Set-up

1 Summarizing Data

1.1 The pipe and summarise()

1.1.1 mean
1.1.2 median
1.1.3 standard deviation
1.1.4 counting observations
1.1.5 multiple summaries
1.1.6 naming variables inside summarise()

1.2 Grouping (group_by())

2 Manipulating data

2.1 Selecting columns
2.2 Slicing

2.2.1 Slicing and grouping

2.3 Filtering
2.4 Mutating

2.4.1 Create a new variable
2.4.2 Create a new variable and store it as a column
2.4.3 Mutating while grouping
2.4.4 Mutating and frequency tables

3 Visualizing data

3.1 Plotting distributions

3.1.1 Histograms
3.1.2 Cumulative distributions
3.1.3 Box plots

3.2 Scatterplot

3.2.1 Scatterplot with regression line

4 Correlation and regression

4.1 Covariance
4.2 Correlation
4.3 Regression
4.4 summary()
4.5 Plotting regression results

5 Quick tables

Last updated: 2021-04-27 18:25:43 EST

Go to quick tables Go home

Set-up

Load the tidyverse:

library(tidyverse)

The tidyverse provides the data mpg to demonstrate methods. mpg has the mileage (cty for city, hwy for highway) for a bunch of different cars:

data("mpg") # load the data mpg

# view the first 5 rows
mpg %>% 
  slice_head(n=5)

ABCDEFGHIJ0123456789

manufacturer <chr>	model <chr>	displ <dbl>	year <int>	cyl <int>	trans <chr>	drv <chr>	cty <int>	hwy <int>	fl <chr>
audi	a4	1.8	1999	4	auto(l5)	f	18	29	p
audi	a4	1.8	1999	4	manual(m5)	f	21	29	p
audi	a4	2.0	2008	4	manual(m6)	f	20	31	p
audi	a4	2.0	2008	4	auto(av)	f	21	30	p
audi	a4	2.8	1999	6	auto(l5)	f	16	26	p

1 Summarizing Data

1.1 The pipe and `summarise()`

All summarizing operations work like this:

data %>% # the pipe: "and then"
  summarise() 

the pipe (%>%, “and then”)
summarise()

Inside summarise() you can use functions like mean(), median() and so on.

1.1.1 mean

mean()

mpg %>% # take the data, THEN
  summarise(mean(cty)) # summarize: mean

ABCDEFGHIJ0123456789

mean(cty) <dbl>
16.85897

Note. cty is a numerical variable.

1.1.2 median

median()

mpg %>% # take the data, THEN
  summarise(median(cty)) # summarize: median

ABCDEFGHIJ0123456789

median(cty) <dbl>
17

1.1.3 standard deviation

sd()

mpg %>% # take the data, THEN
  summarise(sd(cty)) # summarize: standard deviation

ABCDEFGHIJ0123456789

sd(cty) <dbl>
4.255946

1.1.4 counting observations

n() (counting)

mpg %>% # take the data, THEN
  summarise(n()) # summarize: count number of observations

ABCDEFGHIJ0123456789

n() <int>
234

Why doesn’t n() take an argument? Because it counts the number of rows, not columns.

1.1.5 multiple summaries

You can put as many functions as you want inside summarise():

mpg %>% # take the data, THEN
  summarise(mean(cty), median(cty), sd(cty), n()) # summarize: mean, median, standard deviation, count

ABCDEFGHIJ0123456789

mean(cty) <dbl>	median(cty) <dbl>	sd(cty) <dbl>	n() <int>
16.85897	17	4.255946	234

1.1.6 naming variables inside `summarise()`

You can name variables inside summarise() using standard assignment:

mpg %>% # take the data, THEN
  summarise(avg_cty = mean(cty), median_cty = median(cty)) # summarize: mean, median

ABCDEFGHIJ0123456789

avg_cty <dbl>	median_cty <dbl>
16.85897	17

1.2 Grouping (`group_by()`)

group_by():

mpg %>% # take the data, THEN
  group_by(class) %>% # group it by car class (e.g., compact, pickup) THEN
  summarise(mean(cty), median(cty), sd(cty), n()) # summarize

ABCDEFGHIJ0123456789

class <chr>	mean(cty) <dbl>	median(cty) <dbl>	sd(cty) <dbl>	n() <int>
2seater	15.40000	15	0.5477226	5
compact	20.12766	20	3.3854999	47
midsize	18.75610	18	1.9465416	41
minivan	15.81818	16	1.8340219	11
pickup	13.00000	13	2.0463382	33
subcompact	20.37143	19	4.6023377	35
suv	13.50000	13	2.4208791	62

Note. class is a categorical variable.

2 Manipulating data

2.1 Selecting columns

select() certain columns

mpg %>% # all the columns
  slice_head(n=5) # view the first 5 rows

ABCDEFGHIJ0123456789

manufacturer <chr>	model <chr>	displ <dbl>	year <int>	cyl <int>	trans <chr>	drv <chr>	cty <int>	hwy <int>	fl <chr>
audi	a4	1.8	1999	4	auto(l5)	f	18	29	p
audi	a4	1.8	1999	4	manual(m5)	f	21	29	p
audi	a4	2.0	2008	4	manual(m6)	f	20	31	p
audi	a4	2.0	2008	4	auto(av)	f	21	30	p
audi	a4	2.8	1999	6	auto(l5)	f	16	26	p

mpg %>% # all the columns
  select(manufacturer, model, hwy) %>% # select some of the columns
  slice_head(n=5) # view the first 5 rows

ABCDEFGHIJ0123456789

manufacturer <chr>	model <chr>	hwy <int>
audi	a4	29
audi	a4	29
audi	a4	31
audi	a4	30
audi	a4	26

2.2 Slicing

All slice operators begin with slice_ and take an optional n= argument that specifies the number of rows you want to see. More here.

Subsets with slice_head():

mpg %>% 
  slice_head(n=10) # view the first 10 rows

ABCDEFGHIJ0123456789

manufacturer <chr>	model <chr>	displ <dbl>	year <int>	cyl <int>	trans <chr>	drv <chr>	cty <int>	hwy <int>	fl <chr>
audi	a4	1.8	1999	4	auto(l5)	f	18	29	p
audi	a4	1.8	1999	4	manual(m5)	f	21	29	p
audi	a4	2.0	2008	4	manual(m6)	f	20	31	p
audi	a4	2.0	2008	4	auto(av)	f	21	30	p
audi	a4	2.8	1999	6	auto(l5)	f	16	26	p
audi	a4	2.8	1999	6	manual(m5)	f	18	26	p
audi	a4	3.1	2008	6	auto(av)	f	18	27	p
audi	a4 quattro	1.8	1999	4	manual(m5)	4	18	26	p
audi	a4 quattro	1.8	1999	4	auto(l5)	4	16	25	p
audi	a4 quattro	2.0	2008	4	manual(m6)	4	20	28	p

Maximums with slice_max():

mpg %>% 
  slice_max(hwy, n=5) # the five highest highway miles per gallon. if there are ties they all get printed

ABCDEFGHIJ0123456789

manufacturer <chr>	model <chr>	displ <dbl>	year <int>	cyl <int>	trans <chr>	drv <chr>	cty <int>	hwy <int>	fl <chr>
volkswagen	jetta	1.9	1999	4	manual(m5)	f	33	44	d
volkswagen	new beetle	1.9	1999	4	manual(m5)	f	35	44	d
volkswagen	new beetle	1.9	1999	4	auto(l4)	f	29	41	d
toyota	corolla	1.8	2008	4	manual(m5)	f	28	37	r
honda	civic	1.8	2008	4	auto(l5)	f	25	36	r
honda	civic	1.8	2008	4	auto(l5)	f	24	36	c

Minimums with slice_min():

mpg %>% 
  slice_min(hwy, n=2) # the two lowest highway miles per gallon. if there are ties they all get printed

ABCDEFGHIJ0123456789

manufacturer <chr>	model <chr>	displ <dbl>	year <int>	cyl <int>	trans <chr>	drv <chr>	cty <int>	hwy <int>
dodge	dakota pickup 4wd	4.7	2008	8	auto(l5)	4	9	12
dodge	durango 4wd	4.7	2008	8	auto(l5)	4	9	12
dodge	ram 1500 pickup 4wd	4.7	2008	8	auto(l5)	4	9	12
dodge	ram 1500 pickup 4wd	4.7	2008	8	manual(m6)	4	9	12
jeep	grand cherokee 4wd	4.7	2008	8	auto(l5)	4	9	12

Random samples with slice_sample():

mpg %>% 
  slice_sample(n=3) # pick three rows at random

ABCDEFGHIJ0123456789

manufacturer <chr>	model <chr>	displ <dbl>	year <int>	cyl <int>	trans <chr>	drv <chr>	cty <int>	hwy <int>
pontiac	grand prix	3.8	1999	6	auto(l4)	f	16	26
dodge	ram 1500 pickup 4wd	4.7	2008	8	manual(m6)	4	9	12
audi	a4 quattro	1.8	1999	4	manual(m5)	4	18	26

2.2.1 Slicing and grouping

When you group_by() a data frame slice_() will return subsets of each group:

mpg %>% 
  group_by(class) %>% # group by class 
  slice_min(hwy, n=1) # bottom two hwy by class

ABCDEFGHIJ0123456789

manufacturer <chr>	model <chr>	displ <dbl>	year <int>	cyl <int>	trans <chr>	drv <chr>	cty <int>	hwy <int>
chevrolet	corvette	5.7	1999	8	auto(l4)	r	15	23
volkswagen	jetta	2.8	1999	6	auto(l4)	f	16	23
audi	a6 quattro	4.2	2008	8	auto(s6)	4	16	23
dodge	caravan 2wd	3.3	2008	6	auto(l4)	f	11	17
dodge	dakota pickup 4wd	4.7	2008	8	auto(l5)	4	9	12
dodge	ram 1500 pickup 4wd	4.7	2008	8	auto(l5)	4	9	12
dodge	ram 1500 pickup 4wd	4.7	2008	8	manual(m6)	4	9	12
ford	mustang	5.4	2008	8	manual(m6)	r	14	20
dodge	durango 4wd	4.7	2008	8	auto(l5)	4	9	12
jeep	grand cherokee 4wd	4.7	2008	8	auto(l5)	4	9	12

If a data frame is already grouped then slice_() will always subset by group under the hood. If you want subsets not by group then you have to ungroup(). See below in the section on mutate(). This often happens when you group a data frame to create a new variable.

2.3 Filtering

filter() with Boolean logic:

==: “equal to”
!=: “not equal to”
>: “greater than”
>=: “greater than or equal to”
<: “less than”
<=: “less than or equal to”
&: “and”
|: “or”

Boolean logic is any test that returns true or false:

2 == 3

[1] FALSE

2 != 3

[1] TRUE

2 < 3

[1] TRUE

Some examples:

mpg %>% 
  filter(year == "1999") %>% # filter all cars made in 1999
  slice_head(n=5) # view the first 5 rows

ABCDEFGHIJ0123456789

manufacturer <chr>	model <chr>	displ <dbl>	year <int>	cyl <int>	trans <chr>	drv <chr>	cty <int>	hwy <int>	fl <chr>
audi	a4	1.8	1999	4	auto(l5)	f	18	29	p
audi	a4	1.8	1999	4	manual(m5)	f	21	29	p
audi	a4	2.8	1999	6	auto(l5)	f	16	26	p
audi	a4	2.8	1999	6	manual(m5)	f	18	26	p
audi	a4 quattro	1.8	1999	4	manual(m5)	4	18	26	p

mpg %>% 
  filter(hwy >= 25) %>% # filter all cars with at least 25 mpg highway
  slice_head(n=5) # view the first 5 rows

ABCDEFGHIJ0123456789

manufacturer <chr>	model <chr>	displ <dbl>	year <int>	cyl <int>	trans <chr>	drv <chr>	cty <int>	hwy <int>	fl <chr>
audi	a4	1.8	1999	4	auto(l5)	f	18	29	p
audi	a4	1.8	1999	4	manual(m5)	f	21	29	p
audi	a4	2.0	2008	4	manual(m6)	f	20	31	p
audi	a4	2.0	2008	4	auto(av)	f	21	30	p
audi	a4	2.8	1999	6	auto(l5)	f	16	26	p

mpg %>% 
  filter(year == "1999" & model != "a4" & hwy >= 25) %>% # filter cars made in 1999, that aren't a4's, and have at least 25 mgp highway
  slice_head(n=5) # view the first 5 rows

ABCDEFGHIJ0123456789

manufacturer <chr>	model <chr>	displ <dbl>	year <int>	cyl <int>	trans <chr>	drv <chr>	cty <int>	hwy <int>	fl <chr>
audi	a4 quattro	1.8	1999	4	manual(m5)	4	18	26	p
audi	a4 quattro	1.8	1999	4	auto(l5)	4	16	25	p
audi	a4 quattro	2.8	1999	6	auto(l5)	4	15	25	p
audi	a4 quattro	2.8	1999	6	manual(m5)	4	17	25	p
chevrolet	corvette	5.7	1999	8	manual(m6)	r	16	26	p

2.4 Mutating

Create and modify variables (data frame columns) with mutate()

2.4.1 Create a new variable

For example, create a column called mean_hwy that calculates average highway miles per gallon:

mpg %>% 
  mutate(mean_hwy = mean(hwy)) %>% 
  select(manufacturer, model, hwy, mean_hwy) %>% 
  slice_head(n=5)

ABCDEFGHIJ0123456789

manufacturer <chr>	model <chr>	hwy <int>	mean_hwy <dbl>
audi	a4	29	23.44017
audi	a4	29	23.44017
audi	a4	31	23.44017
audi	a4	30	23.44017
audi	a4	26	23.44017

2.4.2 Create a new variable and store it as a column

To save the new variable you have to re-assign the data frame:

mpg = mpg %>% 
  mutate(mean_hwy = mean(hwy)) 

Now mpg has a new column called mean_hwy.

2.4.3 Mutating while grouping

When you create a new variable and save it to the data you re-assign the data.

When grouping with group_by() to create a new column, the re-assigned data will be grouped, which can affect the slice_() functions.

The solution is to ungroup() after mutate().

For instance, add a column called “mean_hwy_class” that calculates average highway miles per gallon by class:

# first create the variable
mpg = mpg %>% # take the data, THEN
  group_by(class) %>% # group by class, THEN
  mutate(mean_hwy_class = mean(hwy)) %>% # create the new variable, THEN
  ungroup() # ungroup the data

Why ungroup()? Because otherwise slice_() and other functions won’t return the output you expect. So better safe than sorry. When grouping to create a variable make sure you ungroup at the end.

Now we can slice in general:

mpg %>% 
  select(manufacturer, model, hwy, mean_hwy_class) %>% 
  slice_head(n=2)

ABCDEFGHIJ0123456789

manufacturer <chr>	model <chr>	hwy <int>	mean_hwy_class <dbl>
audi	a4	29	28.29787
audi	a4	29	28.29787

2.4.4 Mutating and frequency tables

Use n() to calculate frequency and then use mutate() to calculate relative frequency:

mpg %>% 
  group_by(class) %>% 
  summarise(frequency = n()) %>% 
  mutate(relative_frequency = frequency / sum(frequency))

ABCDEFGHIJ0123456789

class <chr>	frequency <int>	relative_frequency <dbl>
2seater	5	0.02136752
compact	47	0.20085470
midsize	41	0.17521368
minivan	11	0.04700855
pickup	33	0.14102564
subcompact	35	0.14957265
suv	62	0.26495726

3 Visualizing data

3.1 Plotting distributions

3.1.1 Histograms

Histograms with ggplot and geom_histogram():

mpg %>% 
  ggplot(aes(x = cty)) + # blank canvas: choose the data and the x-axis variable
  geom_histogram() # add geom layer: distribution

Faceted histograms with facet_wrap():

mpg %>% 
  ggplot(aes(x = cty)) + # blank canvas: choose the data and the x-axis variable
  geom_histogram() + # add geom layer:  distribution
  facet_wrap(~class) # add facetting (note the "~" before the categorical variable)

3.1.2 Cumulative distributions

Percentiles and cumulative distributions with ggplot and stat_ecdf():

mpg %>% 
  ggplot(aes(x=cty)) +  # blank canvas: choose the data and the x-axis variable
  stat_ecdf() # add geom layer: cumulative distribution

You can add a vertical line with geom_vline() to make it easier to see a percentile. For instance, view percent of cars with less than 15 miles per gallon:

mpg %>% 
  ggplot(aes(x=cty)) +  # blank canvas: choose the data and the x-axis variable
  stat_ecdf() + # add geom layer: cumulative distribution
  geom_vline(xintercept = 15, color="red") # verticle 

3.1.3 Box plots

geom_boxplot()

mpg %>% 
  ggplot(aes(x = hwy, y = class)) + # x is continuous, y is categorical
  geom_boxplot() 

or:

mpg %>% 
  ggplot(aes(x = class, y = hwy)) + # x is categorical, y is continuous
  geom_boxplot() 

3.2 Scatterplot

geom_point():

mpg %>% 
  ggplot(aes(x = cty, y = hwy)) + 
  geom_point() 

3.2.1 Scatterplot with regression line

geom_smooth(method = "lm"):

mpg %>% 
  ggplot(aes(x = cty, y = hwy)) + 
  geom_point() + # scatter-plot
  geom_smooth(method = "lm") # regression line

4 Correlation and regression

4.1 Covariance

cov():

mpg %>% 
  summarise(cov(x=cty, y=hwy))

ABCDEFGHIJ0123456789

cov(x = cty, y = hwy) <dbl>
24.22543

4.2 Correlation

cor():

mpg %>% 
  summarise(cor(x=cty, y=hwy))

ABCDEFGHIJ0123456789

cor(x = cty, y = hwy) <dbl>
0.9559159

4.3 Regression

lm()

Simple linear regression (one $x$ variable):

$\begin{aligned} y &= f(x) \\ &= \beta_0 + \beta_1(x) + \epsilon \end{aligned}$ In lm() the $y$ and $x$ variables are separated by ~:

mpg %>% 
  lm(formula = cty ~ hwy, data = .) # the "." means "use the data from the pipe %>%"


Call:
lm(formula = cty ~ hwy, data = .)

Coefficients:
(Intercept)          hwy  
     0.8442       0.6832

Multiple linear regression (multiple $x$ variables):

$\begin{aligned} y &= f(\mathbf{X}) \\ &= f(x_1, x_2, \dots) \\ &= \beta_0 + \beta_1(x_1) + \beta_2(x_2) + \dots + \epsilon \end{aligned}$ In lm() the $x$ variables are separated by +:

mpg %>% 
  lm(formula = cty ~ hwy + cyl + displ, data = .)


Call:
lm(formula = cty ~ hwy + cyl + displ, data = .)

Coefficients:
(Intercept)          hwy          cyl        displ  
    6.08786      0.58092     -0.44827     -0.05935

4.4 `summary()`

View hypothesis tests and regression diagnostics with summary():

mpg %>% 
  lm(formula = cty ~ hwy + cyl + displ, data = .) %>% 
  summary()


Call:
lm(formula = cty ~ hwy + cyl + displ, data = .)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.0347 -0.6012 -0.0229  0.7397  5.2573 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  6.08786    0.83226   7.315 4.25e-12 ***
hwy          0.58092    0.02010  28.900  < 2e-16 ***
cyl         -0.44827    0.13010  -3.446 0.000677 ***
displ       -0.05935    0.16351  -0.363 0.716971    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.148 on 230 degrees of freedom
Multiple R-squared:  0.9281,    Adjusted R-squared:  0.9272 
F-statistic: 989.9 on 3 and 230 DF,  p-value: < 2.2e-16

4.5 Plotting regression results

Use the package sJplot. (If you forgot how to install package, see here.)

library(sjPlot)

The function you want is plot_model. The baseline plot shows the coefficients and standard errors:

mpg %>% 
  lm(formula = cty ~ hwy + class, data = .) %>% 
  plot_model(model = .)

To plot predicted values you can set type = "pred" and then choose which coefficient to plot by setting terms:

mpg %>% 
  lm(formula = cty ~ hwy + class, data = .) %>% 
  plot_model(model = ., type = "pred", terms = c("hwy"))

The terms argument accepts multiple terms:

mpg %>% 
  lm(formula = cty ~ hwy + class, data = .) %>% 
  plot_model(model = ., type = "pred", terms = c("hwy", "class"))

This is useful when you have an interaction effect (e.g., hwy*class):

mpg %>% 
  lm(formula = cty ~ hwy + class + hwy*class, data = .) %>% 
  plot_model(model = ., type = "pred", terms = c("hwy", "class"))

sJplot uses ggplot so you can add ggplot stuff to it, like a different theme and titles:

mpg %>% 
  lm(formula = cty ~ hwy + class + hwy*class, data = .) %>% 
  plot_model(model = ., type = "pred", terms = c("hwy", "class")) + 
  labs(x = "Highway miles per gallon", y = "Predicted city miles per gallon",
       title = "A very interesting linear model", subtitle = "So interesting") + 
  theme_minimal()

The package has tons of great features. Check out the website!

5 Quick tables

5.1 R
5.2 Math

Function	Description
`%>%`	Pipe operator (“and then”)
`summarise()`	Summarize a vector or multiple vectors from a data frame
`mean()`	Calculate the mean of a vector
`median()`	Calculate the median of a vector
`sd()`	Calculate the standard deviation of a vector
`n()`	Count the number of observations. Takes no argument.
`group_by()`	Group observations by a categorical variable
`select()`	Select certain columns
`slice_()`	Slice rows from the data
`slice_head(n=5)`	View the head (first five rows) of the data. `n =` can be any number.
`slice_max(var, n=5)`	View the rows with the 5 highest values of column “var”
`slice_min(var, n=5)`	View the rows with the 5 lowest values of column “var”
`slice_sample(n=5)`	Draw 5 rows at random
`filter()`	Filter observations
`mutate()`	Create a new vector
`cov()`	Calculate the covariation between two variables
`cor()`	Calculate the correlation between two variables
`lm()`	Estimate a linear regression
`ifelse()`	Create a vector based on a “True/False” test
`ggplot()`	Create a base plot
`geom_histogram()`	Histogram
`stat_ecdf()`	Cumulative distribution plot
`geom_boxplot()`	Boxplot
`geom_point()`	Scatter plot
`geom_smooth(method = “lm”)`	Regression line

Term	Meaning	Pronunciation	Formula/Example
$x_i$	data point $i$	“x i”
$n$	sample size
$N$	population size
$\bar{x}$	the sample mean	“x bar”	$\frac{\sum_{i=1}^n x_i}{n}$
$\mu$	the population mean	“mu”
$s^2$	the sample variance		$\frac{\sum (x_i - \bar{x})^2}{n-1}$
$\sigma^2$	the population variance
$s$	the sample standard deviation		$\sqrt{s^2}$
$\sigma$	the population standard deviation	“sigma”
$z_i$	z-score for observation $i$		$z_i = \frac{x_i - \bar{x}}{s}$
$\beta$	regression coefficient	“beta”	$y = \beta_0 + \beta_1 x + \epsilon$
$\hat{\beta}$	estimated value of regression coefficient	“beta hat”
$\epsilon$	regression error	“epsilon”
$\sum$	summation operator	“sum”	$\sum_{i=1}^2 x_i = x_1 + x_2$
$s_{xy}$	covariation between two variables $x$ and $y$		$\frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{n-1} \in [-\infty,\infty]$
$r_{xy}$	correlation between two variables $x$ and $y$		$\frac{s_{xy}}{s_x s_y} \in [-1,1]$

---
title: "R and tidyverse code checkpoints"
subtitle: "SuffolkEcon"
author: ""
date: 
output: 
  html_notebook:
    number_sections: true
    theme: readable
    highlight: pygments
    toc: true
    toc_float: 
      collapsed: yes
---

 
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# Set-up {-}

Load the tidyverse:

```{r setup, message=FALSE, warning=FALSE}
library(tidyverse) 
```

The `tidyverse` provides the data `mpg` to demonstrate methods. `mpg` has the mileage (`cty` for city, `hwy` for highway) for a bunch of different cars:

```{r load data}
data("mpg") # load the data mpg

# view the first 5 rows
mpg %>% 
  slice_head(n=5)
```

# Summarizing Data 

## The pipe and `summarise()`

All summarizing operations work like this: 

```{r, eval=FALSE}
data %>% # the pipe: "and then"
  summarise() 
```


* the pipe (`%>%`, "and then")
* [`summarise()`](https://dplyr.tidyverse.org/reference/summarise.html)

Inside `summarise()` you can use functions like `mean()`, `median()` and so on.


### mean

`mean()`

```{r mean}
mpg %>% # take the data, THEN
  summarise(mean(cty)) # summarize: mean
```

**Note.** `cty` is a numerical variable.

### median

`median()`

```{r median}
mpg %>% # take the data, THEN
  summarise(median(cty)) # summarize: median
```

### standard deviation

`sd()`

```{r sd}
mpg %>% # take the data, THEN
  summarise(sd(cty)) # summarize: standard deviation
```

### counting observations

[`n()` (counting)](https://dplyr.tidyverse.org/reference/n.html)


```{r count}
mpg %>% # take the data, THEN
  summarise(n()) # summarize: count number of observations
```

**Why doesn't `n()` take an argument?** Because it counts the number of rows, not columns.

### multiple summaries

You can put as many functions as you want inside `summarise()`:

```{r summarise}
mpg %>% # take the data, THEN
  summarise(mean(cty), median(cty), sd(cty), n()) # summarize: mean, median, standard deviation, count
```

### naming variables inside `summarise()`

You can name variables inside `summarise()` using standard assignment:

```{r name summarise}
mpg %>% # take the data, THEN
  summarise(avg_cty = mean(cty), median_cty = median(cty)) # summarize: mean, median
```


## Grouping (`group_by()`)  

[`group_by()`](https://dplyr.tidyverse.org/reference/group_by.html):

```{r group_by, message=FALSE}
mpg %>% # take the data, THEN
  group_by(class) %>% # group it by car class (e.g., compact, pickup) THEN
  summarise(mean(cty), median(cty), sd(cty), n()) # summarize
```

**Note.** `class` is a categorical variable.

# Manipulating data

## Selecting columns

`select()` certain columns

```{r no select}
mpg %>% # all the columns
  slice_head(n=5) # view the first 5 rows
```


```{r yes select}
mpg %>% # all the columns
  select(manufacturer, model, hwy) %>% # select some of the columns
  slice_head(n=5) # view the first 5 rows
```

## Slicing

All slice operators begin with `slice_` and take an optional `n=` argument that specifies the number of rows you want to see. More [here](https://dplyr.tidyverse.org/reference/slice.html). 

Subsets with `slice_head()`:

```{r slice_head}
mpg %>% 
  slice_head(n=10) # view the first 10 rows
```


Maximums with `slice_max()`:

```{r slice_max}
mpg %>% 
  slice_max(hwy, n=5) # the five highest highway miles per gallon. if there are ties they all get printed
```

Minimums with `slice_min()`:

```{r slice_min}
mpg %>% 
  slice_min(hwy, n=2) # the two lowest highway miles per gallon. if there are ties they all get printed
```

Random samples with `slice_sample()`:

```{r slice_sample}
mpg %>% 
  slice_sample(n=3) # pick three rows at random
```

### Slicing and grouping

When you `group_by()` a data frame `slice_()` will return subsets of each group:

```{r group_by and slice_}
mpg %>% 
  group_by(class) %>% # group by class 
  slice_min(hwy, n=1) # bottom two hwy by class
```

If a data frame is already grouped then `slice_()` will always subset by group under the hood. If you want subsets not by group then you have to `ungroup()`. See below in the section on `mutate()`. This often happens when you group a data frame to create a new variable. 

## Filtering

[`filter()`](https://dplyr.tidyverse.org/reference/filter.html) with Boolean logic:

* `==`: "equal to"
* `!=`: "not equal to"
* `>`: "greater than"
* `>=`: "greater than or equal to"
* `<`: "less than"
* `<=`: "less than or equal to"
* `&`: "and"
* `|`: "or"

Boolean logic is any test that returns true or false:

```{r boolean equals to}
2 == 3
```

```{r boolean not equals to}
2 != 3
```

```{r boolean less than}
2 < 3
```

Some examples:

```{r filter equals to}
mpg %>% 
  filter(year == "1999") %>% # filter all cars made in 1999
  slice_head(n=5) # view the first 5 rows
```

```{r filter greater than or equals to}
mpg %>% 
  filter(hwy >= 25) %>% # filter all cars with at least 25 mpg highway
  slice_head(n=5) # view the first 5 rows
```


```{r filter many conditions}
mpg %>% 
  filter(year == "1999" & model != "a4" & hwy >= 25) %>% # filter cars made in 1999, that aren't a4's, and have at least 25 mgp highway
  slice_head(n=5) # view the first 5 rows
```


## Mutating

Create and modify variables (data frame columns) with [`mutate()`](https://dplyr.tidyverse.org/reference/mutate.html)

### Create a new variable

For example, create a column called `mean_hwy` that calculates average highway miles per gallon:

```{r mutate dont add column}
mpg %>% 
  mutate(mean_hwy = mean(hwy)) %>% 
  select(manufacturer, model, hwy, mean_hwy) %>% 
  slice_head(n=5)
```

### Create a new variable and store it as a column

To save the new variable you have to re-assign the data frame:

```{r mutate yes add column}
mpg = mpg %>% 
  mutate(mean_hwy = mean(hwy)) 
```

Now `mpg` has a new column called `mean_hwy`.

### Mutating while grouping

When you create a new variable and save it to the data you re-assign the data. 

When grouping with `group_by()` to create a new column, the re-assigned data will be grouped, which can affect the `slice_()` functions. 

The solution is to `ungroup()` after `mutate()`. 

For instance, add a column called "mean_hwy_class" that calculates average highway miles per gallon by class:

```{r group_by and mutate, message=FALSE}
# first create the variable
mpg = mpg %>% # take the data, THEN
  group_by(class) %>% # group by class, THEN
  mutate(mean_hwy_class = mean(hwy)) %>% # create the new variable, THEN
  ungroup() # ungroup the data
```

Why `ungroup()`? Because otherwise `slice_()` and other functions won't return the output you expect. So better safe than sorry. When grouping *to create a variable* make sure you ungroup at the end.

Now we can slice in general:

```{r view group_by mutate output}
mpg %>% 
  select(manufacturer, model, hwy, mean_hwy_class) %>% 
  slice_head(n=2)
```


### Mutating and frequency tables

Use `n()` to calculate frequency and then use `mutate()` to calculate relative frequency:

```{r frequency and relative frequency, message=FALSE}
mpg %>% 
  group_by(class) %>% 
  summarise(frequency = n()) %>% 
  mutate(relative_frequency = frequency / sum(frequency))
```

# Visualizing data

## Plotting distributions 

### Histograms

Histograms with `ggplot` and [`geom_histogram()`](https://ggplot2.tidyverse.org/reference/geom_histogram.html):

```{r histogram}
mpg %>% 
  ggplot(aes(x = cty)) + # blank canvas: choose the data and the x-axis variable
  geom_histogram() # add geom layer: distribution
```

Faceted histograms with [`facet_wrap()`](https://ggplot2.tidyverse.org/reference/facet_wrap.html):

```{r facetted histogram}
mpg %>% 
  ggplot(aes(x = cty)) + # blank canvas: choose the data and the x-axis variable
  geom_histogram() + # add geom layer:  distribution
  facet_wrap(~class) # add facetting (note the "~" before the categorical variable)
```

### Cumulative distributions

Percentiles and cumulative distributions with `ggplot` and [`stat_ecdf()`](https://ggplot2.tidyverse.org/reference/stat_ecdf.html):

```{r percentile (cumulative distribution)}
mpg %>% 
  ggplot(aes(x=cty)) +  # blank canvas: choose the data and the x-axis variable
  stat_ecdf() # add geom layer: cumulative distribution
```

You can add a vertical line with `geom_vline()` to make it easier to see a percentile. For instance, view percent of cars with less than 15 miles per gallon:

```{r percentile (cumulative distribution) with vline}
mpg %>% 
  ggplot(aes(x=cty)) +  # blank canvas: choose the data and the x-axis variable
  stat_ecdf() + # add geom layer: cumulative distribution
  geom_vline(xintercept = 15, color="red") # verticle 
```

### Box plots

[`geom_boxplot()`](https://ggplot2.tidyverse.org/reference/geom_boxplot.html)

```{r box plot x continuous}
mpg %>% 
  ggplot(aes(x = hwy, y = class)) + # x is continuous, y is categorical
  geom_boxplot() 
```

or: 

```{r box plot x categorical}
mpg %>% 
  ggplot(aes(x = class, y = hwy)) + # x is categorical, y is continuous
  geom_boxplot() 
```


## Scatterplot

`geom_point()`:

```{r geom_point}
mpg %>% 
  ggplot(aes(x = cty, y = hwy)) + 
  geom_point() 
```

### Scatterplot with regression line

[`geom_smooth(method = "lm")`](https://ggplot2.tidyverse.org/reference/geom_smooth.html):

```{r geom_smooth}
mpg %>% 
  ggplot(aes(x = cty, y = hwy)) + 
  geom_point() + # scatter-plot
  geom_smooth(method = "lm") # regression line
```

# Correlation and regression

## Covariance

`cov()`:

```{r cov}
mpg %>% 
  summarise(cov(x=cty, y=hwy))
```

## Correlation

`cor()`:

```{r cor}
mpg %>% 
  summarise(cor(x=cty, y=hwy))
```


## Regression

`lm()`

Simple linear regression (one $x$ variable):

$$
\begin{aligned}
y &= f(x) \\
  &= \beta_0 + \beta_1(x) + \epsilon
\end{aligned}
$$
In `lm()` the $y$ and $x$ variables are separated by `~`:

```{r lm1}
mpg %>% 
  lm(formula = cty ~ hwy, data = .) # the "." means "use the data from the pipe %>%"
```

Multiple linear regression (multiple $x$ variables):

$$
\begin{aligned}
y &= f(\mathbf{X}) \\
  &= f(x_1, x_2, \dots) \\
  &= \beta_0 + \beta_1(x_1) + \beta_2(x_2) + \dots + \epsilon
\end{aligned}
$$
In `lm()` the $x$ variables are separated by `+`:

```{r lm2}
mpg %>% 
  lm(formula = cty ~ hwy + cyl + displ, data = .)
```

## `summary()`

View hypothesis tests and regression diagnostics with `summary()`:

```{r summary2}
mpg %>% 
  lm(formula = cty ~ hwy + cyl + displ, data = .) %>% 
  summary()
```

## Plotting regression results

Use the package `sJplot`. (If you forgot how to install package, see [here](https://lrdegeest.github.io/stats/r.html#3_Install_packages).)

```{r library sjplot, message=FALSE}
library(sjPlot)
```

The function you want is `plot_model`. The baseline plot shows the coefficients and standard errors:

```{r sjPlot demo coefficients}
mpg %>% 
  lm(formula = cty ~ hwy + class, data = .) %>% 
  plot_model(model = .)
```

To plot predicted values you can set `type = "pred"` and then choose which coefficient to plot by setting `terms`:

```{r sjPlot demo predicted values}
mpg %>% 
  lm(formula = cty ~ hwy + class, data = .) %>% 
  plot_model(model = ., type = "pred", terms = c("hwy"))
```

The `terms` argument accepts multiple terms:

```{r sjPlot demo predicted values multiple terms}
mpg %>% 
  lm(formula = cty ~ hwy + class, data = .) %>% 
  plot_model(model = ., type = "pred", terms = c("hwy", "class"))
```

This is useful when you have an interaction effect (e.g., `hwy*class`):

```{r sjPlot demo predicted values interaction}
mpg %>% 
  lm(formula = cty ~ hwy + class + hwy*class, data = .) %>% 
  plot_model(model = ., type = "pred", terms = c("hwy", "class"))
```

`sJplot` uses `ggplot` so you can add `ggplot` stuff to it, like a different theme and titles:

```{r sjPlot demo predicted values interaction spiffy}
mpg %>% 
  lm(formula = cty ~ hwy + class + hwy*class, data = .) %>% 
  plot_model(model = ., type = "pred", terms = c("hwy", "class")) + 
  labs(x = "Highway miles per gallon", y = "Predicted city miles per gallon",
       title = "A very interesting linear model", subtitle = "So interesting") + 
  theme_minimal()
```

The package has tons of great features. Check out the [website!](https://strengejacke.github.io/sjPlot/)

# Quick tables {#table .tabset}

## R

**Function**|**Description**
-----|-----
[<code>%>%</code>](https://magrittr.tidyverse.org/reference/pipe.html)|Pipe operator ("and then")
[<code>summarise()</code>](https://dplyr.tidyverse.org/reference/summarise.html)|Summarize a vector or multiple vectors from a data frame
[<code>mean()</code>](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/mean)|Calculate the mean of a vector
[<code>median()</code>](https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/median)|Calculate the median of a vector
[<code>sd()</code>](https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/sd)|Calculate the standard deviation of a vector
[<code>n()</code>](https://dplyr.tidyverse.org/reference/n.html)|Count the number of observations. Takes no argument.
[<code>group\_by()</code>](https://dplyr.tidyverse.org/reference/group\_by.html)|Group observations by a categorical variable
[<code>select()</code>](https://dplyr.tidyverse.org/reference/select.html)|Select certain columns
[<code>slice\_()</code>](https://dplyr.tidyverse.org/reference/slice.html)|Slice rows from the data
<code>slice\_head(n=5)</code>|View the head (first five rows) of the data. <code>n = </code> can be any number.
<code>slice\_max(var, n=5)</code>|View the rows with the 5 highest values of column "var"
<code>slice\_min(var, n=5)</code>|View the rows with the 5 lowest values of column "var"
<code>slice\_sample(n=5)</code>|Draw 5 rows at random
[<code>filter()</code>](https://dplyr.tidyverse.org/reference/filter.html)|Filter observations
[<code>mutate()</code>](https://dplyr.tidyverse.org/reference/mutate.html)|Create a new vector
[<code>cov()</code>](https://www.rdocumentation.org/packages/pbdDMAT/versions/0.5-1/topics/covariance)|Calculate the covariation between two variables
[<code>cor()</code>](https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/cor)|Calculate the correlation between two variables
[<code>lm()</code>](https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/lm)|Estimate a linear regression
[<code>ifelse()</code>](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/ifelse)|Create a vector based on a "True/False" test
[<code>ggplot()</code>](https://ggplot2.tidyverse.org/reference/ggplot.html)|Create a base plot
[<code>geom\_histogram()</code>](https://ggplot2.tidyverse.org/reference/geom\_histogram.html)|Histogram
[<code>stat\_ecdf()</code>](https://ggplot2.tidyverse.org/reference/stat\_ecdf.html)|Cumulative distribution plot
[<code>geom\_boxplot()</code>](https://ggplot2.tidyverse.org/reference/geom\_boxplot.html)|Boxplot
[<code>geom\_point()</code>](https://ggplot2.tidyverse.org/reference/geom\_point.html)|Scatter plot
[<code>geom\_smooth(method = "lm")</code>](https://ggplot2.tidyverse.org/reference/geom\_smooth.html)|Regression line

## Math

**Term**|**Meaning**|**Pronunciation**|**Formula/Example**
:-----:|-----|:-----:|:-----:
$x_i$|data point $i$|"x i" | 
$n$|sample size| | 
$N$|population size| | 
$\bar{x}$|the sample mean|"x bar"|$\frac{\sum_{i=1}^n x_i}{n}$
$\mu$|the population mean|"mu"| 
$s^2$|the sample variance| |$\frac{\sum (x_i - \bar{x})^2}{n-1}$
$\sigma^2$|the population variance| | 
$s$|the sample standard deviation| |$\sqrt{s^2}$
$\sigma$|the population standard deviation|"sigma"| 
$z_i$|z-score for observation $i$| |$z_i = \frac{x_i - \bar{x}}{s}$
$\beta$|regression coefficient|"beta"|$y = \beta_0 + \beta_1 x + \epsilon$
$\hat{\beta}$|estimated value of regression coefficient|"beta hat"| 
$\epsilon$|regression error|"epsilon"| 
$\sum$|summation operator|"sum"|$\sum_{i=1}^2 x_i  = x_1 + x_2$
$s_{xy}$|covariation between two variables $x$ and $y$| |$\frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{n-1} \in [-\infty,\infty]$
$r_{xy}$|correlation between two variables $x$ and $y$| |$\frac{s_{xy}}{s_x s_y} \in [-1,1]$

R and tidyverse code checkpoints

SuffolkEcon

Set-up

1 Summarizing Data

1.1 The pipe and `summarise()`

1.1.1 mean

1.1.2 median

1.1.3 standard deviation

1.1.4 counting observations

1.1.5 multiple summaries

1.1.6 naming variables inside `summarise()`

1.2 Grouping (`group_by()`)

2 Manipulating data

2.1 Selecting columns

2.2 Slicing

2.2.1 Slicing and grouping

2.3 Filtering

2.4 Mutating

2.4.1 Create a new variable

2.4.2 Create a new variable and store it as a column

2.4.3 Mutating while grouping

2.4.4 Mutating and frequency tables

3 Visualizing data

3.1 Plotting distributions

3.1.1 Histograms

3.1.2 Cumulative distributions

3.1.3 Box plots

3.2 Scatterplot

3.2.1 Scatterplot with regression line

4 Correlation and regression

4.1 Covariance

4.2 Correlation

4.3 Regression

4.4 `summary()`

4.5 Plotting regression results

5 Quick tables

R and tidyverse code checkpoints

SuffolkEcon

Set-up

1 Summarizing Data

1.1 The pipe and summarise()

1.1.1 mean

1.1.2 median

1.1.3 standard deviation

1.1.4 counting observations

1.1.5 multiple summaries

1.1.6 naming variables inside summarise()

1.2 Grouping (group_by())

2 Manipulating data

2.1 Selecting columns

2.2 Slicing

2.2.1 Slicing and grouping

2.3 Filtering

2.4 Mutating

2.4.1 Create a new variable

2.4.2 Create a new variable and store it as a column

2.4.3 Mutating while grouping

2.4.4 Mutating and frequency tables

3 Visualizing data

3.1 Plotting distributions

3.1.1 Histograms

3.1.2 Cumulative distributions

3.1.3 Box plots

3.2 Scatterplot

3.2.1 Scatterplot with regression line

4 Correlation and regression

4.1 Covariance

4.2 Correlation

4.3 Regression

4.4 summary()

4.5 Plotting regression results

5 Quick tables

1.1 The pipe and `summarise()`

1.1.6 naming variables inside `summarise()`

1.2 Grouping (`group_by()`)

4.4 `summary()`