Given the model:

```
> Durée <- c(6,5,3.5,3,5,3,2,8, 2.5) 
> Note <- c(18,16,14,10,15,13,8,19,12) 
> model <- lm(Note ~ Durée)

```

I was tasked, among other things, to verify whether homoscedasticity is true.

After running `plot(model)` I was able to visualise the following graphs:

[![Residuals vs Fitted](https://i.stack.imgur.com/liX5Z.png)](https://i.stack.imgur.com/liX5Z.png)
[![enter image description here](https://i.stack.imgur.com/WH1h3.png)](https://i.stack.imgur.com/WH1h3.png)

[![enter image description here](https://i.stack.imgur.com/OshNM.png)](https://i.stack.imgur.com/OshNM.png)

From the *Residuals vs Fitted* and *Scale-Location* plots, we can see that the line is very far from being straight, which indicates the presence of heteroscedasticity.

However, when I run the studentized Breusch-Pagan test using the command `bptest(model)`, I got the following output:

```
    studentized Breusch-Pagan test

data:  model
BP = 1.8622, df = 1, p-value = 0.1724

```

The test gives a p-value of 0.1724, which is greater than 0.05. This means that we can't reject the hypothesis of homoscedasticity, which contradicts, at least in my understanding, the output of the plots previously mentioned.