# Exercise 2 Linear regression in 1D

The goal of this exercise is to understand how the linear regression works in one dimension. To do so, we will generate a data in one dimension. Using `make regression` from Scikit-learn, generate a data set with 100 observations:

```python
X, y, coef = make_regression(n_samples=100,
                         n_features=1,
                         n_informative=1,
                         noise=10,
                         coef=True,
                         random_state=0,
                         bias=100.0)
```

1. Plot the data using matplotlib. The plot should look like this:

![alt text][q1]

[q1]: ./w2_day1_ex2_q1.png "Scatter plot"

2. Fit a LinearRegression from Scikit-learn on the generated data and give the equation of the fitted line. The expected output is: `y = coef * x + intercept`

3. Add the fitted line to the plot. the plot should look like this:

![alt text][q3]

[q3]: ./w2_day1_ex2_q3.png "Scatter plot + fitted line"

4. Predict on X

5. Create a function that computes the Mean Squared Error (MSE) and compute the MSE on the data set. *The MSE is frequently used as well as other regression metrics that will be studied later this week.*
    ```
    def compute_mse(y_true, y_pred):
        #TODO
        return mse
    ```

Change the `noise` parameter of `make_regression` to 50

6. Repeat question 2, 4 and compute the MSE on the new data.

https://scikit-learn.org/stable/modules/generated/sklearn.metrics.mean_squared_error.html