class: center, middle, inverse, title-slide .title[ # An RMarkdown report ] .author[ ### Your name ] --- ## 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 <div data-pagedtable="false"> <script data-pagedtable-source type="application/json"> {"columns":[{"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"},{"1":"4.9","2":"3.0","3":"1.4","4":"0.2","5":"setosa"},{"1":"4.7","2":"3.2","3":"1.3","4":"0.2","5":"setosa"},{"1":"4.6","2":"3.1","3":"1.5","4":"0.2","5":"setosa"},{"1":"5.0","2":"3.6","3":"1.4","4":"0.2","5":"setosa"},{"1":"5.4","2":"3.9","3":"1.7","4":"0.4","5":"setosa"},{"1":"4.6","2":"3.4","3":"1.4","4":"0.3","5":"setosa"},{"1":"5.0","2":"3.4","3":"1.5","4":"0.2","5":"setosa"},{"1":"4.4","2":"2.9","3":"1.4","4":"0.2","5":"setosa"},{"1":"4.9","2":"3.1","3":"1.5","4":"0.1","5":"setosa"},{"1":"5.4","2":"3.7","3":"1.5","4":"0.2","5":"setosa"},{"1":"4.8","2":"3.4","3":"1.6","4":"0.2","5":"setosa"},{"1":"4.8","2":"3.0","3":"1.4","4":"0.1","5":"setosa"},{"1":"4.3","2":"3.0","3":"1.1","4":"0.1","5":"setosa"},{"1":"5.8","2":"4.0","3":"1.2","4":"0.2","5":"setosa"},{"1":"5.7","2":"4.4","3":"1.5","4":"0.4","5":"setosa"},{"1":"5.4","2":"3.9","3":"1.3","4":"0.4","5":"setosa"},{"1":"5.1","2":"3.5","3":"1.4","4":"0.3","5":"setosa"},{"1":"5.7","2":"3.8","3":"1.7","4":"0.3","5":"setosa"},{"1":"5.1","2":"3.8","3":"1.5","4":"0.3","5":"setosa"},{"1":"5.4","2":"3.4","3":"1.7","4":"0.2","5":"setosa"},{"1":"5.1","2":"3.7","3":"1.5","4":"0.4","5":"setosa"},{"1":"4.6","2":"3.6","3":"1.0","4":"0.2","5":"setosa"},{"1":"5.1","2":"3.3","3":"1.7","4":"0.5","5":"setosa"},{"1":"4.8","2":"3.4","3":"1.9","4":"0.2","5":"setosa"},{"1":"5.0","2":"3.0","3":"1.6","4":"0.2","5":"setosa"},{"1":"5.0","2":"3.4","3":"1.6","4":"0.4","5":"setosa"},{"1":"5.2","2":"3.5","3":"1.5","4":"0.2","5":"setosa"},{"1":"5.2","2":"3.4","3":"1.4","4":"0.2","5":"setosa"},{"1":"4.7","2":"3.2","3":"1.6","4":"0.2","5":"setosa"},{"1":"4.8","2":"3.1","3":"1.6","4":"0.2","5":"setosa"},{"1":"5.4","2":"3.4","3":"1.5","4":"0.4","5":"setosa"},{"1":"5.2","2":"4.1","3":"1.5","4":"0.1","5":"setosa"},{"1":"5.5","2":"4.2","3":"1.4","4":"0.2","5":"setosa"},{"1":"4.9","2":"3.1","3":"1.5","4":"0.2","5":"setosa"},{"1":"5.0","2":"3.2","3":"1.2","4":"0.2","5":"setosa"},{"1":"5.5","2":"3.5","3":"1.3","4":"0.2","5":"setosa"},{"1":"4.9","2":"3.6","3":"1.4","4":"0.1","5":"setosa"},{"1":"4.4","2":"3.0","3":"1.3","4":"0.2","5":"setosa"},{"1":"5.1","2":"3.4","3":"1.5","4":"0.2","5":"setosa"},{"1":"5.0","2":"3.5","3":"1.3","4":"0.3","5":"setosa"},{"1":"4.5","2":"2.3","3":"1.3","4":"0.3","5":"setosa"},{"1":"4.4","2":"3.2","3":"1.3","4":"0.2","5":"setosa"},{"1":"5.0","2":"3.5","3":"1.6","4":"0.6","5":"setosa"},{"1":"5.1","2":"3.8","3":"1.9","4":"0.4","5":"setosa"},{"1":"4.8","2":"3.0","3":"1.4","4":"0.3","5":"setosa"},{"1":"5.1","2":"3.8","3":"1.6","4":"0.2","5":"setosa"},{"1":"4.6","2":"3.2","3":"1.4","4":"0.2","5":"setosa"},{"1":"5.3","2":"3.7","3":"1.5","4":"0.2","5":"setosa"},{"1":"5.0","2":"3.3","3":"1.4","4":"0.2","5":"setosa"},{"1":"7.0","2":"3.2","3":"4.7","4":"1.4","5":"versicolor"},{"1":"6.4","2":"3.2","3":"4.5","4":"1.5","5":"versicolor"},{"1":"6.9","2":"3.1","3":"4.9","4":"1.5","5":"versicolor"},{"1":"5.5","2":"2.3","3":"4.0","4":"1.3","5":"versicolor"},{"1":"6.5","2":"2.8","3":"4.6","4":"1.5","5":"versicolor"},{"1":"5.7","2":"2.8","3":"4.5","4":"1.3","5":"versicolor"},{"1":"6.3","2":"3.3","3":"4.7","4":"1.6","5":"versicolor"},{"1":"4.9","2":"2.4","3":"3.3","4":"1.0","5":"versicolor"},{"1":"6.6","2":"2.9","3":"4.6","4":"1.3","5":"versicolor"},{"1":"5.2","2":"2.7","3":"3.9","4":"1.4","5":"versicolor"},{"1":"5.0","2":"2.0","3":"3.5","4":"1.0","5":"versicolor"},{"1":"5.9","2":"3.0","3":"4.2","4":"1.5","5":"versicolor"},{"1":"6.0","2":"2.2","3":"4.0","4":"1.0","5":"versicolor"},{"1":"6.1","2":"2.9","3":"4.7","4":"1.4","5":"versicolor"},{"1":"5.6","2":"2.9","3":"3.6","4":"1.3","5":"versicolor"},{"1":"6.7","2":"3.1","3":"4.4","4":"1.4","5":"versicolor"},{"1":"5.6","2":"3.0","3":"4.5","4":"1.5","5":"versicolor"},{"1":"5.8","2":"2.7","3":"4.1","4":"1.0","5":"versicolor"},{"1":"6.2","2":"2.2","3":"4.5","4":"1.5","5":"versicolor"},{"1":"5.6","2":"2.5","3":"3.9","4":"1.1","5":"versicolor"},{"1":"5.9","2":"3.2","3":"4.8","4":"1.8","5":"versicolor"},{"1":"6.1","2":"2.8","3":"4.0","4":"1.3","5":"versicolor"},{"1":"6.3","2":"2.5","3":"4.9","4":"1.5","5":"versicolor"},{"1":"6.1","2":"2.8","3":"4.7","4":"1.2","5":"versicolor"},{"1":"6.4","2":"2.9","3":"4.3","4":"1.3","5":"versicolor"},{"1":"6.6","2":"3.0","3":"4.4","4":"1.4","5":"versicolor"},{"1":"6.8","2":"2.8","3":"4.8","4":"1.4","5":"versicolor"},{"1":"6.7","2":"3.0","3":"5.0","4":"1.7","5":"versicolor"},{"1":"6.0","2":"2.9","3":"4.5","4":"1.5","5":"versicolor"},{"1":"5.7","2":"2.6","3":"3.5","4":"1.0","5":"versicolor"},{"1":"5.5","2":"2.4","3":"3.8","4":"1.1","5":"versicolor"},{"1":"5.5","2":"2.4","3":"3.7","4":"1.0","5":"versico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</script> </div> <!-- see https://github.com/yihui/knitr/releases/tag/v1.37 --> --- ## 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 | | | |3rd Qu.:6.40 |3rd Qu.:3.30 |3rd Qu.:5.10 |3rd Qu.:1.8 | | | |Max. :7.90 |Max. :4.40 |Max. :6.90 |Max. :2.5 | | --- 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| --- Here are 3 scatter plots that show the association between `Petal.Length` and the other numerical variables. <img src="data:image/png;base64,#3S_files/figure-html/unnamed-chunk-10-1.png" width="50%" /><img src="data:image/png;base64,#3S_files/figure-html/unnamed-chunk-10-2.png" width="50%" /> --- <img src="data:image/png;base64,#3S_files/figure-html/unnamed-chunk-12-1.png" width="50%" /> --- 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| 0.00e+00| |Petal.Length | 0.409| 0.019| 21.6| 1.04e-47| The model's equation is $$ \widehat{Sepal.Length} = 4.307+ 0.409 Petal.Length. $$ Here are the data with the regression line: --- <img src="data:image/png;base64,#3S_files/figure-html/unnamed-chunk-16-1.png" width="80%" style="display: block; margin: auto;" /> --- Finally, we use the `plot(reg)` command to get some graphical representations of the residuals. <div class="figure"> <img src="data:image/png;base64,#3S_files/figure-html/unnamed-chunk-18-1.png" alt="Residuals plot 1" width="50%" /><img src="data:image/png;base64,#3S_files/figure-html/unnamed-chunk-18-2.png" alt="Residuals plot 1" width="50%" /> <p class="caption">Residuals plot 1</p> </div> --- <div class="figure"> <img src="data:image/png;base64,#3S_files/figure-html/unnamed-chunk-20-1.png" alt="Residuals plot 2" width="50%" /><img src="data:image/png;base64,#3S_files/figure-html/unnamed-chunk-20-2.png" alt="Residuals plot 2" width="50%" /> <p class="caption">Residuals plot 2</p> </div>