977 16.720
## 1923   city  0.977  1.182
## 1924   city  0.977  0.703
## 1925   city  0.977  0.977
## 1926   city  0.977 15.622
## 1927   city  0.977  0.257
## 1928   city  0.977  0.555
## 1929   city  0.977  2.088
## 1930   city  0.977 13.555
## 1931   city  0.977  0.169
## 1932   city  0.977 13.577
## 1933   city  0.977 14.094
## 1934   city  0.977  0.777
## 1935   city  0.977  7.849
## 1936   city  0.977  3.827
## 1937   city  0.977  0.079
## 1938   city  0.977 14.650
## 1939   city  0.977  7.041
## 1940   city  0.977  0.334
## 1941   city  0.977  3.433
## 1942   city  0.977 13.275
## 1943   city  0.977  0.405
## 1944   city  0.977 12.520
## 1945   city  0.977 10.160
## 1946   city  0.977 15.906
## 1947   city  0.977  1.308
## 1948   city  0.977 19.942
## 1949   city  0.977  0.251
## 1950   city  0.977 14.297
## 1951   city  0.977 15.520
## 1952   city  0.977  0.295
## 1953   city  0.977 11.759
## 1954   city  0.977 15.893
## 1955   city  0.977 10.157
## 1956   city  0.977 17.579
## 1957   city  0.977 10.945
## 1958   city  0.977 16.268
## 1959   city  0.977 15.304
## 1960   city  0.977 13.656
## 1961   city  0.977 20.030
## 1962   city  0.977 13.656
## 1963   city  0.977 11.665
## 1964   city  0.977 14.332
## 1965   city  0.977  1.697
## 1966   city  0.977 18.453
## 1967   city  0.977  0.689
## 1968   city  0.977  9.034
## 1969   city  0.977  1.853
## 1970   city  0.977 11.545
## 1971   city  0.977 16.547
## 1972   city 15.622 12.646
## 1973   city 15.622 13.300
## 1974   city 15.622  0.788
## 1975   city 15.622  0.714
## 1976   city 15.622  1.242
## 1977   city 15.622  1.938
## 1978   city 15.622  0.147
## 1979   city 15.622  1.062
## 1980   city 15.622 11.791
## 1981   city 15.622 10.477
## 1982   city 15.622  7.600
## 1983   city 15.622  0.254
## 1984   city 15.622 17.023
## 1985   city 15.622 13.500
## 1986   city 15.622 18.850
## 1987   city 15.622  0.550
## 1988   city 15.622  5.338
## 1989   city 15.622 12.996
## 1990   city 15.622 16.443
## 1991   city 15.622  1.210
## 1992   city 15.622  0.172
## 1993   city 15.622  0.271
## 1994   city 15.622  3.099
## 1995   city 15.622 16.720
## 1996   city 15.622  1.182
## 1997   city 15.622  0.703
## 1998   city 15.622  0.977
## 1999   city 15.622 15.622
## 2000   city 15.622  0.257
## 2001   city 15.622  0.555
## 2002   city 15.622  2.088
## 2003   city 15.622 13.555
## 2004   city 15.622  0.169
## 2005   city 15.622 13.577
## 2006   city 15.622 14.094
## 2007   city 15.622  0.777
## 2008   city 15.622  7.849
## 2009   city 15.622  3.827
## 2010   city 15.622  0.079
## 2011   city 15.622 14.650
## 2012   city 15.622  7.041
## 2013   city 15.622  0.334
## 2014   city 15.622  3.433
## 2015   city 15.622 13.275
## 2016   city 15.622  0.405
## 2017   city 15.622 12.520
## 2018   city 15.622 10.160
## 2019   city 15.622 15.906
## 2020   city 15.622  1.308
## 2021   city 15.622 19.942
## 2022   city 15.622  0.251
## 2023   city 15.622 14.297
## 2024   city 15.622 15.520
## 2025   city 15.622  0.295
## 2026   city 15.622 11.759
## 2027   city 15.622 15.893
## 2028   city 15.622 10.157
## 2029   city 15.622 17.579
## 2030   city 15.622 10.945
## 2031   city 15.622 16.268
## 2032   city 15.622 15.304
## 2033   city 15.622 13.656
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## 2035   city 15.622 13.656
## 2036   city 15.622 11.665
## 2037   city 15.622 14.332
## 2038   city 15.622  1.697
## 2039   city 15.622 18.453
## 2040   city 15.622  0.689
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## 2052   city  0.257  1.062
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## 2067   city  0.257  3.099
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## 2077   city  0.257  0.169
## 2078   city  0.257 13.577
## 2079   city  0.257 14.094
## 2080   city  0.257  0.777
## 2081   city  0.257  7.849
## 2082   city  0.257  3.827
## 2083   city  0.257  0.079
## 2084   city  0.257 14.650
## 2085   city  0.257  7.041
## 2086   city  0.257  0.334
## 2087   city  0.257  3.433
## 2088   city  0.257 13.275
## 2089   city  0.257  0.405
## 2090   city  0.257 12.520
## 2091   city  0.257 10.160
## 2092   city  0.257 15.906
## 2093   city  0.257  1.308
## 2094   city  0.257 19.942
## 2095   city  0.257  0.251
## 2096   city  0.257 14.297
## 2097   city  0.257 15.520
## 2098   city  0.257  0.295
## 2099   city  0.257 11.759
## 2100   city  0.257 15.893
## 2101   city  0.257 10.157
## 2102   city  0.257 17.579
## 2103   city  0.257 10.945
## 2104   city  0.257 16.268
## 2105   city  0.257 15.304
## 2106   city  0.257 13.656
## 2107   city  0.257 20.030
## 2108   city  0.257 13.656
## 2109   city  0.257 11.665
## 2110   city  0.257 14.332
## 2111   city  0.257  1.697
## 2112   city  0.257 18.453
## 2113   city  0.257  0.689
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## 2116   city  0.257 11.545
## 2117   city  0.257 16.547
## 2118   city  0.555 12.646
## 2119   city  0.555 13.300
## 2120   city  0.555  0.788
## 2121   city  0.555  0.714
## 2122   city  0.555  1.242
## 2123   city  0.555  1.938
## 2124   city  0.555  0.147
## 2125   city  0.555  1.062
## 2126   city  0.555 11.791
## 2127   city  0.555 10.477
## 2128   city  0.555  7.600
## 2129   city  0.555  0.254
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## 2131   city  0.555 13.500
## 2132   city  0.555 18.850
## 2133   city  0.555  0.550
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## 2136   city  0.555 16.443
## 2137   city  0.555  1.210
## 2138   city  0.555  0.172
## 2139   city  0.555  0.271
## 2140   city  0.555  3.099
## 2141   city  0.555 16.720
## 2142   city  0.555  1.182
## 2143   city  0.555  0.703
## 2144   city  0.555  0.977
## 2145   city  0.555 15.622
## 2146   city  0.555  0.257
## 2147   city  0.555  0.555
## 2148   city  0.555  2.088
## 2149   city  0.555 13.555
## 2150   city  0.555  0.169
## 2151   city  0.555 13.577
## 2152   city  0.555 14.094
## 2153   city  0.555  0.777
## 2154   city  0.555  7.849
## 2155   city  0.555  3.827
## 2156   city  0.555  0.079
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## 2158   city  0.555  7.041
## 2159   city  0.555  0.334
## 2160   city  0.555  3.433
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## 2162   city  0.555  0.405
## 2163   city  0.555 12.520
## 2164   city  0.555 10.160
## 2165   city  0.555 15.906
## 2166   city  0.555  1.308
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## 2168   city  0.555  0.251
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## 2170   city  0.555 15.520
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## 2173   city  0.555 15.893
## 2174   city  0.555 10.157
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## 2176   city  0.555 10.945
## 2177   city  0.555 16.268
## 2178   city  0.555 15.304
## 2179   city  0.555 13.656
## 2180   city  0.555 20.030
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## 2182   city  0.555 11.665
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## 2184   city  0.555  1.697
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## 2186   city  0.555  0.689
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## 2188   city  0.555  1.853
## 2189   city  0.555 11.545
## 2190   city  0.555 16.547
## 2191   city  2.088 12.646
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## 2196   city  2.088  1.938
## 2197   city  2.088  0.147
## 2198   city  2.088  1.062
## 2199   city  2.088 11.791
## 2200   city  2.088 10.477
## 2201   city  2.088  7.600
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## 2210   city  2.088  1.210
## 2211   city  2.088  0.172
## 2212   city  2.088  0.271
## 2213   city  2.088  3.099
## 2214   city  2.088 16.720
## 2215   city  2.088  1.182
## 2216   city  2.088  0.703
## 2217   city  2.088  0.977
## 2218   city  2.088 15.622
## 2219   city  2.088  0.257
## 2220   city  2.088  0.555
## 2221   city  2.088  2.088
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## 2223   city  2.088  0.169
## 2224   city  2.088 13.577
## 2225   city  2.088 14.094
## 2226   city  2.088  0.777
## 2227   city  2.088  7.849
## 2228   city  2.088  3.827
## 2229   city  2.088  0.079
## 2230   city  2.088 14.650
## 2231   city  2.088  7.041
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## 2233   city  2.088  3.433
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## 2235   city  2.088  0.405
## 2236   city  2.088 12.520
## 2237   city  2.088 10.160
## 2238   city  2.088 15.906
## 2239   city  2.088  1.308
## 2240   city  2.088 19.942
## 2241   city  2.088  0.251
## 2242   city  2.088 14.297
## 2243   city  2.088 15.520
## 2244   city  2.088  0.295
## 2245   city  2.088 11.759
## 2246   city  2.088 15.893
## 2247   city  2.088 10.157
## 2248   city  2.088 17.579
## 2249   city  2.088 10.945
## 2250   city  2.088 16.268
## 2251   city  2.088 15.304
## 2252   city  2.088 13.656
## 2253   city  2.088 20.030
## 2254   city  2.088 13.656
## 2255   city  2.088 11.665
## 2256   city  2.088 14.332
## 2257   city  2.088  1.697
## 2258   city  2.088 18.453
## 2259   city  2.088  0.689
## 2260   city  2.088  9.034
## 2261   city  2.088  1.853
## 2262   city  2.088 11.545
## 2263   city  2.088 16.547
## 2264   city 13.555 12.646
## 2265   city 13.555 13.300
## 2266   city 13.555  0.788
## 2267   city 13.555  0.714
## 2268   city 13.555  1.242
## 2269   city 13.555  1.938
## 2270   city 13.555  0.147
## 2271   city 13.555  1.062
## 2272   city 13.555 11.791
## 2273   city 13.555 10.477
## 2274   city 13.555  7.600
## 2275   city 13.555  0.254
## 2276   city 13.555 17.023
## 2277   city 13.555 13.500
## 2278   city 13.555 18.850
## 2279   city 13.555  0.550
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## 2281   city 13.555 12.996
## 2282   city 13.555 16.443
## 2283   city 13.555  1.210
## 2284   city 13.555  0.172
## 2285   city 13.555  0.271
## 2286   city 13.555  3.099
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## 2288   city 13.555  1.182
## 2289   city 13.555  0.703
## 2290   city 13.555  0.977
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## 2292   city 13.555  0.257
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## 2296   city 13.555  0.169
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## 2298   city 13.555 14.094
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## 2302   city 13.555  0.079
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## 2304   city 13.555  7.041
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## 2308   city 13.555  0.405
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## 2310   city 13.555 10.160
## 2311   city 13.555 15.906
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## 2314   city 13.555  0.251
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## 33074 north  1.292  0.673
## 33075 north  1.292 15.704
## 33076 north  1.292 11.728
## 33077 north  1.292  3.304
## 33078 north  1.292  2.198
## 33079 north  1.292  2.020
## 33080 north  1.292 16.900
## 33081 north  1.292 18.959
## 33082 north  1.292 19.011
## 33083 north  1.292 15.912
## 33084 north  1.292 15.926
## 33085 north  1.292  1.793
## 33086 north  1.292 19.471
## 33087 north  1.292 19.501
## 33088 north  1.292 15.268
## 33089 north  1.292 17.911
## 33090 north  1.292 17.327
## 33091 north  1.292  2.576
## 33092 north  1.292 12.457
## 33093 north  1.292  8.859
## 33094 north  1.292 13.839
## 33095 north  1.292 17.426
## 33096 north  1.292 16.156
## 33097 north  1.292 16.175
## 33098 north  1.292 19.926
## 33099 north  1.292 15.474
## 33100 north  1.292 13.924
## 33101 north  1.292  2.929
## 33102 north  1.292 15.507
## 33103 north  1.292  9.119
## 33104 north  1.292 20.032
## 33105 north  1.292 16.399
## 33106 north  1.292  0.996
## 33107 north  1.292 20.323
## 33108 north  1.292 14.069
## 33109 north  1.292 20.429
## 33110 north  1.292 19.028
## 33111 north  1.292 14.099
## 33112 north  1.292 20.813
## 33113 north  1.292 16.605
## 33114 north  0.142 13.190
## 33115 north  0.142  1.530
## 33116 north  0.142 14.494
## 33117 north  0.142  0.093
## 33118 north  0.142  9.303
## 33119 north  0.142 16.741
## 33120 north  0.142 13.891
## 33121 north  0.142 15.989
## 33122 north  0.142  0.147
## 33123 north  0.142 13.604
## 33124 north  0.142 17.694
## 33125 north  0.142  7.540
## 33126 north  0.142  5.782
## 33127 north  0.142 14.543
## 33128 north  0.142 11.655
## 33129 north  0.142  0.117
## 33130 north  0.142 11.222
## 33131 north  0.142 11.011
## 33132 north  0.142 18.507
## 33133 north  0.142 14.877
## 33134 north  0.142  3.184
## 33135 north  0.142 15.416
## 33136 north  0.142  1.292
## 33137 north  0.142  0.142
## 33138 north  0.142 18.677
## 33139 north  0.142 14.811
## 33140 north  0.142  1.798
## 33141 north  0.142 18.406
## 33142 north  0.142 15.025
## 33143 north  0.142  1.481
## 33144 north  0.142  1.848
## 33145 north  0.142 15.542
## 33146 north  0.142 15.556
## 33147 north  0.142  4.197
## 33148 north  0.142 18.929
## 33149 north  0.142 17.678
## 33150 north  0.142 12.996
## 33151 north  0.142  1.040
## 33152 north  0.142  0.594
## 33153 north  0.142 14.997
## 33154 north  0.142 17.467
## 33155 north  0.142  0.673
## 33156 north  0.142 15.704
## 33157 north  0.142 11.728
## 33158 north  0.142  3.304
## 33159 north  0.142  2.198
## 33160 north  0.142  2.020
## 33161 north  0.142 16.900
## 33162 north  0.142 18.959
## 33163 north  0.142 19.011
## 33164 north  0.142 15.912
## 33165 north  0.142 15.926
## 33166 north  0.142  1.793
## 33167 north  0.142 19.471
## 33168 north  0.142 19.501
## 33169 north  0.142 15.268
## 33170 north  0.142 17.911
## 33171 north  0.142 17.327
## 33172 north  0.142  2.576
## 33173 north  0.142 12.457
## 33174 north  0.142  8.859
## 33175 north  0.142 13.839
## 33176 north  0.142 17.426
## 33177 north  0.142 16.156
## 33178 north  0.142 16.175
## 33179 north  0.142 19.926
## 33180 north  0.142 15.474
## 33181 north  0.142 13.924
## 33182 north  0.142  2.929
## 33183 north  0.142 15.507
## 33184 north  0.142  9.119
## 33185 north  0.142 20.032
## 33186 north  0.142 16.399
## 33187 north  0.142  0.996
## 33188 north  0.142 20.323
## 33189 north  0.142 14.069
## 33190 north  0.142 20.429
## 33191 north  0.142 19.028
## 33192 north  0.142 14.099
## 33193 north  0.142 20.813
## 33194 north  0.142 16.605
## 33195 north 18.677 13.190
## 33196 north 18.677  1.530
## 33197 north 18.677 14.494
## 33198 north 18.677  0.093
## 33199 north 18.677  9.303
## 33200 north 18.677 16.741
## 33201 north 18.677 13.891
## 33202 north 18.677 15.989
## 33203 north 18.677  0.147
## 33204 north 18.677 13.604
## 33205 north 18.677 17.694
## 33206 north 18.677  7.540
## 33207 north 18.677  5.782
## 33208 north 18.677 14.543
## 33209 north 18.677 11.655
## 33210 north 18.677  0.117
## 33211 north 18.677 11.222
## 33212 north 18.677 11.011
## 33213 north 18.677 18.507
## 33214 north 18.677 14.877
## 33215 north 18.677  3.184
## 33216 north 18.677 15.416
## 33217 north 18.677  1.292
## 33218 north 18.677  0.142
## 33219 north 18.677 18.677
## 33220 north 18.677 14.811
## 33221 north 18.677  1.798
## 33222 north 18.677 18.406
## 33223 north 18.677 15.025
## 33224 north 18.677  1.481
## 33225 north 18.677  1.848
## 33226 north 18.677 15.542
## 33227 north 18.677 15.556
## 33228 north 18.677  4.197
## 33229 north 18.677 18.929
## 33230 north 18.677 17.678
## 33231 north 18.677 12.996
## 33232 north 18.677  1.040
## 33233 north 18.677  0.594
## 33234 north 18.677 14.997
## 33235 north 18.677 17.467
## 33236 north 18.677  0.673
## 33237 north 18.677 15.704
## 33238 north 18.677 11.728
## 33239 north 18.677  3.304
## 33240 north 18.677  2.198
## 33241 north 18.677  2.020
## 33242 north 18.677 16.900
## 33243 north 18.677 18.959
## 33244 north 18.677 19.011
## 33245 north 18.677 15.912
## 33246 north 18.677 15.926
## 33247 north 18.677  1.793
## 33248 north 18.677 19.471
## 33249 north 18.677 19.501
## 33250 north 18.677 15.268
## 33251 north 18.677 17.911
## 33252 north 18.677 17.327
## 33253 north 18.677  2.576
## 33254 north 18.677 12.457
## 33255 north 18.677  8.859
## 33256 north 18.677 13.839
## 33257 north 18.677 17.426
## 33258 north 18.677 16.156
## 33259 north 18.677 16.175
## 33260 north 18.677 19.926
## 33261 north 18.677 15.474
## 33262 north 18.677 13.924
## 33263 north 18.677  2.929
## 33264 north 18.677 15.507
## 33265 north 18.677  9.119
## 33266 north 18.677 20.032
## 33267 north 18.677 16.399
## 33268 north 18.677  0.996
## 33269 north 18.677 20.323
## 33270 north 18.677 14.069
## 33271 north 18.677 20.429
## 33272 north 18.677 19.028
## 33273 north 18.677 14.099
## 33274 north 18.677 20.813
## 33275 north 18.677 16.605
## 33276 north 14.811 13.190
## 33277 north 14.811  1.530
## 33278 north 14.811 14.494
## 33279 north 14.811  0.093
## 33280 north 14.811  9.303
## 33281 north 14.811 16.741
## 33282 north 14.811 13.891
## 33283 north 14.811 15.989
## 33284 north 14.811  0.147
## 33285 north 14.811 13.604
## 33286 north 14.811 17.694
## 33287 north 14.811  7.540
## 33288 north 14.811  5.782
## 33289 north 14.811 14.543
## 33290 north 14.811 11.655
## 33291 north 14.811  0.117
## 33292 north 14.811 11.222
## 33293 north 14.811 11.011
## 33294 north 14.811 18.507
## 33295 north 14.811 14.877
## 33296 north 14.811  3.184
## 33297 north 14.811 15.416
## 33298 north 14.811  1.292
## 33299 north 14.811  0.142
## 33300 north 14.811 18.677
## 33301 north 14.811 14.811
## 33302 north 14.811  1.798
## 33303 north 14.811 18.406
## 33304 north 14.811 15.025
## 33305 north 14.811  1.481
## 33306 north 14.811  1.848
## 33307 north 14.811 15.542
## 33308 north 14.811 15.556
## 33309 north 14.811  4.197
## 33310 north 14.811 18.929
## 33311 north 14.811 17.678
## 33312 north 14.811 12.996
## 33313 north 14.811  1.040
## 33314 north 14.811  0.594
## 33315 north 14.811 14.997
## 33316 north 14.811 17.467
## 33317 north 14.811  0.673
## 33318 north 14.811 15.704
## 33319 north 14.811 11.728
## 33320 north 14.811  3.304
## 33321 north 14.811  2.198
## 33322 north 14.811  2.020
## 33323 north 14.811 16.900
## 33324 north 14.811 18.959
## 33325 north 14.811 19.011
## 33326 north 14.811 15.912
## 33327 north 14.811 15.926
## 33328 north 14.811  1.793
## 33329 north 14.811 19.471
## 33330 north 14.811 19.501
## 33331 north 14.811 15.268
## 33332 north 14.811 17.911
## 33333 north 14.811 17.327
##  [ reached 'max' / getOption("max.print") -- omitted 98089 rows ]

tidyverse

#Similar syntax, but much faster! (sorts ascendingly)
system.time(
  merg <- dplyr::inner_join(data, data, by = "reg")
  )
## Warning in dplyr::inner_join(data, data, by = "reg"): Detected an unexpected many-to-many relationship between `x` and `y`.
## ℹ Row 1 of `x` matches multiple rows in `y`.
## ℹ Row 1 of `y` matches multiple rows in `x`.
## ℹ If a many-to-many relationship is expected, set `relationship =
##   "many-to-many"` to silence this warning.
##    user  system elapsed 
##   0.014   0.001   0.014
select(merg, reg,age.x,age.y)
## # A tibble: 131,422 × 3
##    reg   age.x age.y
##    <chr> <dbl> <dbl>
##  1 south 0.035 0.035
##  2 south 0.035 0.038
##  3 south 0.035 0.057
##  4 south 0.035 0.06 
##  5 south 0.035 0.062
##  6 south 0.035 0.068
##  7 south 0.035 0.068
##  8 south 0.035 0.084
##  9 south 0.035 0.104
## 10 south 0.035 0.117
## # ℹ 131,412 more rows

Main data structure

base R: data.frame

  • Prints okay
data.frame(x=1:2, y=2:1)
##   x y
## 1 1 2
## 2 2 1
# 
# 
  • Recycle rules are error-prone
data.frame(x=1:4, y=c(1,2))
##   x y
## 1 1 1
## 2 2 2
## 3 3 1
## 4 4 2

tidyverse: tibble

  • Prints nicely
tibble(x=1:2, y=2:1)
## # A tibble: 2 × 2
##       x     y
##   <int> <int>
## 1     1     2
## 2     2     1
  • Does not recycle arguments of length > 1
tibble(x=1:4, y=c(1,2))
## Error in `tibble()`:
## ! Tibble columns must have compatible sizes.
## • Size 4: Existing data.
## • Size 2: Column `y`.
## ℹ Only values of size one are recycled.

Main structure

base R: data.frame

  • Tries to read your mind (error-prone)
d <- data.frame(variable=1:4)
d$var
## [1] 1 2 3 4
  • Subsetting a data.frame returns often a vector
#
d <- data.frame(x=1:4, y=1)
d[, "x"] #d["x"] returns a data.frame
## [1] 1 2 3 4

tidyverse: tibble

  • Does not try to read your mind
d <- tibble(variable=1:4)
d$var
## Warning: Unknown or uninitialised column: `var`.
## NULL
  • Subsetting a tibble returns a tibble
d <- tibble(x=1:4, y=1)
d[, "x"]  # d[["x"]] or d$x returns a vector
## # A tibble: 4 × 1
##       x
##   <int>
## 1     1
## 2     2
## 3     3
## 4     4
  • Renaming columns
rename(d, new_var_x = x)
## # A tibble: 4 × 2
##   new_var_x     y
##       <int> <dbl>
## 1         1     1
## 2         2     1
## 3         3     1
## 4         4     1

Main structure

base R: data.frame

  • Renaming is annoying and does not scale well
d_new <- d
names(d_new)[names(d_new) == 'x'] <- 'new_var_x'
  • Works with all packages. Can be converted to a tibble easily.
as_tibble(d_new)
## # A tibble: 4 × 2
##   new_var_x     y
##       <int> <dbl>
## 1         1     1
## 2         2     1
## 3         3     1
## 4         4     1

tidyverse: tibble

  • Renaming columns
d_new <- dplyr::rename(d, new_var_x = x)
#
  • Does not work with some old packages. Can be converted to a data.frame easily.
as.data.frame(d_new)
##   new_var_x y
## 1         1 1
## 2         2 1
## 3         3 1
## 4         4 1

Summarize by group

base R - Drops the entire row if there is one missing value

aggregate(cbind(age, wgt, bmi) ~ reg, 
          data = data, 
          FUN = mean)
##     reg       age      wgt      bmi
## 1  city  8.453606 34.53199 18.20000
## 2  east  9.333038 37.26796 17.89862
## 3 north 12.157506 50.79620 19.39329
## 4 south  8.770527 35.07836 17.76161
## 5  west  9.191642 37.08493 17.97629

tidyverse - Does not drop the entire row if there is one missing value

data |> 
  dplyr::group_by(reg) |> 
  dplyr::summarise_all(mean, na.rm = TRUE)
## # A tibble: 6 × 4
##   reg     age   wgt   bmi
##   <chr> <dbl> <dbl> <dbl>
## 1 city   8.27 34.0   18.2
## 2 east   9.24 37.0   17.9
## 3 north 11.9  49.9   19.4
## 4 south  8.59 34.5   17.8
## 5 west   9.00 36.4   18.0
## 6 <NA>   1.33  9.26  15.2

Pipes: A short intro

Step by step

grouped_data <- dplyr::group_by(data, reg) 
summarized_data <- dplyr::summarise_all(grouped_data, mean, na.rm = TRUE)

The pipe takes the output of the command before |> and passes it as input for the command after |>.

It reduces the overhead (no need to save intermediate output), organizes the code into coherent blocks, and increases readability.

summarized_data <- data |> 
  dplyr::group_by(reg) |>  
  dplyr::summarise_all(mean, na.rm = TRUE)
  • Base R has since version 4.1 its own pipe (|>), before the pipe was provided by the magrittr package and it looked like: %>%.

Data wrangling summary

  • Cheatsheet data tidying with tidyr

  • Cheatsheet data transformation with dplyr

  • Main functions dplyr:

    • mutate: add column
    • select: select columns
    • filter: filter rows
    • distinct: remove duplicates
    • arrange: sort rows
    • group_by + summarize / summarize_all: apply function to groups
  • Main functions tidyr:

    • drop_na: remove rows with missing values
    • fill: fill missing values with a value
    • pivot_wider(data, names_from = “name”, values_from = “value”)
    • pivot_longer(data, cols, names_to = “name”, values_to = “value”, values_drop_na = FALSE)

Why tidyverse

  • Perfect to work with tidy data
  • Easier syntax
  • More intuitive
  • Less error prone
  • It has its own ecosystem of complementary packages
  • All/most functions in the tidyverse can be used in pipes
  • Huge community of fanatics

Practical

Bigger data

IMDB data

Their data on movies and actors is freely available at https://developer.imdb.com/non-commercial-datasets/

#Download data
download.file("https://datasets.imdbws.com/title.basics.tsv.gz", "db/title_basics.tsv.gz", mode = "wb")
data_imdb <- readr::read_delim("db/title_basics.tsv.gz", delim = "\t", na = "\\N", show_col_types = FALSE)

#10,375,265 rows, 9 columns
data_imdb
## # A tibble: 10,375,265 × 9
##    tconst    titleType primaryTitle      originalTitle isAdult startYear endYear
##    <chr>     <chr>     <chr>             <chr>           <dbl>     <dbl>   <dbl>
##  1 tt0000001 short     Carmencita        Carmencita          0      1894      NA
##  2 tt0000002 short     Le clown et ses … Le clown et …       0      1892      NA
##  3 tt0000003 short     Pauvre Pierrot    Pauvre Pierr…       0      1892      NA
##  4 tt0000004 short     Un bon bock       Un bon bock         0      1892      NA
##  5 tt0000005 short     Blacksmith Scene  Blacksmith S…       0      1893      NA
##  6 tt0000006 short     Chinese Opium Den Chinese Opiu…       0      1894      NA
##  7 tt0000007 short     Corbett and Cour… Corbett and …       0      1894      NA
##  8 tt0000008 short     Edison Kinetosco… Edison Kinet…       0      1894      NA
##  9 tt0000009 movie     Miss Jerry        Miss Jerry          0      1894      NA
## 10 tt0000010 short     Leaving the Fact… La sortie de…       0      1895      NA
## # ℹ 10,375,255 more rows
## # ℹ 2 more variables: runtimeMinutes <dbl>, genres <chr>

Time to read data

Time to read data:

system.time(
  data_imdb <- readr::read_delim("db/title_basics.tsv.gz", delim = "\t", na = "\\N", show_col_types = FALSE)
)
##    user  system elapsed 
##  12.519   1.412  12.389

Time to query:

system.time(
  results <- data_imdb |> 
    dplyr::group_by(startYear) |> 
    dplyr::summarize(number_movies = n()) |> 
    arrange(number_movies)
)
##    user  system elapsed 
##   0.264   0.034   0.300

Speed up using a database (SQL)

Use database instead of a file

#install.packages("DBI")
#install.packages("RSQLite")
#install.packages("dbplyr")
library(DBI) #Database access
library(RSQLite) #SQLite
library(dbplyr) #query without using SQL
## 
## Attaching package: 'dbplyr'
## The following objects are masked from 'package:dplyr':
## 
##     ident, sql

Dump the data to a SQLite.database

SQLite is a lightweight, self-contained, and serverless relational database management system (RDBMS). It’s contained as a file in your computer. It’s designed for simplicity and efficiency.

# Connect to SQLite database
db <- DBI::dbConnect(RSQLite::SQLite(), "db/imdb.db") #try :memory: instead of a file
# Write the data frame to the SQLite database using dbplyr
DBI::dbWriteTable(db, "title_basics", data_imdb, overwrite = TRUE)
DBI::dbWriteTable(db, "title_basics_no_index", data_imdb, overwrite = TRUE)
# Create an index on startYear
DBI::dbExecute(db, "CREATE INDEX idx_startYear ON title_basics(startYear);")
## [1] 0
# Close the database connection
DBI::dbDisconnect(db)

Some operations on the table

Reading the tables

db <- DBI::dbConnect(RSQLite::SQLite(), "db/imdb.db") #try :memory: instead of a file
DBI::dbListTables(db)
## [1] "title_basics"          "title_basics_no_index"

Reading the fields of a table

DBI::dbListFields(db, "title_basics")
## [1] "tconst"         "titleType"      "primaryTitle"   "originalTitle" 
## [5] "isAdult"        "startYear"      "endYear"        "runtimeMinutes"
## [9] "genres"

Running query

# Connect to the table
con <- DBI::dbConnect(RSQLite::SQLite(), "db/imdb.db")
data_imdb_db <- dplyr::tbl(con, "title_basics")

# Create the query (note that it's exactly the same code)
data_imdb_query <- data_imdb_db |> 
                   dplyr::group_by(startYear) |> 
                   dplyr::summarize(number_movies = n()) |> 
                   dplyr::arrange(desc(number_movies))

# Show query
data_imdb_query |> dplyr::show_query()
## <SQL>
## SELECT `startYear`, COUNT(*) AS `number_movies`
## FROM `title_basics`
## GROUP BY `startYear`
## ORDER BY `number_movies` DESC
# Disconnect from server (done at the end)
DBI::dbDisconnect(con)

Performance (without index)

# Run the query
system.time({
  # Connect to database
  con <- DBI::dbConnect(RSQLite::SQLite(), "db/imdb.db")
  data_imdb_db <- dplyr::tbl(con, "title_basics_no_index")
  
  # Create the query (note that it's exactly the same code)
  data_imdb_query <- data_imdb_db |> 
                     dplyr::group_by(startYear) |> 
                     dplyr::summarize(number_movies = n()) |> 
                     dplyr::arrange(desc(number_movies))
  
  # Collect the data (query is run here)
  results <- data_imdb_query |> dplyr::collect()
})
##    user  system elapsed 
##   3.429   0.610   5.626
# Disconnect
DBI::dbDisconnect(con)

Performance (with index)

# Run the query
system.time({
  # Connect to database
  con <- DBI::dbConnect(RSQLite::SQLite(), "db/imdb.db")
  data_imdb_db <- dplyr::tbl(con, "title_basics")
  
  # Create the query (note that it's exactly the same code)
  data_imdb_query <- data_imdb_db |> 
                     dplyr::group_by(startYear) |> 
                     dplyr::summarize(number_movies = n()) |> 
                     dplyr::arrange(desc(number_movies))
  
  # Collect the data (query is run here)
  results <- data_imdb_query |> dplyr::collect()
})
##    user  system elapsed 
##   0.348   0.034   0.455
# Disconnect
DBI::dbDisconnect(con)

Results

head(results, 10)
## # A tibble: 10 × 2
##    startYear number_movies
##        <dbl>         <int>
##  1        NA       1387132
##  2      2021        473952
##  3      2022        442202
##  4      2018        440447
##  5      2017        435954
##  6      2019        434586
##  7      2016        412339
##  8      2020        411821
##  9      2015        388877
## 10      2014        368696

Results (visually)

library(ggplot2)

ggplot(data = results, aes(y=number_movies, x=startYear)) + 
  geom_line(color = "cornflowerblue", linewidth = 1) +
  theme_minimal() +
  labs(x = "Year", y = "Number of movies") +
  lims(y = c(0, 5E5))
## Warning: Removed 1 row containing missing values (`geom_line()`).

SQLite summary

We sped the query from ~12 seconds (~11 to read the file + ~0.40 for the query) to ~0.38 seconds. And there are many other perks of using SQLite (e..g data integrity).

However: dbplyr is not great at creating efficient queries from tidyverse.