Welcome to the presentation on Multivariate Linear Regression using the Iris dataset. Goal: To understand and apply multivariate linear regression on the Iris dataset to predict Sepal.Length based on Sepal.Width and Petal.Length.

Simple Linear Regression models the relationship between two variables using a linear equation.

\[ y = \beta_0 + \beta_1x + \epsilon \]

Where:

• \(y\) is the dependent variable.
• \(x\) is the independent variable.
• \(\beta_0\) is the intercept.
• \(\beta_1\) is the slope.
• \(\epsilon\) is the error term.

Multivariate Linear Regression extends Simple Linear Regression to multiple predictors. \[ y = \beta_0 + \beta_1x_1 + \beta_2x_2 + \cdots + \beta_nx_n + \epsilon \] Where:

• \(y\) is the dependent variable.
• \(x_1, x_2, \ldots, x_n\) are the independent variables.
• \(\beta_0\) is the intercept.
• \(\beta_1, \beta_2, \ldots, \beta_n\) are the slopes.
• \(\epsilon\) is the error term.

First, let’s install necessary packages and load the dataset:

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The Iris dataset contains measurements of sepals and petals for three species of iris flowers: Setosa, Versicolor, and Virginica.

##   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

Exploratory Data Analysis for Sepal.Width

Exploratory Data Analysis for Petal.Length

Exploratory Data Analysis for Sepal.Length

Code for fitting the multivariate linear regression model:

##               Estimate Std. Error   t value     Pr(>|t|)
## (Intercept)  2.2491402 0.24796963  9.070224 7.038510e-16
## Sepal.Width  0.5955247 0.06932816  8.589940 1.163254e-14
## Petal.Length 0.4719200 0.01711768 27.569160 5.847914e-60

Finally, let us visualise the regression output: