Analisi Esplorativa

class: center, middle, inverse, title-slide

# Analisi Esplorativa
## Rappresentazioni grafiche di tre o più dimensioni
### Aldo Solari

---

# Outline

1. Matrice dei diagrammi di dispersione

2. Diagramma tridimensionale

3. Facce di Chernhoff / Stelle

4. Diagramma di dispersione condizionato

---

# Dati Measures

*Argomenti: diagramma tridimensionale; matrice dei diagrammi di dispersione; facce di Chernoff; stelle*

I dati `measures` sono `$n=20$` osservazioni su `$p=4$` variabili:

* `chest`: misura petto
* `waist` : misura vita
* `hips` : misura fianchi
* `gender` : sesso (`male` o `female`)

---

Importiamo i dati `measures`.

```r
rm(list=ls())
# i dati si trovano sezione "dati" della pagina web del corso:
# potete scaricarli cliccando il tasto destro "Save as"
# oppure usare il loro URL (Uniform Resource Locator)
url <- "https://raw.githubusercontent.com/aldosolari/AE/master/docs/dati/measure.csv"
measure <- read.csv(url)
head(measure)
```

```
  chest waist hips gender
1    34    30   32   male
2    37    32   37   male
3    38    30   36   male
4    36    33   39   male
5    38    29   33   male
6    43    32   38   male
```

---

Costruire il diagramma tridimensionale per le variabili `chest`, `waist` e `hips`,  utilizzando il comando `cloud()` che è disponibile nel pacchetto `lattice`

---

```r
library(lattice)
cloud(chest ~ waist + hips, data=measure)
```

![](3_rapgraf_slide_files/figure-html/unnamed-chunk-2-1.png)

---

Costruire il diagramma tridimensionale colorando le unità statistiche con colori diversi a seconda del sesso.

---

```r
cloud(chest ~ waist + hips, group=gender, data=measure)
```

![](3_rapgraf_slide_files/figure-html/unnamed-chunk-3-1.png)

---

Funzioni R più avanzate permettono di costruire un diagramma tridimensionale interattivo:

```r
library(plotly)
p <- plot_ly(measure, x = ~waist, y = ~hips, z = ~chest, color = ~gender, colors = c("pink","blue")) %>%
 add_markers() %>%
 layout(scene = list(xaxis = list(title = 'x = waist (vita)'),
 yaxis = list(title = 'y = hips (fianchi)'),
 zaxis = list(title = 'z= chest (petto)')))
```

---

```r
p
```

<div id="htmlwidget-cc3ba35dce6f88eacb8a" style="width:504px;height:504px;" class="plotly html-widget"></div>
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---

Costruire la matrice dei diagrammi di dispersione colorando le unità statistiche con colori diversi a seconda del sesso.

---

```r
column.gender <- which(names(measure)=="gender")
plot(measure[,-column.gender], col=(measure$gender=="male")+1)
```

![](3_rapgraf_slide_files/figure-html/unnamed-chunk-6-1.png)

---

Funzioni R più avanzate permettono di aggiungere e.g. gli istogrammi sulla diagonale e i valori assoluti delle correlazioni

```r
panel.hist <- function(x, ...)
{
 usr <- par("usr"); on.exit(par(usr))
 par(usr = c(usr[1:2], 0, 1.5) )
 h <- hist(x, plot = FALSE)
 breaks <- h$breaks; nB <- length(breaks)
 y <- h$counts; y <- y/max(y)
 rect(breaks[-nB], 0, breaks[-1], y, 
 col = "cyan", ...)
}

panel.cor <- function(x, y, digits = 2, 
 prefix = "", cex.cor, ...)
{
 usr <- par("usr"); on.exit(par(usr))
 par(usr = c(0, 1, 0, 1))
 r <- abs(cor(x, y))
 txt <- format(c(r, 0.123456789), digits = digits)[1]
 txt <- paste0(prefix, txt)
 if(missing(cex.cor)) cex.cor <- 0.8/strwidth(txt)
 text(0.5, 0.5, txt, cex = cex.cor * r)
}
```

---

```r
library(MASS)
pairs(measure[,-column.gender], panel=panel.smooth, 
      upper.panel=panel.cor, diag.panel=panel.hist)
```

![](3_rapgraf_slide_files/figure-html/unnamed-chunk-8-1.png)

---

# Facce di Chernov

Herman Chernoff ha introdotto una tecnica di visualizzazione per
illustrare le tendenze nei dati multidimensionali.

Questo metodo consiste nel visualizzare i dati multidimensionali a forma
di volto umano; i diversi valori dei dati sono abbinati alle caratteristiche
del volto, per esempio la larghezza della faccia, il livello delle orecchie,
la lunghezza o la curvatura della bocca, la lunghezza del naso, ecc.

L'idea che sta dietro all’uso delle facce è che le persone riconoscono i
volti e notano piccoli cambiamenti senza difficoltà.

Nella pratica questo metodo viene raramente utilizzato

---

Costruire le facce di Chernoff corrispondenti ai 20 individui escludendo la variabile `gender` utilizzando il comando `faces()` presente nel pacchetto `TeachingDemos`

---

```r
library("TeachingDemos")
faces(measure[,-column.gender], scale=TRUE) #scale=TRUE standardizza i dati
```

![](3_rapgraf_slide_files/figure-html/unnamed-chunk-9-1.png)

---

# Stelle

Questa rappresentazione grafica consiste di una sequenza di raggi che
hanno origine da un centro e formano angoli uguali tra loro; ogni raggio
rappresenta una delle variabili.

La distanza dal centro del punto marcato sul raggio è proporzionale al
valore della variabile rispetto al valore massimo raggiungibile.

I punti sui raggi vengono congiunti con segmenti, così che il grafico ha
la forma di una stella o di una ragnatela.

Anche questo metodo viene scarsamente utilizzato

---

Rappresentare gli individui con le stelle utilizzando il comando `stars()`, aggiungendo la legenda con l’argomento `key.loc = c(10,10)`.

---

```r
stars(measure[,-column.gender], scale=TRUE, 
      key.loc = c(10, 10)) # per posizionare la legenda alle coordinate (x,y)
```

![](3_rapgraf_slide_files/figure-html/unnamed-chunk-10-1.png)

---

# Dati Quakes

*Argomento: diagramma di dispersione condizionato*

Il data.frame `quakes` è presente nel pacchetto `dataset`. Si tratta di `$n=1000$` osservazioni misurate su `$p=5$` variabili:

* `lat`		Latitude of event
*	`long`		Longitude
*	`depth`		Depth (km)
*	`mag`		Richter Magnitude
*	`stations`	Number of stations reporting

---

Il diagramma di dispersione per latitudine e longitudine dei terremoti, utilizzando il simbolo `.` per indicare le osservazioni, si ottiene con:

```r
data("quakes")
plot(lat ~ long, quakes, pch=".")
```

![](3_rapgraf_slide_files/figure-html/unnamed-chunk-11-1.png)

---

Funzioni R più avanzate permettono di aggiungere la posizione degli eventi sismici sulla mappa geografica

```r
library(leaflet)

mybins <- seq(4, 6.5, by=0.5)
mypalette <- colorBin( palette="YlOrBr", domain=quakes$mag, na.color="transparent", bins=mybins)

mytext <- paste(
 "Depth: ", quakes$depth, " ", 
 "Stations: ", quakes$stations, " ", 
 "Magnitude: ", quakes$mag, sep="") %>%
 lapply(htmltools::HTML)

m <- leaflet(quakes) %>% 
 addTiles() %>% 
 setView( lat=-27, lng=170 , zoom=4) %>%
 addProviderTiles("Esri.WorldImagery") %>%
 addCircleMarkers(~long, ~lat, 
 fillColor = ~mypalette(mag), fillOpacity = 0.7, color="white", radius=4, stroke=FALSE,
 label = mytext,
 labelOptions = labelOptions( style = list("font-weight" = "normal", padding = "3px 8px"), textsize = "13px", direction = "auto")
 ) %>%
 addLegend( pal=mypalette, values=~mag, opacity=0.9, title = "Magnitude", position = "bottomright" )
```

---

```r
m 
```

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Stations: 40 Magnitude: 4.4","Depth: 246 Stations: 23 Magnitude: 4.3","Depth: 47 Stations: 19 Magnitude: 4.8","Depth: 484 Stations: 27 Magnitude: 4.3","Depth: 119 Stations: 29 Magnitude: 4.5","Depth: 70 Stations: 22 Magnitude: 4.1","Depth: 579 Stations: 58 Magnitude: 5.1","Depth: 57 Stations: 44 Magnitude: 4.7","Depth: 176 Stations: 28 Magnitude: 4.6","Depth: 602 Stations: 44 Magnitude: 4.7","Depth: 488 Stations: 12 Magnitude: 4.6","Depth: 149 Stations: 15 Magnitude: 4.4","Depth: 546 Stations: 23 Magnitude: 4.2","Depth: 343 Stations: 10 Magnitude: 4.1","Depth: 530 Stations: 22 Magnitude: 4.7","Depth: 563 Stations: 17 Magnitude: 4","Depth: 537 Stations: 33 Magnitude: 4.8","Depth: 325 Stations: 19 Magnitude: 4.4","Depth: 80 Stations: 14 Magnitude: 4.3","Depth: 259 Stations: 21 Magnitude: 4.4","Depth: 476 Stations: 10 Magnitude: 4.5","Depth: 499 Stations: 29 Magnitude: 4.5","Depth: 257 Stations: 30 Magnitude: 4.7","Depth: 165 Stations: 18 Magnitude: 4.3","Depth: 136 Stations: 29 Magnitude: 4.7","Depth: 146 Stations: 33 Magnitude: 4.8","Depth: 524 Stations: 14 Magnitude: 4.6","Depth: 82 Stations: 68 Magnitude: 5.1","Depth: 90 Stations: 19 Magnitude: 4.7","Depth: 138 Stations: 21 Magnitude: 4.3","Depth: 499 Stations: 91 Magnitude: 5.1","Depth: 538 Stations: 104 Magnitude: 5.5","Depth: 467 Stations: 25 Magnitude: 4.5","Depth: 184 Stations: 11 Magnitude: 4.3","Depth: 538 Stations: 21 Magnitude: 4.3","Depth: 45 Stations: 23 Magnitude: 4.7","Depth: 237 Stations: 18 Magnitude: 4.3","Depth: 162 Stations: 20 Magnitude: 4.3","Depth: 136 Stations: 20 Magnitude: 4.6","Depth: 604 Stations: 23 Magnitude: 4.5","Depth: 107 Stations: 15 Magnitude: 4.5","Depth: 538 Stations: 87 Magnitude: 5.4","Depth: 639 Stations: 39 Magnitude: 4.6","Depth: 45 Stations: 11 Magnitude: 4.4","Depth: 636 Stations: 100 Magnitude: 5","Depth: 628 Stations: 72 Magnitude: 5.2","Depth: 632 Stations: 15 Magnitude: 4.4","Depth: 215 Stations: 51 Magnitude: 5.1","Depth: 556 Stations: 17 Magnitude: 4.4","Depth: 135 Stations: 21 Magnitude: 4.4","Depth: 297 Stations: 25 Magnitude: 4.8","Depth: 568 Stations: 22 Magnitude: 4.4","Depth: 168 Stations: 39 Magnitude: 4.7","Depth: 269 Stations: 31 Magnitude: 4.7","Depth: 143 Stations: 29 Magnitude: 4.4","Depth: 95 Stations: 12 Magnitude: 4.3","Depth: 142 Stations: 40 Magnitude: 5","Depth: 104 Stations: 19 Magnitude: 4.5","Depth: 169 Stations: 27 Magnitude: 4.6","Depth: 65 Stations: 65 Magnitude: 5.4","Depth: 54 Stations: 23 Magnitude: 4.6","Depth: 474 Stations: 13 Magnitude: 4.5","Depth: 125 Stations: 13 Magnitude: 4.4","Depth: 617 Stations: 18 Magnitude: 4.5","Depth: 294 Stations: 10 Magnitude: 4.1","Depth: 180 Stations: 13 Magnitude: 4","Depth: 47 Stations: 39 Magnitude: 4.9","Depth: 593 Stations: 13 Magnitude: 4.1","Depth: 94 Stations: 79 Magnitude: 5.2","Depth: 201 Stations: 41 Magnitude: 4.4","Depth: 537 Stations: 11 Magnitude: 4.1","Depth: 594 Stations: 43 Magnitude: 4.9","Depth: 638 Stations: 20 Magnitude: 4.6","Depth: 80 Stations: 17 Magnitude: 4.5","Depth: 211 Stations: 30 Magnitude: 4.8","Depth: 520 Stations: 19 Magnitude: 4.2","Depth: 384 Stations: 23 Magnitude: 4.2","Depth: 223 Stations: 15 Magnitude: 4.1","Depth: 54 Stations: 71 Magnitude: 5.5","Depth: 57 Stations: 19 Magnitude: 4.4","Depth: 49 Stations: 20 Magnitude: 4.8","Depth: 508 Stations: 23 Magnitude: 4.2","Depth: 242 Stations: 36 Magnitude: 4.8","Depth: 62 Stations: 46 Magnitude: 4.9","Depth: 63 Stations: 19 Magnitude: 4.6","Depth: 203 Stations: 34 Magnitude: 4.5","Depth: 132 Stations: 24 Magnitude: 4.4","Depth: 543 Stations: 28 Magnitude: 4.6","Depth: 589 Stations: 19 Magnitude: 4.2","Depth: 51 Stations: 28 Magnitude: 4.7","Depth: 45 Stations: 51 Magnitude: 4.4","Depth: 63 Stations: 51 Magnitude: 4.5","Depth: 485 Stations: 48 Magnitude: 4.9","Depth: 66 Stations: 34 Magnitude: 4.7","Depth: 58 Stations: 92 Magnitude: 5.5","Depth: 70 Stations: 30 Magnitude: 4.7","Depth: 541 Stations: 32 Magnitude: 4.6","Depth: 598 Stations: 14 Magnitude: 4.1","Depth: 50 Stations: 28 Magnitude: 4.7","Depth: 102 Stations: 21 Magnitude: 4.6","Depth: 144 Stations: 25 Magnitude: 4.3","Depth: 58 Stations: 20 Magnitude: 4.4","Depth: 460 Stations: 44 Magnitude: 4.7","Depth: 69 Stations: 25 Magnitude: 4.3","Depth: 570 Stations: 22 Magnitude: 4.1","Depth: 70 Stations: 30 Magnitude: 4.7","Depth: 137 Stations: 16 Magnitude: 4.5","Depth: 41 Stations: 81 Magnitude: 5.5","Depth: 586 Stations: 17 Magnitude: 4.5","Depth: 140 Stations: 44 Magnitude: 4.6","Depth: 213 Stations: 70 Magnitude: 5.1","Depth: 393 Stations: 28 Magnitude: 4.4","Depth: 51 Stations: 35 Magnitude: 4.7","Depth: 64 Stations: 73 Magnitude: 5.5","Depth: 45 Stations: 39 Magnitude: 4.6","Depth: 296 Stations: 16 Magnitude: 4","Depth: 50 Stations: 24 Magnitude: 4.6","Depth: 44 Stations: 34 Magnitude: 4.8","Depth: 68 Stations: 36 Magnitude: 4.7","Depth: 549 Stations: 33 Magnitude: 4.7","Depth: 150 Stations: 20 Magnitude: 4.2","Depth: 47 Stations: 87 Magnitude: 5.4","Depth: 543 Stations: 34 Magnitude: 4.6","Depth: 40 Stations: 86 Magnitude: 5.5","Depth: 100 Stations: 15 Magnitude: 4.2","Depth: 85 Stations: 22 Magnitude: 4.5","Depth: 98 Stations: 21 Magnitude: 4.5","Depth: 58 Stations: 20 Magnitude: 4.8","Depth: 125 Stations: 18 Magnitude: 4.6","Depth: 89 Stations: 80 Magnitude: 5.4","Depth: 590 Stations: 34 Magnitude: 4.6","Depth: 49 Stations: 30 Magnitude: 5","Depth: 543 Stations: 17 Magnitude: 4.3","Depth: 506 Stations: 24 Magnitude: 4.3","Depth: 40 Stations: 38 Magnitude: 4.8","Depth: 42 Stations: 23 Magnitude: 4.7","Depth: 76 Stations: 36 Magnitude: 4.7","Depth: 63 Stations: 27 Magnitude: 4.8","Depth: 104 Stations: 17 Magnitude: 4.2","Depth: 93 Stations: 16 Magnitude: 4.2","Depth: 64 Stations: 118 Magnitude: 5.9","Depth: 587 Stations: 28 Magnitude: 4.6","Depth: 83 Stations: 25 Magnitude: 4.5","Depth: 579 Stations: 49 Magnitude: 4.9","Depth: 40 Stations: 17 Magnitude: 4.7","Depth: 62 Stations: 25 Magnitude: 4.9","Depth: 273 Stations: 78 Magnitude: 5.3","Depth: 393 Stations: 21 Magnitude: 4.2","Depth: 264 Stations: 23 Magnitude: 4.2","Depth: 174 Stations: 18 Magnitude: 4.5","Depth: 574 Stations: 67 Magnitude: 5.2","Depth: 309 Stations: 23 Magnitude: 4.5","Depth: 75 Stations: 79 Magnitude: 5.6","Depth: 195 Stations: 87 Magnitude: 5.2","Depth: 44 Stations: 35 Magnitude: 4.8","Depth: 420 Stations: 29 Magnitude: 4.5","Depth: 63 Stations: 28 Magnitude: 5","Depth: 609 Stations: 26 Magnitude: 4.4","Depth: 40 Stations: 18 Magnitude: 4.5","Depth: 575 Stations: 42 Magnitude: 4.6","Depth: 559 Stations: 24 Magnitude: 4.5","Depth: 405 Stations: 74 Magnitude: 5.2","Depth: 70 Stations: 54 Magnitude: 5.1","Depth: 41 Stations: 42 Magnitude: 4.8","Depth: 605 Stations: 18 Magnitude: 4.3","Depth: 130 Stations: 55 Magnitude: 5.1","Depth: 577 Stations: 19 Magnitude: 4.7","Depth: 599 Stations: 20 Magnitude: 4.6","Depth: 82 Stations: 51 Magnitude: 4.8","Depth: 50 Stations: 23 Magnitude: 4.6","Depth: 480 Stations: 25 Magnitude: 4.4","Depth: 559 Stations: 27 Magnitude: 4.6","Depth: 566 Stations: 49 Magnitude: 5.1","Depth: 611 Stations: 20 Magnitude: 4.3","Depth: 409 Stations: 19 Magnitude: 4.4","Depth: 209 Stations: 30 Magnitude: 4.7","Depth: 70 Stations: 47 Magnitude: 4.8","Depth: 74 Stations: 15 Magnitude: 4.1","Depth: 134 Stations: 33 Magnitude: 4.6","Depth: 150 Stations: 35 Magnitude: 4.9","Depth: 406 Stations: 17 Magnitude: 4","Depth: 243 Stations: 32 Magnitude: 4.7","Depth: 89 Stations: 32 Magnitude: 4.7","Depth: 53 Stations: 89 Magnitude: 5.2","Depth: 68 Stations: 18 Magnitude: 4.6","Depth: 605 Stations: 34 Magnitude: 4.6","Depth: 615 Stations: 23 Magnitude: 4.9","Depth: 546 Stations: 99 Magnitude: 5.7","Depth: 176 Stations: 26 Magnitude: 4.7","Depth: 52 Stations: 18 Magnitude: 4.4","Depth: 66 Stations: 38 Magnitude: 4.9","Depth: 377 Stations: 43 Magnitude: 4.8","Depth: 186 Stations: 27 Magnitude: 4.6","Depth: 51 Stations: 18 Magnitude: 4.4","Depth: 67 Stations: 35 Magnitude: 4.8","Depth: 234 Stations: 28 Magnitude: 4.7","Depth: 597 Stations: 18 Magnitude: 4.2","Depth: 64 Stations: 54 Magnitude: 5.1","Depth: 511 Stations: 56 Magnitude: 4.8","Depth: 47 Stations: 47 Magnitude: 4.9","Depth: 49 Stations: 49 Magnitude: 5.1","Depth: 546 Stations: 28 Magnitude: 4.3","Depth: 75 Stations: 30 Magnitude: 4.4","Depth: 60 Stations: 33 Magnitude: 4.7","Depth: 278 Stations: 24 Magnitude: 4.7","Depth: 550 Stations: 86 Magnitude: 5.3","Depth: 518 Stations: 71 Magnitude: 5.1","Depth: 116 Stations: 38 Magnitude: 4.9","Depth: 518 Stations: 23 Magnitude: 4.5","Depth: 75 Stations: 41 Magnitude: 4.7","Depth: 491 Stations: 23 Magnitude: 4.2","Depth: 56 Stations: 50 Magnitude: 5.1","Depth: 376 Stations: 57 Magnitude: 4.8","Depth: 584 Stations: 18 Magnitude: 4.2","Depth: 48 Stations: 56 Magnitude: 4.8","Depth: 53 Stations: 20 Magnitude: 4.4","Depth: 617 Stations: 26 Magnitude: 4.5","Depth: 294 Stations: 18 Magnitude: 4.3","Depth: 417 Stations: 129 Magnitude: 5.6","Depth: 280 Stations: 16 Magnitude: 4","Depth: 332 Stations: 36 Magnitude: 5","Depth: 85 Stations: 28 Magnitude: 4.2","Depth: 525 Stations: 31 Magnitude: 4.6","Depth: 613 Stations: 18 Magnitude: 4.6","Depth: 182 Stations: 28 Magnitude: 4.5","Depth: 57 Stations: 32 Magnitude: 5","Depth: 79 Stations: 42 Magnitude: 4.7","Depth: 595 Stations: 36 Magnitude: 4.6","Depth: 164 Stations: 50 Magnitude: 4.8","Depth: 148 Stations: 44 Magnitude: 4.6","Depth: 82 Stations: 17 Magnitude: 4.4","Depth: 153 Stations: 87 Magnitude: 5.6","Depth: 556 Stations: 13 Magnitude: 4.2","Depth: 649 Stations: 88 Magnitude: 5.4","Depth: 651 Stations: 43 Magnitude: 4.8","Depth: 93 Stations: 94 Magnitude: 5.6","Depth: 533 Stations: 27 Magnitude: 4.4","Depth: 642 Stations: 29 Magnitude: 4.7","Depth: 47 Stations: 27 Magnitude: 4.6","Depth: 548 Stations: 79 Magnitude: 5.1","Depth: 154 Stations: 22 Magnitude: 4.6","Depth: 627 Stations: 29 Magnitude: 4.5","Depth: 622 Stations: 23 Magnitude: 4.2","Depth: 286 Stations: 43 Magnitude: 4.8","Depth: 390 Stations: 48 Magnitude: 4.9","Depth: 624 Stations: 105 Magnitude: 5.5","Depth: 539 Stations: 41 Magnitude: 5","Depth: 624 Stations: 21 Magnitude: 4.2","Depth: 631 Stations: 69 Magnitude: 5.2","Depth: 631 Stations: 36 Magnitude: 4.8","Depth: 299 Stations: 30 Magnitude: 4.4","Depth: 498 Stations: 40 Magnitude: 4.8","Depth: 255 Stations: 31 Magnitude: 4.4","Depth: 539 Stations: 12 Magnitude: 4.1","Depth: 195 Stations: 45 Magnitude: 4.9","Depth: 594 Stations: 24 Magnitude: 4.6","Depth: 573 Stations: 32 Magnitude: 4.5","Depth: 128 Stations: 18 Magnitude: 5.3","Depth: 137 Stations: 40 Magnitude: 4.8","Depth: 143 Stations: 41 Magnitude: 4.6","Depth: 511 Stations: 37 Magnitude: 4.8","Depth: 564 Stations: 17 Magnitude: 4.7","Depth: 559 Stations: 50 Magnitude: 4.9","Depth: 248 Stations: 60 Magnitude: 5.3","Depth: 210 Stations: 27 Magnitude: 4.4","Depth: 390 Stations: 33 Magnitude: 4.6","Depth: 616 Stations: 17 Magnitude: 4.3","Depth: 98 Stations: 17 Magnitude: 4.4","Depth: 218 Stations: 27 Magnitude: 4.2","Depth: 655 Stations: 14 Magnitude: 4.1","Depth: 356 Stations: 15 Magnitude: 4.2","Depth: 564 Stations: 64 Magnitude: 5","Depth: 548 Stations: 10 Magnitude: 4.1","Depth: 655 Stations: 20 Magnitude: 4.3","Depth: 385 Stations: 67 Magnitude: 5.2","Depth: 518 Stations: 10 Magnitude: 4.2","Depth: 598 Stations: 36 Magnitude: 4.5","Depth: 476 Stations: 29 Magnitude: 4.4","Depth: 579 Stations: 16 Magnitude: 4.4","Depth: 603 Stations: 65 Magnitude: 5","Depth: 249 Stations: 11 Magnitude: 4","Depth: 208 Stations: 25 Magnitude: 4.8","Depth: 587 Stations: 51 Magnitude: 5","Depth: 221 Stations: 21 Magnitude: 4.2","Depth: 545 Stations: 91 Magnitude: 5.2","Depth: 586 Stations: 68 Magnitude: 5.2","Depth: 488 Stations: 10 Magnitude: 4.5","Depth: 246 Stations: 15 Magnitude: 4.3","Depth: 61 Stations: 19 Magnitude: 4.5","Depth: 524 Stations: 11 Magnitude: 4.6","Depth: 104 Stations: 71 Magnitude: 5.1","Depth: 271 Stations: 36 Magnitude: 4.4","Depth: 487 Stations: 16 Magnitude: 4.3","Depth: 83 Stations: 37 Magnitude: 4.7","Depth: 183 Stations: 109 Magnitude: 5.6","Depth: 55 Stations: 46 Magnitude: 4.9","Depth: 166 Stations: 22 Magnitude: 5.1","Depth: 586 Stations: 13 Magnitude: 4.6","Depth: 618 Stations: 18 Magnitude: 4.4","Depth: 524 Stations: 49 Magnitude: 4.8","Depth: 133 Stations: 17 Magnitude: 4.2","Depth: 201 Stations: 57 Magnitude: 4.7","Depth: 383 Stations: 11 Magnitude: 4.1","Depth: 86 Stations: 33 Magnitude: 4.7","Depth: 555 Stations: 17 Magnitude: 4","Depth: 605 Stations: 43 Magnitude: 4.9","Depth: 609 Stations: 50 Magnitude: 5","Depth: 204 Stations: 16 Magnitude: 4.5","Depth: 287 Stations: 23 Magnitude: 4.4","Depth: 390 Stations: 14 Magnitude: 4","Depth: 348 Stations: 30 Magnitude: 4.5","Depth: 550 Stations: 23 Magnitude: 4.7","Depth: 487 Stations: 20 Magnitude: 4.4","Depth: 578 Stations: 43 Magnitude: 4.7","Depth: 361 Stations: 32 Magnitude: 4.7","Depth: 275 Stations: 14 Magnitude: 4","Depth: 498 Stations: 14 Magnitude: 4.2","Depth: 162 Stations: 18 Magnitude: 4.5","Depth: 78 Stations: 44 Magnitude: 4.7","Depth: 134 Stations: 17 Magnitude: 4.5","Depth: 554 Stations: 15 Magnitude: 4.1","Depth: 608 Stations: 13 Magnitude: 4.6","Depth: 367 Stations: 25 Magnitude: 4.3","Depth: 599 Stations: 30 Magnitude: 4.6","Depth: 45 Stations: 65 Magnitude: 5.2","Depth: 50 Stations: 22 Magnitude: 4.6","Depth: 162 Stations: 36 Magnitude: 4.7","Depth: 302 Stations: 65 Magnitude: 5","Depth: 57 Stations: 49 Magnitude: 5.2","Depth: 203 Stations: 20 Magnitude: 4.4","Depth: 66 Stations: 18 Magnitude: 4.6","Depth: 591 Stations: 18 Magnitude: 4.5","Depth: 440 Stations: 12 Magnitude: 4","Depth: 611 Stations: 20 Magnitude: 4.2","Depth: 57 Stations: 69 Magnitude: 5.3","Depth: 627 Stations: 119 Magnitude: 5.9","Depth: 89 Stations: 42 Magnitude: 4.9","Depth: 500 Stations: 34 Magnitude: 4.5","Depth: 264 Stations: 14 Magnitude: 4.4","Depth: 127 Stations: 75 Magnitude: 5.4","Depth: 85 Stations: 86 Magnitude: 5.3","Depth: 50 Stations: 47 Magnitude: 5.1","Depth: 75 Stations: 20 Magnitude: 4.1","Depth: 182 Stations: 17 Magnitude: 4.3","Depth: 619 Stations: 18 Magnitude: 4.5","Depth: 223 Stations: 10 Magnitude: 4.1","Depth: 156 Stations: 70 Magnitude: 5.1","Depth: 46 Stations: 71 Magnitude: 5.3","Depth: 50 Stations: 29 Magnitude: 4.5","Depth: 230 Stations: 16 Magnitude: 4.1","Depth: 184 Stations: 26 Magnitude: 4.4","Depth: 188 Stations: 24 Magnitude: 4.7","Depth: 80 Stations: 10 Magnitude: 4","Depth: 86 Stations: 61 Magnitude: 5.1","Depth: 391 Stations: 16 Magnitude: 4","Depth: 199 Stations: 21 Magnitude: 4.3","Depth: 592 Stations: 21 Magnitude: 4.3","Depth: 595 Stations: 22 Magnitude: 4","Depth: 618 Stations: 10 Magnitude: 4.1","Depth: 213 Stations: 17 Magnitude: 4.4","Depth: 616 Stations: 10 Magnitude: 4.3","Depth: 175 Stations: 12 Magnitude: 4.2","Depth: 589 Stations: 12 Magnitude: 4","Depth: 83 Stations: 25 Magnitude: 4.5","Depth: 119 Stations: 32 Magnitude: 4.7","Depth: 70 Stations: 48 Magnitude: 5","Depth: 74 Stations: 22 Magnitude: 4.3","Depth: 40 Stations: 54 Magnitude: 5.1","Depth: 87 Stations: 34 Magnitude: 4.7","Depth: 63 Stations: 69 Magnitude: 5.3","Depth: 537 Stations: 63 Magnitude: 5","Depth: 47 Stations: 29 Magnitude: 4.5","Depth: 490 Stations: 77 Magnitude: 5","Depth: 593 Stations: 16 Magnitude: 4.1","Depth: 644 Stations: 27 Magnitude: 4.9","Depth: 576 Stations: 16 Magnitude: 4.1","Depth: 199 Stations: 16 Magnitude: 4","Depth: 589 Stations: 27 Magnitude: 4.4","Depth: 178 Stations: 19 Magnitude: 4.5","Depth: 248 Stations: 33 Magnitude: 4.4","Depth: 500 Stations: 37 Magnitude: 4.5","Depth: 71 Stations: 19 Magnitude: 4.3","Depth: 568 Stations: 36 Magnitude: 4.3","Depth: 42 Stations: 36 Magnitude: 5","Depth: 510 Stations: 37 Magnitude: 4.5","Depth: 97 Stations: 13 Magnitude: 4.5","Depth: 663 Stations: 30 Magnitude: 4.4","Depth: 625 Stations: 35 Magnitude: 4.5","Depth: 210 Stations: 22 Magnitude: 4.1","Depth: 557 Stations: 78 Magnitude: 4.9","Depth: 582 Stations: 27 Magnitude: 4.7","Depth: 402 Stations: 18 Magnitude: 4.3","Depth: 474 Stations: 32 Magnitude: 4.6","Depth: 577 Stations: 43 Magnitude: 4.6","Depth: 56 Stations: 49 Magnitude: 5.2","Depth: 43 Stations: 19 Magnitude: 4.5","Depth: 118 Stations: 11 Magnitude: 4.3","Depth: 544 Stations: 52 Magnitude: 4.6","Depth: 532 Stations: 14 Magnitude: 4","Depth: 237 Stations: 39 Magnitude: 4.5","Depth: 111 Stations: 30 Magnitude: 4.8","Depth: 595 Stations: 30 Magnitude: 4.6","Depth: 603 Stations: 11 Magnitude: 4.1","Depth: 505 Stations: 50 Magnitude: 4.9","Depth: 100 Stations: 40 Magnitude: 4.7","Depth: 587 Stations: 23 Magnitude: 4.1","Depth: 364 Stations: 20 Magnitude: 4.3","Depth: 100 Stations: 17 Magnitude: 4.4","Depth: 350 Stations: 12 Magnitude: 4","Depth: 228 Stations: 15 Magnitude: 4.8","Depth: 93 Stations: 25 Magnitude: 4.4","Depth: 66 Stations: 34 Magnitude: 4.4","Depth: 225 Stations: 21 Magnitude: 4.6","Depth: 334 Stations: 28 Magnitude: 4.2","Depth: 70 Stations: 15 Magnitude: 4.1","Depth: 220 Stations: 18 Magnitude: 4.2","Depth: 397 Stations: 12 Magnitude: 4","Depth: 326 Stations: 15 Magnitude: 4.1","Depth: 121 Stations: 17 Magnitude: 4.1","Depth: 209 Stations: 29 Magnitude: 4.7","Depth: 510 Stations: 44 Magnitude: 4.8","Depth: 54 Stations: 44 Magnitude: 5.1","Depth: 242 Stations: 41 Magnitude: 5","Depth: 574 Stations: 38 Magnitude: 4.8","Depth: 82 Stations: 39 Magnitude: 4.4","Depth: 102 Stations: 36 Magnitude: 5","Depth: 43 Stations: 56 Magnitude: 5.2","Depth: 432 Stations: 19 Magnitude: 4.2","Depth: 580 Stations: 16 Magnitude: 4.1","Depth: 464 Stations: 60 Magnitude: 4.8","Depth: 479 Stations: 27 Magnitude: 4.5","Depth: 581 Stations: 54 Magnitude: 5","Depth: 513 Stations: 81 Magnitude: 5.1","Depth: 77 Stations: 16 Magnitude: 4.1","Depth: 68 Stations: 41 Magnitude: 4.7","Depth: 71 Stations: 59 Magnitude: 5.2","Depth: 68 Stations: 48 Magnitude: 4.8","Depth: 586 Stations: 33 Magnitude: 4.5","Depth: 243 Stations: 11 Magnitude: 4","Depth: 658 Stations: 49 Magnitude: 4.7","Depth: 315 Stations: 15 Magnitude: 4.1","Depth: 210 Stations: 17 Magnitude: 4.3","Depth: 278 Stations: 17 Magnitude: 4.3","Depth: 638 Stations: 14 Magnitude: 4","Depth: 615 Stations: 51 Magnitude: 4.7","Depth: 567 Stations: 27 Magnitude: 4.1","Depth: 560 Stations: 13 Magnitude: 4.2","Depth: 99 Stations: 36 Magnitude: 4.8","Depth: 266 Stations: 31 Magnitude: 4.8","Depth: 397 Stations: 15 Magnitude: 4.2","Depth: 180 Stations: 29 Magnitude: 4.2","Depth: 40 Stations: 78 Magnitude: 5.7","Depth: 242 Stations: 132 Magnitude: 6","Depth: 530 Stations: 20 Magnitude: 4.2","Depth: 133 Stations: 32 Magnitude: 4.5","Depth: 62 Stations: 36 Magnitude: 4.9","Depth: 580 Stations: 22 Magnitude: 4.4","Depth: 530 Stations: 15 Magnitude: 4","Depth: 566 Stations: 20 Magnitude: 4.3","Depth: 501 Stations: 23 Magnitude: 4.2","Depth: 548 Stations: 30 Magnitude: 4.5","Depth: 587 Stations: 31 Magnitude: 4.8","Depth: 592 Stations: 28 Magnitude: 4.4","Depth: 221 Stations: 18 Magnitude: 4.2","Depth: 560 Stations: 12 Magnitude: 4.2","Depth: 94 Stations: 31 Magnitude: 5","Depth: 139 Stations: 15 Magnitude: 4.2","Depth: 162 Stations: 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---

oppure per visualizzare i punti con un diagramma tridimensionale (latitudine, logitudine, profondità) colorando i punti per magnitudine del terremoto:

```r
p <- plot_ly(quakes, x = ~lat, y = ~long, z = ~ -depth, color=~mag, colors="YlOrBr") %>%
 add_markers(size=.01) %>%
 layout(scene = list(xaxis = list(title = 'Latitudine'),
 yaxis = list(title = 'Longitudine'),
 zaxis = list(title = 'Profondità')))
```

---

```r
p
```

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---

La magnitudo del terremoto dipende dalla profondità dello stesso? Si costruisca un grafico appropriato per rispondere a questa domanda.

---

```r
plot(quakes$depth, jitter(quakes$mag), xlab="profondità del terremoto",
ylab="magnitudo del terremoto")
```

![](3_rapgraf_slide_files/figure-html/unnamed-chunk-16-1.png)

---

Il numero di stazioni che riportano l'evento dipende dalla magnitudo? Si costruisca un grafico appropriato per rispondere a questa domanda.

---

```r
plot(jitter(quakes$mag), quakes$stations, xlab="magnitudo del terremoto",
ylab="numbero di stazioni che rilevano il terremoto")
```

![](3_rapgraf_slide_files/figure-html/unnamed-chunk-17-1.png)

---

In che modo la profondità dell'evento dipende dalla longitudine e dalla latitudine?

Costruire un diagramma di dispersione colorando ogni punto (posizione geografica) con i colori verde, arancione o rosso a seconda della profondità utilizzando gli intervalli (0-250], (250-450], (450,700].

---

```r
intervalli <- cut(quakes$depth, breaks = c(0, 250, 450, 700),
labels = c("green", "orange", "red"))
intervalli<- as.character(intervalli)
plot(quakes$long, quakes$lat, pch = 20, col = intervalli, xlab="longitudine",
ylab="latitudine")
```

![](3_rapgraf_slide_files/figure-html/unnamed-chunk-18-1.png)

---

Proviamo a costruire il diagramma di dispersione di latitudine e longitudine condizionato a 4 intervalli (non necessariamente disgiunti) utilizzando il comando `co.intervals()`

---

```r
intervalli <- co.intervals(quakes$depth, number=4, overlap=0.1)
coplot(lat ~ long | depth, data = quakes, given.v = intervalli, rows = 1)
```

![](3_rapgraf_slide_files/figure-html/unnamed-chunk-19-1.png)