STA 326 2.0 Programming and Data Analysis with R

.title[
# STA 326 2.0 Programming and Data Analysis with R
]
.subtitle[
## 🚦Working with built-in functions in R
]
.author[
### 
]
.author[
### Dr Thiyanga Talagala
]

---

# Today's menu

- How to call a built-in function

- Arguments matching

- Basic functions

- Test and type conversion functions

- Probability distribution functions

- Reproducibility of scientific results

- Data visualization: `qplot`

]

---
## Functions in R

👉🏻 Perform a specific task according to a set of instructions.

👉🏻  Some functions we have discussed so far,

> `c`, `matrix`, `array`, `list`, `data.frame`, `str`, `dim`, `length`, `nrow`, `which.max`, `diag`, `summary`

👉🏻 In R, functions are **objects** of **class** *function*.

```r
class(length)
```

```
[1] "function"
```

---

## Functions in R (cont.)

👉🏻 There are basically two types of functions:

> 💻 Built-in functions 
  
Already created or defined in the programming framework to make our work easier.

> 👨 User-defined functions

Sometimes we need to create our own functions for a specific purpose.
      
---

### How to call a built-in function in R

```r
function_name(arg1 = 1, arg2 = 3)

```

**Argument matching**

The following calls to `mean` are all equivalent

```r
mydata <- c(rnorm(20), 100000)
mean(mydata) # matched by position
mean(x = mydata) # matched by name
mean(mydata, na.rm = FALSE)
mean(x = mydata, na.rm = FALSE) 
mean(na.rm = FALSE, x = mydata) 
mean(na.rm = FALSE, mydata)
```

```
[1] 4761.73
```

⚠️ Even though it works, do not change the order of the arguments too much.

---

## Argument matching (cont.)

- some arguments have default values

```r
mean(mydata, trim=0)
```

```
[1] 4761.73
```

```r
mean(mydata) # Default value for trim is 0
```

```
[1] 4761.73
```

]

```r
mean(mydata, trim=0.1)
```

```
[1] -0.1063261
```

```r
mean(mydata, tr=0.1) # Partial Matching
```

```
[1] -0.1063261
```

]

---

background-image: url('helpmean.png')
background-position: center
background-size: contain

## ?mean

---

# Your turn

---

1. Calculate the mean of 1, 2, 3, 8, 10, 20, 56, NA.

---

# Basic maths functions

|  Operator | Description  |
|---|---|
|<img width=400/>|<img width=500/>|
|  abs(x) | absolute value of x   |
| log(x, base = y)  |  logarithm of x with base y; if base is not specified, returns the natural logarithm |
|exp(x)| exponential of x|
|sqrt(x)|square root of x|
|factorial(x)| factorial of x|

---
# Basic statistic functions

|  Operator | Description  |
|---|---|
|<img width=400/>|<img width=400/>|
|  mean(x) | mean of x   |
| median(x)  |  median of x |
|mode(x)| mode of x|
|var(x)|variance of x|
|sd(x)|standard deviation of x|
|scale(x)| z-score of x|
|quantile(x)| quantiles of x|
|summary(x)|summary of x: mean, minimum, maximum, etc.|

---

## Test and Type conversion functions

|  Test | Convert  |
|---|---|
|<img width=400/>|<img width=400/>|
|  is.numeric() | as.numeric()   |
| is.character()  |  as.character() |
|is.vector()| as.vector()|
|is.matrix()|as.matrix()|
|is.data.frame()| as.data.frame()|
|is.factor()| as.factor()|
|is.logical()|as.logical()|
|is.na()||
]

```r
a <- c(1, 2, 3); a
```

```
[1] 1 2 3
```

```r
is.numeric(a)
```

```
[1] TRUE
```

```r
is.vector(a)
```

```
[1] TRUE
```

```r
b <- as.character(a); b
```

```
[1] "1" "2" "3"
```

```r
is.vector(b)
```

```
[1] TRUE
```

```r
is.character(b)
```

```
[1] TRUE
```
]

---

# Your turn

---

Remove missing values in the following vector

```r
a
```

```
 [1]  0.61940020 -0.93808729  0.95518590 -0.22663938  0.29591186          NA
 [7]  0.36788089  0.71791098  0.71202022  0.22765782          NA          NA
[13] -0.74024324  0.02081516 -0.14979979 -0.22351308  0.98729725          NA
[19]          NA          NA          NA          NA          NA          NA
[25]          NA          NA          NA -1.50016003  0.18682734  0.20808590
[31]  0.70102264 -0.10633074 -1.18460046  0.06475501  0.11568817 -0.04333140
[37] -0.22020064  0.02764713  0.10165760 -0.18234246  1.32914659 -1.29704248
[43]  1.05317749 -0.70109051  0.09798707  0.10457263 -0.21449845
```
---

### Probability distribution functions

- Each probability distribution in R is associated with four functions.

- Naming convention for the four functions:

For each function there is a root name. For example, the **root name** for the normal distribution is `norm`. This root is prefixed by one of the letters `d`, `p`, `q`, `r`.
    
  - **d** prefix for the **distribution** function

- **p** prefix for the **cumulative probability**

- **q** prefix for the **quantile**

- **r** prefix for the **random** number generator

- Example: `dnorm`, `pnorm`, `qnorm`, `rnorm`

---

background-image: url('dis.jpeg')
background-position: center
background-size: contain

---

### Illustration with Standard normal distribution

The general formula for the probability density function of the normal distribution with mean `$\mu$` and variance `$\sigma$` is given by

$$
f_X(x) = \frac{1}{\sigma\sqrt{(2\pi)}} e^{-(x-\mu)^2/2\sigma^2}
$$

If we let the mean `$\mu=0$` and the standard deviation `$\sigma=1$`, we get the probability density function for the standard normal distribution.

$$
f_X(x) = \frac{1}{\sqrt{(2\pi)}} e^{-(x)^2/2}
$$

---

### Standard Normal Distribution

$$
f_X(x) = \frac{1}{\sqrt{(2\pi)}} e^{-(x)^2/2}
$$

```r
dnorm(0)
```

```
[1] 0.3989423
```

]

<div class="figure">
<img src="l42022_files/figure-html/unnamed-chunk-11-1.png" alt="Standard normal probability density function: dnorm(0)" width="100%" />
<p class="caption">Standard normal probability density function: dnorm(0)</p>
</div>

]

---

### Standard Normal Distribution

$$
f_X(x) = \frac{1}{\sqrt{(2\pi)}} e^{-(x)^2/2}
$$

```r
pnorm(0)
```

```
[1] 0.5
```

]

<div class="figure">
<img src="l42022_files/figure-html/unnamed-chunk-13-1.png" alt="Standard normal probability density function: pnorm(0)" width="100%" />
<p class="caption">Standard normal probability density function: pnorm(0)</p>
</div>

]

---

## Standard Normal Distribution

$$
f_X(x) = \frac{1}{\sqrt{(2\pi)}} e^{-(x)^2/2}
$$

```r
qnorm(0.5)
```

```
[1] 0
```

]

<div class="figure">
<img src="l42022_files/figure-html/unnamed-chunk-15-1.png" alt="Standard normal probability density function: qnorm(0.5)" width="100%" />
<p class="caption">Standard normal probability density function: qnorm(0.5)</p>
</div>

]

---

## Normal distribution: `norm`

![](norm.png)

]

```r
pnorm(3)
```

```
[1] 0.9986501
```

```r
pnorm(3, sd=1, mean=0)
```

```
[1] 0.9986501
```

```r
pnorm(3, sd=2, mean=1)
```

```
[1] 0.8413447
```

]

---

### Binomial distribution

```r
dbinom(2, size=10, prob=0.2)
```

```
[1] 0.3019899
```

```r
a <- dbinom(0:10, size=10, prob=0.2)
a
```

```
 [1] 0.1073741824 0.2684354560 0.3019898880 0.2013265920 0.0880803840
 [6] 0.0264241152 0.0055050240 0.0007864320 0.0000737280 0.0000040960
[11] 0.0000001024
```

```r
cumsum(a)
```

```
 [1] 0.1073742 0.3758096 0.6777995 0.8791261 0.9672065 0.9936306 0.9991356
 [8] 0.9999221 0.9999958 0.9999999 1.0000000
```

---

```r
cumsum(a)
```

```
 [1] 0.1073742 0.3758096 0.6777995 0.8791261 0.9672065 0.9936306 0.9991356
 [8] 0.9999221 0.9999958 0.9999999 1.0000000
```

```r
pbinom(0:10, size=10, prob=0.2)
```

```
 [1] 0.1073742 0.3758096 0.6777995 0.8791261 0.9672065 0.9936306 0.9991356
 [8] 0.9999221 0.9999958 0.9999999 1.0000000
```

```r
qbinom(0.4, size=10, prob=0.2)
```

```
[1] 2
```

---

### Standard Normal Distribution: rnorm

```r
set.seed(262020)
random_numbers <- rnorm(5)
random_numbers
```

```
[1] 0.2007818 0.9587335 1.1836906 1.4951375 1.1810922
```

```r
sort(random_numbers) ## sort the numbers then it is easy to map with the graph
```

```
[1] 0.2007818 0.9587335 1.1810922 1.1836906 1.4951375
```

]

]

---
class: inverse, center, middle

# Other distributions in R

---

- **`beta`**: beta distribution

- **`binom`**: binomial distribution

- **`cauchy`**: Cauchy distribution

- **`chisq`**: chi-squared distribution

- **`exp`**: exponential distribution

- **`f`**: F distribution

- **`gamma`**: gamma distribution

- **`geom`**: geometric distribution

- **`hyper`**: hyper-geometric distribution

]

- **`lnorm`**: log-normal distribution

- **`multinom`**: multinomial distribution

- **`nbinom`**: negative binomial distribution

- **`norm`**: normal distribution

- **`pois`**: Poisson distribution

- **`t`**: Student's t distribution

- **`unif`**: uniform distribution

- **`weibull`**: Weibull distribution

]

---

🙋 Getting help with R:  **`?Distributions`**

---

# Your turn

---

**Q1** Suppose `$Z \sim  N(0,1)$`. Calculate the following standard normal probabilities.

- `$P(Z \le 1.25)$`,

- `$P(Z > 1.25)$`,

- `$P(Z \leq -1.25)$`,

- `$P(-.38 \leq Z \leq 1.25)$`.

**Q2** Find the following percentiles for the standard normal distribution.

- 90th, 
     
  - 95th,
     
  - 97.5th,
     
---

**Q3** Determine the `$Z_\alpha$` for the following

- `$\alpha = 0.1$`
      
  - `$\alpha = 0.95$`

**Q4** Suppose `$X \sim N(15, 9)$`. Calculate the following probabilities

- `$P(X \leq 15)$`,
  
  - `$P(X < 15)$`,
  
  - `$P(X \geq 10)$`.
  
<div class="countdown" id="timer_62e1e854" style="right:0;bottom:0;" data-warnwhen="0">
<code class="countdown-time"><span class="countdown-digits minutes">02</span><span class="countdown-digits colon">:</span><span class="countdown-digits seconds">00</span></code>
</div>
  
  
---

**Q5** A particular mobile phone number is used to receive both voice messages and text messages. Suppose 20% of the messages involve text messages, and consider a sample of 15 messages. What is the probability that

- At most 8 of the messages involve a text message?
    
  - Exactly 8 of the messages involve a text message.
  
<div class="countdown" id="timer_62e1e889" style="right:0;bottom:0;" data-warnwhen="0">
<code class="countdown-time"><span class="countdown-digits minutes">02</span><span class="countdown-digits colon">:</span><span class="countdown-digits seconds">00</span></code>
</div>
  
---

**Q6** Generate 20 random values from a Poisson distribution with mean 10 and calculate the mean. Compare your answer with others.

---

# Reproducibility of scientific results

```r
rnorm(10) # first attempt
```

```
 [1]  1.6582609 -1.8912734 -2.8471112 -2.1617741  0.6401224 -0.4295948
 [7] -0.3122580 -1.0267992  1.4231150  0.8661058
```

```r
rnorm(10) # second attempt
```

```
 [1] -0.91879540 -0.06053766 -0.20263170 -0.26301690  0.97964620 -0.46034817
 [7]  0.81826880 -0.60935778  1.71086661  0.49294451
```

As you can see above you will get different results.

---

# Reproducibility of scientific results (cont.)

```r
set.seed(1)
rnorm(10) # First attempt with set.seed
```

```
 [1] -0.6264538  0.1836433 -0.8356286  1.5952808  0.3295078 -0.8204684
 [7]  0.4874291  0.7383247  0.5757814 -0.3053884
```

```r
set.seed(1)
rnorm(10) # Second attempt with set.seed
```

```
 [1] -0.6264538  0.1836433 -0.8356286  1.5952808  0.3295078 -0.8204684
 [7]  0.4874291  0.7383247  0.5757814 -0.3053884
```
 
---
## R Apply family and its variants

- **`apply()`** function

```r
marks <- data.frame(maths=c(10, 20, 30), chemistry=c(100, NA, 60)); marks
```

```
  maths chemistry
1    10       100
2    20        NA
3    30        60
```

```r
apply(marks, 1, mean)
```

```
[1] 55 NA 45
```

```r
apply(marks, 2, mean)
```

```
    maths chemistry 
       20        NA 
```

```r
apply(marks, 1, mean, na.rm=TRUE)
```

```
[1] 55 20 45
```

---

# Your turn

---

Calculate the row and column wise standard deviation of the following matrix

```
     [,1] [,2] [,3] [,4]
[1,]    1    6   11   16
[2,]    2    7   12   17
[3,]    3    8   13   18
[4,]    4    9   14   19
[5,]    5   10   15   20
```

---

# Your turn

---

**Your turn**

Find about the following variants of apply family functions in R **`lapply()`**, **`sapply()`**, **`vapply()`**, **`mapply()`**, **`rapply()`**, and **`tapply()`** functions.

Resourses: You can follow the DataCamp tutorial [here](https://www.datacamp.com/community/tutorials/r-tutorial-apply-family?utm_source=adwords_ppc&utm_campaignid=1658343524&utm_adgroupid=63833882055&utm_device=c&utm_keyword=%2Bapply%20%2Br&utm_matchtype=b&utm_network=g&utm_adpostion=&utm_creative=319558765408&utm_targetid=aud-299261629574:kwd-309818754193&utm_loc_interest_ms=&utm_loc_physical_ms=1009919&gclid=EAIaIQobChMImfeQkOTq5wIVVQwrCh1BngrmEAAYASAAEgLEa_D_BwE).

- You should clearly explain,

- syntax for each function

- function inputs
    
    - how each function works?/ The task of the function.
    
    - output of the function.
    
    - differences between the functions (apply vs lapply, apply vs sapply, etc.)

- Provide your own example for each function.

---

## Data Visualization: qplot()

?qplot
--

---
# Installing R Packages

## Method 1

![](inst.png)
---

# Installing R Packages

## Method 2

```r
install.packages("ggplot2")
```

---

## Load package

```r
library(ggplot2)
```

Now search `?qplot`

Note: You shouldn't have to re-install packages each time you open R. However, you do need to load the packages you want to use in that session via `library`.

---

# `install.packages` vs `library`

![](loadpkg.jpeg)

Image credit: [Professor Di Cook](http://dicook.org/)
---

## colmozzie dataset

```r
library(colmozzie)
data(colmozzie)
```

---

## Data Visualization with R

```r
boxplot(mpg ~ cyl, data = mtcars,   
        xlab = "Quantity of Cylinders",  
        ylab = "Miles Per Gallon",   
        main = "Boxplot Example",  
        notch = TRUE,   
        varwidth = TRUE,   
        col = c("green","yellow","red"),  
        names = c("High","Medium","Low")  
)  
```

]

```r
counts <- table(mtcars$gear)
barplot(counts, main="Car Distribution",
   xlab="Number of Gears")
```

]

---

Default R installation: graphics package

```
 [1] "abline"          "arrows"          "assocplot"       "axis"           
 [5] "Axis"            "axis.Date"       "axis.POSIXct"    "axTicks"        
 [9] "barplot"         "barplot.default" "box"             "boxplot"        
[13] "boxplot.default" "boxplot.matrix"  "bxp"             "cdplot"         
[17] "clip"            "close.screen"    "co.intervals"    "contour"        
[21] "contour.default" "coplot"          "curve"           "dotchart"       
[25] "erase.screen"    "filled.contour"  "fourfoldplot"    "frame"          
[29] "grconvertX"      "grconvertY"      "grid"            "hist"           
[33] "hist.default"    "identify"        "image"           "image.default"  
[37] "layout"          "layout.show"     "lcm"             "legend"         
[41] "lines"           "lines.default"   "locator"         "matlines"       
[45] "matplot"         "matpoints"       "mosaicplot"      "mtext"          
[49] "pairs"           "pairs.default"   "panel.smooth"    "par"            
[53] "persp"           "pie"             "plot"            "plot.default"   
[57] "plot.design"     "plot.function"   "plot.new"        "plot.window"    
[61] "plot.xy"         "points"          "points.default"  "polygon"        
[65] "polypath"        "rasterImage"     "rect"            "rug"            
[69] "screen"          "segments"        "smoothScatter"   "spineplot"      
[73] "split.screen"    "stars"           "stem"            "strheight"      
[77] "stripchart"      "strwidth"        "sunflowerplot"   "symbols"        
[81] "text"            "text.default"    "title"           "xinch"          
[85] "xspline"         "xyinch"          "yinch"          
```

---

![](qplot.png)
---

]

]

---

background-image: url('qplottheory.png')
background-position: center
background-size: contain

---

## colmozzie

```r
head(colmozzie)
```

```
# A tibble: 6 × 12
  Cases  Year  Week   TEM  TMAX    Tm SLP         H    PP    VV     V    VM
  <int> <int> <int> <dbl> <dbl> <dbl> <chr>   <dbl> <dbl> <dbl> <dbl> <dbl>
1    44  2009     1  27.3  32.7  23.6 1010.7   68     0    13   11.1  20.6 
2    39  2009     2  26.4  29.8  23.9 1010.7   78.7   0    18.3  5.83  9.2 
3    57  2009     3  27.1  32.0  23.5 1012.58  67     0    20    6.12 10.5 
4    53  2009     4  26.8  31    23.4 1009.9   68     0    20    7.15 11.1 
5    29  2009     5  26.8  30.1  23.6 1010.1   78    17.2  19.0  3.2   6.82
6    45  2009     6  26.8  30.6  23   1012.05  72.5   0    20    5.55 10.3 
```

---

## mozzie

```r
devtools::install_github("thiyangt/mozzie")
```

```r
library(mozzie)
data(mozzie)
```

---
## Data Visualization with `qplot`

## plot vs qplot

```r
plot(mozzie$Colombo, mozzie$Gampaha)
```

<img src="l42022_files/figure-html/unnamed-chunk-40-1.png" width="100%" />
]

```r
qplot(Colombo, Gampaha, data=mozzie)
```

<img src="l42022_files/figure-html/unnamed-chunk-41-1.png" width="100%" />
]
---
## Data Visualization with `qplot`

```r
qplot(Colombo, Gampaha, data=mozzie)
```

<img src="l42022_files/figure-html/unnamed-chunk-42-1.png" width="100%" />
]

```r
qplot(Colombo, Gampaha, data=mozzie,
      colour=Year)
```

<img src="l42022_files/figure-html/unnamed-chunk-43-1.png" width="100%" />
]
---
## Data Visualization with `qplot`

```r
qplot(Colombo, Gampaha, data=mozzie)
```

<img src="l42022_files/figure-html/unnamed-chunk-44-1.png" width="100%" />
]

```r
qplot(Colombo, Gampaha, data=mozzie, 
      size=Year)
```

<img src="l42022_files/figure-html/unnamed-chunk-45-1.png" width="100%" />
]

---
## Data Visualization with `qplot`

```r
qplot(Colombo, Gampaha, data=mozzie)
```

<img src="l42022_files/figure-html/unnamed-chunk-46-1.png" width="100%" />
]

```r
qplot(Colombo, Gampaha, data=mozzie, 
      size=Year, alpha=0.5)
```

<img src="l42022_files/figure-html/unnamed-chunk-47-1.png" width="100%" />
]

---

## Data Visualization with `qplot`

```r
qplot(Colombo, Gampaha, data=mozzie)
```

<img src="l42022_files/figure-html/unnamed-chunk-48-1.png" width="100%" />
]

```r
qplot(Colombo, Gampaha, data=mozzie,
      geom="point")
```

<img src="l42022_files/figure-html/unnamed-chunk-49-1.png" width="100%" />
]

---
## Data Visualization with `qplot`

```r
qplot(ID, Gampaha, data=mozzie)
```

<img src="l42022_files/figure-html/unnamed-chunk-50-1.png" width="100%" />
]

```r
qplot(ID, Gampaha, data=mozzie, 
      geom="line")
```

<img src="l42022_files/figure-html/unnamed-chunk-51-1.png" width="100%" />
]

---
## Data Visualization with `qplot`

```r
qplot(ID, Gampaha, data=mozzie)
```

<img src="l42022_files/figure-html/unnamed-chunk-52-1.png" width="100%" />
]

```r
qplot(ID, Gampaha, data=mozzie,
      geom="path")
```

<img src="l42022_files/figure-html/unnamed-chunk-53-1.png" width="100%" />
]

---

## Data Visualization with `qplot`

```r
qplot(Colombo, Gampaha, data=mozzie,
      geom="line")
```

<img src="l42022_files/figure-html/unnamed-chunk-54-1.png" width="100%" />
]

```r
qplot(Colombo, Gampaha, data=mozzie, 
      geom="path")
```

<img src="l42022_files/figure-html/unnamed-chunk-55-1.png" width="100%" />
]

---
## Data Visualization with `qplot`

```r
qplot(Colombo, Gampaha, data=mozzie, 
      geom=c("line", "point"))
```

<img src="l42022_files/figure-html/unnamed-chunk-56-1.png" width="100%" />
]

```r
qplot(Colombo, Gampaha, data=mozzie,
      geom=c("path", "point"))
```

<img src="l42022_files/figure-html/unnamed-chunk-57-1.png" width="100%" />
]
---

## Data Visualization with `qplot`

```r
boxplot(Colombo~Year, data=mozzie)
```

<img src="l42022_files/figure-html/unnamed-chunk-58-1.png" width="100%" />
]

```r
qplot(factor(Year), Colombo, data=mozzie,
      geom="boxplot")
```

<img src="l42022_files/figure-html/unnamed-chunk-59-1.png" width="100%" />
]

---

## Data Visualization with `qplot`

```r
qplot(factor(Year), Colombo, data=mozzie,
      geom="boxplot")
```

<img src="l42022_files/figure-html/unnamed-chunk-60-1.png" width="100%" />
]

```r
qplot(factor(Year), Colombo, data=mozzie) # geom="point"-default
```

<img src="l42022_files/figure-html/unnamed-chunk-61-1.png" width="100%" />
]

---
## Data Visualization with `qplot`
.pull-left[

```r
qplot(factor(Year), Colombo, data=mozzie, 
      geom="point")
```

<img src="l42022_files/figure-html/unnamed-chunk-62-1.png" width="100%" />
]

```r
qplot(factor(Year), Colombo, data=mozzie, 
      geom="jitter") # geom="point"-default
```

<img src="l42022_files/figure-html/unnamed-chunk-63-1.png" width="100%" />
]

---

## Data Visualization with `qplot`
.pull-left[

```r
qplot(factor(Year), Colombo, data=mozzie,
      geom="jitter")
```

<img src="l42022_files/figure-html/unnamed-chunk-64-1.png" width="100%" />
]

```r
qplot(factor(Year), Colombo, data=mozzie,
      geom=c("jitter", "boxplot")) # geom="point"-default
```

<img src="l42022_files/figure-html/unnamed-chunk-65-1.png" width="100%" />
]

---

]

```r
qplot(factor(Year), Colombo, data=mozzie,
      geom=c("jitter", "boxplot")) # geom="point"-default
```

<img src="l42022_files/figure-html/unnamed-chunk-68-1.png" width="100%" />
]

---

```r
qplot(factor(Year), Colombo, data=mozzie,
      geom=c("jitter", "boxplot")) # geom="point"-default
```

<img src="l42022_files/figure-html/unnamed-chunk-69-1.png" width="100%" />
]

```r
qplot(factor(Year), Colombo, data=mozzie,
      geom=c("jitter", "boxplot"),
      outlier.shape = NA) # geom="point"-default
```

<img src="l42022_files/figure-html/unnamed-chunk-70-1.png" width="100%" />
]

---

## Data Visualization with `qplot`
.pull-left[

```r
qplot(Colombo, data=mozzie)
```

<img src="l42022_files/figure-html/unnamed-chunk-71-1.png" width="100%" />
]

```r
qplot(Colombo, data=mozzie, geom="density") 
```

<img src="l42022_files/figure-html/unnamed-chunk-72-1.png" width="100%" />
]

---

# Your turn

---

Explore `iris` dataset with suitable graphics.

```r
head(iris)
```

```
  Sepal.Length Sepal.Width Petal.Length Petal.Width Species
1          5.1         3.5          1.4         0.2  setosa
2          4.9         3.0          1.4         0.2  setosa
3          4.7         3.2          1.3         0.2  setosa
4          4.6         3.1          1.5         0.2  setosa
5          5.0         3.6          1.4         0.2  setosa
6          5.4         3.9          1.7         0.4  setosa
```

## Thank you!

Slides available at: hellor.netlify.app