An RMarkdown report

class: center, middle, inverse, title-slide

.title[
# An RMarkdown report
]
.date[
### 2024-03-09
]

---

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# Data description

In this project we consider the classical `iris` data set that can be found in the base R package `datasets`. `iris` has 5 columns named **`Sepal.Length`**, **`Sepal.Width`**, **`Petal.Length`**, **`Petal.Width`**, **`Species`** and **150** observations.

To get help about columns, run `?iris`.

The data set `iris` is

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{"columns":[{"label":[""],"name":["_rn_"],"type":[""],"align":["left"]},{"label":["Sepal.Length"],"name":[1],"type":["dbl"],"align":["right"]},{"label":["Sepal.Width"],"name":[2],"type":["dbl"],"align":["right"]},{"label":["Petal.Length"],"name":[3],"type":["dbl"],"align":["right"]},{"label":["Petal.Width"],"name":[4],"type":["dbl"],"align":["right"]},{"label":["Species"],"name":[5],"type":["fct"],"align":["left"]}],"data":[{"1":"5.1","2":"3.5","3":"1.4","4":"0.2","5":"setosa","_rn_":"1"},{"1":"4.9","2":"3.0","3":"1.4","4":"0.2","5":"setosa","_rn_":"2"},{"1":"4.7","2":"3.2","3":"1.3","4":"0.2","5":"setosa","_rn_":"3"},{"1":"4.6","2":"3.1","3":"1.5","4":"0.2","5":"setosa","_rn_":"4"},{"1":"5.0","2":"3.6","3":"1.4","4":"0.2","5":"setosa","_rn_":"5"},{"1":"5.4","2":"3.9","3":"1.7","4":"0.4","5":"setosa","_rn_":"6"},{"1":"4.6","2":"3.4","3":"1.4","4":"0.3","5":"setosa","_rn_":"7"},{"1":"5.0","2":"3.4","3":"1.5","4":"0.2","5":"setosa","_rn_":"8"},{"1":"4.4","2":"2.9","3":"1.4","4":"0.2","5":"setosa","_rn_":"9"},{"1":"4.9","2":"3.1","3":"1.5","4":"0.1","5":"setosa","_rn_":"10"}],"options":{"columns":{"min":{},"max":[10]},"rows":{"min":[10],"max":[10]},"pages":{}}}
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---

# Descriptive analysis

First, we compute some descriptive statistics with the `summary()` function:

Table: Descriptive statistics

|   | Sepal.Length | Sepal.Width | Petal.Length | Petal.Width |      Species |
|:--|:-------------|:------------|:-------------|:------------|:-------------|
|   |Min.   :4.30  |Min.   :2.00 |Min.   :1.00  |Min.   :0.1  |setosa    :50 |
|   |1st Qu.:5.10  |1st Qu.:2.80 |1st Qu.:1.60  |1st Qu.:0.3  |versicolor:50 |
|   |Median :5.80  |Median :3.00 |Median :4.35  |Median :1.3  |virginica :50 |
|   |Mean   :5.84  |Mean   :3.06 |Mean   :3.76  |Mean   :1.2  |NA            |
|   |3rd Qu.:6.40  |3rd Qu.:3.30 |3rd Qu.:5.10  |3rd Qu.:1.8  |NA            |
|   |Max.   :7.90  |Max.   :4.40 |Max.   :6.90  |Max.   :2.5  |NA            |

---

Second, we use the function `aggregate` to get the following table that shows the means of the 4 numerical variables for each species.

Table: Means by species

|Species    | Sepal Length| Sepal Width| Petal Length| Petal width|
|:----------|------------:|-----------:|------------:|-----------:|
|setosa     |         5.01|        3.43|         1.46|       0.246|
|versicolor |         5.94|        2.77|         4.26|       1.326|
|virginica  |         6.59|        2.97|         5.55|       2.026|

---

# Linear regression

We use the function `cor()` to get the Pearson’s coefficients of correlation between all our numeric variables:

Table: Pearson’s coefficients of correlation

|             | Sepal.Length| Sepal.Width| Petal.Length| Petal.Width|
|:------------|------------:|-----------:|------------:|-----------:|
|Sepal.Length |        1.000|      -0.118|        0.872|       0.818|
|Sepal.Width  |       -0.118|       1.000|       -0.428|      -0.366|
|Petal.Length |        0.872|      -0.428|        1.000|       0.963|
|Petal.Width  |        0.818|      -0.366|        0.963|       1.000|

---

Hered are 3 scatter plots that show the association between `Petal.Length` and the other numerical variables.

---

---

Now, we would like to explain the variations in the length of the sepal as a function of the length of the petal. To do so, we use the following linear regression `lm(Sepal.Length ~ Petal.Length, data = iris)`. Here is the summary of this model:

Table: Summary of lm: Sepal.Length ~ Petal. Length

|             | Estimate| Std. Error| t value| Pr(>&#124;t&#124;)|
|:------------|--------:|----------:|-------:|------------------:|
|(Intercept)  |    4.307|      0.078|    54.9|                  0|
|Petal.Length |    0.409|      0.019|    21.6|                  0|

The model's equation is

`$$\widehat{Sepal.Length} = 4.307 + 0.409Petal.Length$$`

Here are the data with the regression line:

---

```
Warning in par(margin = c(3, 3, 3, 3)): "margin" is not a graphical parameter
```

---

Finally, we use the `plot(reg)` command to get some graphical representations of the residuals.

<div class="figure" style="text-align: defaut">
<img src="data:image/png;base64,#3_files/figure-html/unnamed-chunk-8-1.png" alt="Residuals plot 1" width="50%" /><img src="data:image/png;base64,#3_files/figure-html/unnamed-chunk-8-2.png" alt="Residuals plot 1" width="50%" />
<p class="caption">Residuals plot 1</p>
</div>

---

<div class="figure" style="text-align: defaut">
<img src="data:image/png;base64,#3_files/figure-html/unnamed-chunk-9-1.png" alt="Residuals plot 2" width="50%" /><img src="data:image/png;base64,#3_files/figure-html/unnamed-chunk-9-2.png" alt="Residuals plot 2" width="50%" />
<p class="caption">Residuals plot 2</p>
</div>