Zrobiono rodziały 4,5

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# author: Cezary Pukownik
# indeks: s444337
library(tidyverse)
#' # 2.3.1
#' ## Zadanie 1
airquality %>%
select(Ozone, Solar.R, Wind, Temp) %>%
filter(Ozone>80)
#' ## Zadanie 2
#install.packages('weathermetrics')
library(weathermetrics)
airquality %>%
mutate(TempC=fahrenheit.to.celsius(Temp))
#' # 2.4.1
#' ## Zadanie 1
as_tibble(airquality)
#' ## Zadanie 2
tibble(litery=letters[6:11],
miesiace=month.name[1:6])
#' # 3.2.4
#' ## Zadanie 1
ggplot(data=mpg)
#' Co widzisz?
#' Szare. puste pole
#' ## Zadanie 2
as_tibble(mtcars)
#' liczba wierszy: 32
#' ## Zadanie 3
?mpg
#' drv
#' f = front-wheel drive, r = rear wheel drive, 4 = 4wd
#' ## Zadanie 4
ggplot(aes(x=hwy, y=cyl), data=as_tibble(mpg)) + geom_point()
#' ## Zadanie 5
ggplot(aes(x=class, y=drv), data=as_tibble(mpg)) + geom_point()
#' Dlaczego wykres jest bezuzyteczny?
#' Wykres nie pokazuje żadnych liczbowych informacji na temat danych
#' Zostały wykorzystane dwie cechy typu categorical
#' Jedyną informacją jest to, czy dana kombinacja drv i class istanieje.
#' # 3.3.1
#' ## Zadanie 1
#' ustalenie parametru color wewnątrz funckcji aes
#' powinno być nazwą kolumny z categoriami, po których
#' punkty zostaną pogrupowane, a nie istanieje kolumna "blue"
#' w zbriorze danych
#'
#' parametr color powinien zostać ustalony wewnątrz
#' funkcji geom_point. Poprawiony kod poniżej.
ggplot(data = mpg) +
geom_point(mapping = aes(x = displ, y = hwy), color = "blue")
#' ## Zadanie 2
mpg
#' kolumny z danymi kategorialnymi to:
#' manufacturer, model, trans, frv, fl, class
#' można zwrócić uwagę na typ danych w kolumnie
#' jeśli typ to <chr>, to najprawdopodobniej jest to dana kategorialna
#' ## Zadanie 3
ggplot(data = mpg) +
geom_point(mapping = aes(x=displ, y=hwy, color=displ, size=displ))
#' zmienna ciągła jest interpolowania między dwoma kolorami tworząc gradient
#' tak jak samo z rozmiarem, rozmiar jest skalowany
#' w przypadku shape powoduje to błąd. Gdyby podać dane kategorialne
#' podział byłby dyskretny, na różne kolory, wielkości, kształty
#' ## Zadanie 4
#' Przykład w punkcie wyżej
#' Ta sama zmienna bedzie przedstawiona różnymi metodami
#' ## Zadanie 5
#' stroke wpływa na grubuść konturu, obrysu, mozna stosować z punktami i liniami
?geom_point
#' ## Zadanie 6
ggplot(data = mpg) +
geom_point(mapping = aes(x=displ, y=hwy, color=displ < 5))
mpg %>%
filter(displ < 5) %>%
mutate(is_less_than_5=displ < 5)
#' Przypisanie displ < 5 podzieliło data set na dwie grupy
#' TRUE oraz FALSE, w zalezności od tego czy warunek był spełniony
#' czy nie.
#' # 3.5.1
#' ## Zadanie 1
ggplot(data = mpg) +
geom_point(mapping = aes(x = displ, y = hwy)) +
facet_grid(drv ~ displ)
#' ggplot potraktuje ją jako zmienną kategorialną,
#' tworząc siatkę dla kazdej unikatowej wartości zmiennej ciagłęj
#' ## Zadanie 2
ggplot(data = mpg) +
geom_point(mapping = aes(x = drv, y = cyl))
ggplot(data = mpg) +
geom_point(mapping = aes(x = drv, y = cyl)) +
facet_grid(cyl~drv)
#' puste komórki oznacznaczają brak danych
#' ## Zadanie 3
ggplot(data = mpg) +
geom_point(mapping = aes(x = displ, y = hwy)) +
facet_grid(drv ~ .)
ggplot(data = mpg) +
geom_point(mapping = aes(x = displ, y = hwy)) +
facet_grid(. ~ cyl)
#' kropka traktowana jest jako puste pole,
#' wtedy jedna z osi, nie bedzie kategoryzowana
#' ## Zadanie 4
ggplot(data = mpg) +
geom_point(mapping = aes(x = displ, y = hwy)) +
facet_wrap(~ class, nrow = 2)
#' # 3.6.1
#' ## Zadanie 1
#' liniowy - geom_line()
#' pudełkowy - geom_boxplot()
#' histogram - geom_histogram()
#' warstwowy - geom_area()
#' ## Zadanie 2
ggplot(data = mpg, mapping = aes(x = displ, y = hwy, color = drv)) +
geom_point() +
geom_smooth(se = FALSE)
#' ## Zadanie 3
#' show.legend = FALSE, sluży do ukrycia legendy
#' ## Zadanie 4
#' parametr se w funcji geom_smooth() służy do pokazania, lub ukrycia przedziałów ufnośći na wykresie.
#' ## Zadanie 5
#' dwa poniższe wyresy są takie same, różnią się tylko sposobem denifincji mapowania.
#' mapowanie wewnątrz aes w ggplot, przenosi mapowania na wszystkie geometrie, gdy nie sa zdefiniowane inne.
ggplot(data = mpg, mapping = aes(x = displ, y = hwy)) +
geom_point() +
geom_smooth()
ggplot() +
geom_point(data = mpg, mapping = aes(x = displ, y = hwy)) +
geom_smooth(data = mpg, mapping = aes(x = displ, y = hwy))
#' ## Zadanie 6
#' Wykres 1
mpg %>%
ggplot(aes(x=displ, y=hwy)) +
geom_point() +
geom_smooth(se=FALSE)
#' Wykres 2
mpg %>%
ggplot(aes(x=displ, y=hwy, group=drv)) +
geom_point() +
geom_smooth(se=FALSE)
#' Wykres 3
mpg %>%
ggplot(aes(x=displ, y=hwy, color=drv)) +
geom_point() +
geom_smooth(se=FALSE)
#' Wykres 4
mpg %>%
ggplot(aes(x=displ, y=hwy)) +
geom_point(aes(color=drv)) +
geom_smooth(se=FALSE)
#' Wykres 5
mpg %>%
ggplot(aes(x=displ, y=hwy)) +
geom_point(aes(color=drv)) +
geom_smooth(aes(linetype=drv), se=FALSE)
#' Wykres 6
mpg %>%
ggplot(aes(x=displ, y=hwy)) +
geom_point(aes(fill=drv), shape=21, stroke=2, color='white', size=2)
#' # 3.7.1
# Zadanie 1
?stat_summary
#' Funcja stat_summary jest związana w funcją geom_pointrange()
diamonds %>%
ggplot() +
geom_pointrange(aes(x = cut, y = depth), stat='summary')
#' ## Zadanie 2
#' funkcja geom_bar służy do wykresów słupkowych/kolumnowych i jej domyslna statystyka do 'count',
#' funcja geom_col, ma domyślną statystykę 'identity'
#' ## Zadanie 3
#'
#' geom_bar : stat_count
#' geom_col : identity
#' geom_histogram: stat_bin
#' geom_line : identity
#' geom_path : identity
#' geom_step : identity
#' geom_segment : identity
#' geom_curve : identity
#' geom_spoke : identity
#' geom_polygon : identity
#' geom_ribbot : identity
#' geom_area : identity
#' geom_freqpoly : stat_bin
#'
#' ## Zadanie 4
#' ?geom_smmoth : stat_smooth
#' y - predicted value
#' ymin - lower pointwise confidence interval around the mean
#' yman - upper pointwise confidence interval around the mean
#' se = standard error
#'
#' ## Zadanie 5
#' każdy "słupek" jest taki sam
ggplot(data = diamonds) +
geom_bar(mapping = aes(x = cut, y = ..prop..))
ggplot(data = diamonds) +
geom_bar(mapping = aes(x = cut, fill = color, y = ..prop..))
# uzyliśmy group=1, aby nadpisać domysle grupowanie funcji geom_bar, które grupuje po x, czyli po cut,
# dlatego każdy słupek wyglądał identycznie, ponieważ powinniśmy w tym przypadku zgrupować po całym zbiorze, usunąć grupy.
# równie dobrze będzie działać group=2, albo group='abc'
ggplot(data = diamonds) +
geom_bar(mapping = aes(x = cut, fill = color, y = ..prop.., group=1))
#' # 3.8.1
#'
#' ## Zadanie 1
ggplot(data = mpg, mapping = aes(x = cty, y = hwy)) +
geom_point()
#' ## Zadanie 2
#' nakładają się na siebie punkty i nie widać dobrze zagęszczenia
#' mozna poprawić przez dodanie posiiton='jitter'
ggplot(data = mpg, mapping = aes(x = cty, y = hwy)) +
geom_point(position='jitter')
#' ## Zadanie 3
?geom_jitter
#' paremtry width i height
#'
ggplot(data = mpg, mapping = aes(x = cty, y = hwy)) +
geom_jitter(position='jitter')
ggplot(data = mpg, mapping = aes(x = cty, y = hwy)) +
geom_count(position='jitter')
#' obie funcje pokazują zagęszczenie, geom jitter, rozsuwa je aby było widać kazdy punkt.
#' geom count pokazuje zagęszczenie przez parametr size.
#' Zadanie 4
?geom_boxplot
#' domyślne dopasowanie dla geom_boxplot to 'dodge2
mpg %>%
ggplot(aes(x=cty, y=factor(cyl))) +
geom_boxplot()
#' # 3.9.1
#' ## Zadanie 1
mpg %>%
ggplot(aes(x=1, fill=class))+
geom_bar() +
coord_polar()
#' ## Zadanie 2
#' Funcjka labs, służy do dodania etykiet tetułu, opisy osi, i innnych tektów na wykresie
mpg %>%
ggplot(aes(x=1, fill=class))+
geom_bar() +
coord_polar() +
labs(title='Słupkotwy wykres skumulowany',
subtitle='O kordynatach polarnych',
y='Liczba',
x='Wartość dummy')
#' ## Zadanie 3
#' coord_map posiada więcej parametrów, np projectiom, parameters i orientation
#' coord_quickmap, nie posiada tych parametrów.
#' coord_map nada się do większych powirzchni świata, to jest pojekcją powierzchni sfery
#' na plaski 2D. coord_quickmap, nadaje się do map o małym rozmiarze i zachowuje proste linie.
#' ## Zadanie 4
#'
#'
ggplot(data = mpg, mapping = aes(x = cty, y = hwy)) +
geom_point() +
geom_abline() +
coord_fixed()
#' Z wykresu wnioskujemy, że spalanie w mieście i na autostradzie są skorelowane.
#' Jeśli samochód pali dużo w mieście, to pali duzo na autostradzie i odwotnie.
#'
#' Linia ab, pokazuje tam prostą y=x, dzięki temu mamy odniesienie i dodatkowo możemy wywnioskować,
#' że na galonie paliwa, na autostradzie zawsze przejedziemy wiecej niż w mieście.
#'
#' Coord fixed, sprawia że wartości obu osi są w tej samej skali. Obie wartości to liczba przejechanych kilometrów, więc
#' ważne jest zachowanie jednolitej skali.
#'
#' Funckja abline() tworzy linię prostą y=Ax+B stąd nazawa AB Line. Domyslnie A=1, B=0 dlatego abline() to y=x

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---
title: "Cezary Pukownik"
output: html_document
---
***
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```
# Wykształcenie
- **2017 - ...** - Uniwersytet Adama Mickiewicza w Poznaniu kier. Analiza i przetwarzanie danych
- **2013 - 2016** - Uniwesytet Mikołaja Kopernika kier. Matematyka i ekonomia
- **2010 - 2013** - I Liceum im. Mikołaja Kopernika w Toruniu spec. Matematyczno-Informatyczna
# Doświadczenie zawodowe
- **2018 - ...** - Impakt S.A, jako Analityk danych
- **2017 - 2018** - Impakt S.A, jako Młodszy analilityk
- **2016 - 2017** - Impakt S.A, jako Kontroler
> Cytat blokowy[^1]
[^1]: Stopka

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---
title: "Rozmiary diamentów"
date: 2016-08-25
output: html_document
---
```{r setup, include = FALSE}
knitr::opts_chunk$set(echo = FALSE)
library(ggplot2)
library(dplyr)
library(tidyverse)
smaller <- diamonds %>%
filter(carat <= 2.5)
```
Mamy dane o `r nrow(diamonds)` diamentach. Tylko
`r nrow(diamonds) - nrow(smaller)` diamentów jest większych niż 2,5 karata.
Poniżej przedstawiony jest rozkład pozostałych:
```{r, echo = FALSE}
smaller %>%
ggplot(aes(carat)) +
geom_freqpoly(binwidth = 0.01)
```
# Wielkość diamentów w zależności od szlifu, koloru i przejrzystości.
## Wielkość vs. Szlif
```{r}
diamonds %>%
ggplot(aes(x=cut, y=carat)) +
geom_boxplot()
```
## Wielkość vs. Kolor
```{r}
diamonds %>%
ggplot(aes(x=color, y=carat)) +
geom_boxplot()
```
## Wielkość vs. Przejrzystość
```{r}
diamonds %>%
ggplot(aes(x=clarity, y=carat)) +
geom_boxplot()
```
## TOP 20 diamnetów pod względem wielkości
```{r}
diamonds %>%
top_n(20, wt=carat) %>%
knitr::kable()
```
```{r}
comma <- function(x) format(x, digits = 2, big.mark = ",")
diamonds %>%
group_by(carat > 2.5) %>%
summarise(count=n()) %>%
pivot_wider(names_from=`carat > 2.5`, values_from=count) %>%
mutate(bigger_than_2.5 = as.numeric(`TRUE`)/as.numeric(sum(`TRUE`+`FALSE`))) %>%
select(bigger_than_2.5) -> bigger_than_2.5
percent <- bigger_than_2.5$bigger_than_2.5*100
```
Odsetek diamentów większych niż 2.5 karata wynosi `r comma(percent)`%.
```{r a, cache=TRUE}
lubridate::now()
```
```{r b, cache=TRUE}
lubridate::now()
```
```{r c, cache=TRUE}
lubridate::now()
```
```{r d, cache=TRUE}
lubridate::now()
```

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base
ggplot2
dplyr
tidyverse
tibble
tidyr
readr
purrr
stringr
forcats

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---
title: "R Notebook"
output: html_notebook
---
This is an [R Markdown](http://rmarkdown.rstudio.com) Notebook. When you execute code within the notebook, the results appear beneath the code.
Try executing this chunk by clicking the *Run* button within the chunk or by placing your cursor inside it and pressing *Ctrl+Shift+Enter*.
```{r}
plot(cars)
```
Add a new chunk by clicking the *Insert Chunk* button on the toolbar or by pressing *Ctrl+Alt+I*.
When you save the notebook, an HTML file containing the code and output will be saved alongside it (click the *Preview* button or press *Ctrl+Shift+K* to preview the HTML file).
The preview shows you a rendered HTML copy of the contents of the editor. Consequently, unlike *Knit*, *Preview* does not run any R code chunks. Instead, the output of the chunk when it was last run in the editor is displayed.

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---
title: "Ćwiczenie 4.2.1"
output:
pdf_document: default
html_document: default
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```
## R Markdown
This is an R Markdown document. Markdown is a simple formatting syntax for authoring HTML, PDF, and MS Word documents. For more details on using R Markdown see <http://rmarkdown.rstudio.com>.
When you click the **Knit** button a document will be generated that includes both content as well as the output of any embedded R code chunks within the document. You can embed an R code chunk like this:
```{r cars}
summary(cars)
```
## Including Plots
You can also embed plots, for example:
```{r pressure, echo=FALSE}
plot(pressure)
```
Note that the `echo = FALSE` parameter was added to the code chunk to prevent printing of the R code that generated the plot.

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---
title: "R Notebook"
output:
word_document: default
pdf_document: default
html_document:
df_print: paged
---
This is an [R Markdown](http://rmarkdown.rstudio.com) Notebook. When you execute code within the notebook, the results appear beneath the code.
Try executing this chunk by clicking the *Run* button within the chunk or by placing your cursor inside it and pressing *Ctrl+Shift+Enter*.
```{r}
plot(cars)
```
Add a new chunk by clicking the *Insert Chunk* button on the toolbar or by pressing *Ctrl+Alt+I*.
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The preview shows you a rendered HTML copy of the contents of the editor. Consequently, unlike *Knit*, *Preview* does not run any R code chunks. Instead, the output of the chunk when it was last run in the editor is displayed.

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\title{Ćwiczenie 4.2.1}
\author{}
\date{\vspace{-2.5em}}
\begin{document}
\maketitle
\hypertarget{r-markdown}{%
\subsection{R Markdown}\label{r-markdown}}
This is an R Markdown document. Markdown is a simple formatting syntax
for authoring HTML, PDF, and MS Word documents. For more details on
using R Markdown see \url{http://rmarkdown.rstudio.com}.
When you click the \textbf{Knit} button a document will be generated
that includes both content as well as the output of any embedded R code
chunks within the document. You can embed an R code chunk like this:
\begin{Shaded}
\begin{Highlighting}[]
\KeywordTok{summary}\NormalTok{(cars)}
\end{Highlighting}
\end{Shaded}
\begin{verbatim}
## speed dist
## Min. : 4.0 Min. : 2.00
## 1st Qu.:12.0 1st Qu.: 26.00
## Median :15.0 Median : 36.00
## Mean :15.4 Mean : 42.98
## 3rd Qu.:19.0 3rd Qu.: 56.00
## Max. :25.0 Max. :120.00
\end{verbatim}
\hypertarget{including-plots}{%
\subsection{Including Plots}\label{including-plots}}
You can also embed plots, for example:
\includegraphics{Ćwiczenie-421_files/figure-latex/pressure-1.pdf}
Note that the \texttt{echo\ =\ FALSE} parameter was added to the code
chunk to prevent printing of the R code that generated the plot.
\end{document}

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library(tidyverse)
#' # 5.2.1 Ćwiczenia
ggplot(mpg, aes(displ, hwy)) +
geom_point(aes(colour = class)) +
geom_smooth(se = FALSE, method='lm') +
labs(
title = 'Wraz ze wzrostem objętości silnika, spada zasięg mil na galon',
subtitle = 'Wyjątkiem są pojazdy 2-osobowe',
x = "Objętość skokowa silnika (l)",
y = "Gospodarka paliwowa na autostradzie (mpg)",
colour = "Rodzaj samochodu",
caption = 'Cezary Pukownik'
)
#' # 5.3.1 Ćwiczenia
#' ## Zadanie 1
label_11 <- tibble(
displ = Inf,
hwy = Inf,
label = "Większy rozmiar silnika \njest związany z gorszą gospodarką paliwową."
)
label_01 <- tibble(
displ = -Inf,
hwy = Inf,
label = "Większy rozmiar silnika \njest związany z gorszą gospodarką paliwową."
)
label_10 <- tibble(
displ = Inf,
hwy = -Inf,
label = "Większy rozmiar silnika \njest związany z gorszą gospodarką paliwową."
)
label_00 <- tibble(
displ = -Inf,
hwy = -Inf,
label = "Większy rozmiar silnika \njest związany z gorszą gospodarką paliwową."
)
ggplot(mpg, aes(displ, hwy)) +
geom_point() +
geom_text(aes(label = label),
data = label_11,
vjust = "top",
hjust = "right") +
geom_text(aes(label = label),
data = label_01,
vjust = "top",
hjust = "left") +
geom_text(aes(label = label),
data = label_10,
vjust = "bottom",
hjust = "right") +
geom_text(aes(label = label),
data = label_00,
vjust = "bottom",
hjust = "left")
#' ## Zadanie 2
?annotate()
#' można zrobić np w ten sposób, podając bezpośrednio np text, oraz położenie wpisująć ręcznie, bez danych.
p <- ggplot(mtcars, aes(x = wt, y = mpg)) + geom_point()
p + annotate('label', x = 4, y = 25, label = "Some text")
# Jak etykiety utworzone za pomocą funkcji geom_text() działają z panelami?
# Jak dodać etykietę do pojedynczego panelu? Jak umieścić różne etykiety na każdym panelu?
# (Wskazówka: pomyśl o danych, na podstawie których utworzyłeś wykres).
#' Zadanie 3
mpg %>%
group_by(drv) %>%
summarise(count=n()) %>%
ggplot(aes(x=drv, y=count, label=count)) +
geom_bar(stat='identity') +
geom_text(size=10, nudge_y = 5)
mpg %>%
group_by(drv, class) %>%
summarise(count=n()) %>%
ggplot(aes(x=drv, y=count, label=count)) +
geom_bar(stat='sum') +
geom_text(size=10, nudge_y = 5) +
facet_wrap(~class)
#' na różnych panelach dane automatycznie się dostosowują do wykresu
#' aby pokazać dane np ja jednym panelu można zrobić coś takiego:
mpg %>%
group_by(drv, class) %>%
summarise(count=n()) %>%
mutate(label = if_else(class=='compact', as.character(count), '')) %>%
ggplot(aes(x=drv, y=count, label=label)) +
geom_bar(stat='sum') +
geom_text(size=10, nudge_y = 5) +
facet_wrap(~class) +
labs(title='Liczba samochodów klasy compakt ma znacznie więcej\nsamochodów napędzanych na przód niż na 4 koła.',
x = 'rodzaj napędu',
y = 'liczba samochodów')
#' teraz etykiety pokazywane są tylko na panelu gdzie clasa = compact
#' Zadanie 4
#'
#' label.padding = unit(0.25, "lines"),
#' label.r = unit(0.15, "lines"),
#' label.size = 0.25,
#' Zadanie 5
# Jakie są cztery argumenty funkcji arrow()?
# Jak działają?
# Utwórz zestaw wykresów, który zaprezentuje najważniejsze opcje.
?arrow()
#' angle
#' length
#' ends
#' type
#' agnle - opisuje jak szeroni bedzie grot strzałki, im mniejsza wartość tym węższa bedzie strzałka
#' lenght - opisuja jak długi bedzie grot sprzałki
#' ends - jedno z "last", "first", "both" - wskazuje które końce lini, bedą zakończone grotem.
#' type - jedno z "open", "closed" - wskazuje, czy grot będzie otwrty, -> jak strzła, czy zamknięty jak trojkąt -|>
data <- data.frame('a'=c(1,2), 'b'=c(2,3))
ggplot(data, aes(x=a, y=b)) +
geom_line(arrow=arrow(angle=45, length = unit(5, "cm"), ends='both', type='closed')) +
annotate('text', x=1.25, y=2.75, label="ładna duża strzałka :)", size=9)
ggplot(data, aes(x=a, y=b)) +
geom_line(arrow=arrow(angle=25, length = unit(2, "cm"), ends='last', type='open')) +
annotate('text', x=1.3, y=2.75, label="smukła strzałka w jedną stronę", size=7)
#' ## 5.4.4 Ćwiczenia
#' install.packages('hexbin')
df <- tibble(
x = rnorm(10000),
y = rnorm(10000)
)
ggplot(df, aes(x, y)) +
geom_hex() +
scale_color_gradient(low = "white", high = "red") +
coord_fixed()
#' ten kod przysłania domyslną skalę, ale nie tą którą chcemy.
#' Poprawiony kod powinien wyglądać tak.
#' Zmieniono _color_ na _fill_
ggplot(df, aes(x, y)) +
geom_hex() +
scale_fill_gradient(low = "white", high = "red") +
coord_fixed()
?scale_fill_gradient
# pierwrszy argument to colors.
#' # Zadanie 3
years <- lubridate::make_date(seq(lubridate::year(min(presidential$start)),
lubridate::year(max(presidential$end)),
by = 4), 1, 1)
library(glue)
presidential %>%
mutate(id = 33 + row_number()) %>%
mutate(x_label = glue('{name} ({id})')) -> x_label
x_label = x_label$x_label
x_label = as.vector(x_label)
presidential %>%
mutate(id = 33 + row_number()) %>%
ggplot(aes(start, reorder(x_label, id), colour = party)) +
geom_point() +
geom_segment(aes(xend = end, yend = reorder(x_label, id))) +
scale_colour_manual(values = c(Republican = "red", Democratic = "blue")) +
scale_x_date(NULL, breaks = years, date_labels = "'%y") +
scale_y_discrete(breaks = x_label)
#' # Zadanie 4
ggplot(diamonds, aes(carat, price)) +
geom_point(aes(colour = cut), alpha = 1/20) +
guides(colour = guide_legend(override.aes = list(alpha = 1, size=4)))

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