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#### Linear regression with Scikit Learn
#### Exercise 0: Environment and libraries
##### The exercise is validated is all questions of the exercise are validated
##### Activate the virtual environment. If you used `conda` run `conda activate your_env`
##### Run `python --version`
###### Does it print `Python 3.x`? x >= 8
###### Do `import jupyter`, `import numpy`, `import pandas`, `import matplotlib` and `import sklearn` run without any error?
---
---
#### Exercise 1: Scikit-learn estimator
###### For question 1, is the output the following?
```python
array([[3.96013289]])
```
###### For question 2, is the output the following?
```output
Coefficients: [[0.99667774]]
Intercept: [-0.02657807]
Score: 0.9966777408637874
```
---
---
#### Exercise 2: Linear regression in 1D
##### The exercise is validated if all questions of the exercise are validated
###### For question 1, does the plot look like the following?
![alt text][q1]
[q1]: ../w2_day1_ex2_q1.png "Scatter plot"
###### For question 2, is the equation of the fitted line the following? `y = 42.619430291366946 * x + 99.18581817296929`
###### For question 3, does the plot look like the following?
![alt text][q3]
[q3]: ../w2_day1_ex2_q3.png "Scatter plot + fitted line"
###### For question 4, is the outputted prediction for the first 10 values the following?
```python
array([ 83.86186727, 140.80961751, 116.3333897 , 64.52998689,
61.34889539, 118.10301628, 57.5347917 , 117.44107847,
108.06237908, 85.90762675])
```
###### For question 5, is the MSE returned `114.17148616819485`?
###### For question 6, is the MSE returned `2854.2871542048706`?
---
---
#### Exercise 3: Train test split
###### For question 1, do X_train, y_train, X_test, y_test match this output?
```console
X_train:
[[ 1 2]
[ 3 4]
[ 5 6]
[ 7 8]
[ 9 10]
[11 12]
[13 14]
[15 16]]
y_train:
[1 2 3 4 5 6 7 8]
X_test:
[[17 18]
[19 20]]
y_test:
[ 9 10]
```
---
---
#### Exercise 4: Forecast diabetes progression
##### The exercise is validated if all questions of the exercise are validated
###### For question 1, is the output of `y_train.values[:10]` and `y_test.values[:10]` the following?
```console
y_train.values[:10]:
[[202.]
[ 55.]
[202.]
[ 42.]
[214.]
[173.]
[118.]
[ 90.]
[129.]
[151.]]
y_test.values[:10]:
[[ 71.]
[ 72.]
[235.]
[277.]
[109.]
[ 61.]
[109.]
[ 78.]
[ 66.]
[192.]]
```
###### For question 2, are the coefficients and the intercept the following?
```console
[('age', -60.40163046086952),
('sex', -226.08740652083418),
('bmi', 529.383623302316),
('bp', 259.96307686274605),
('s1', -859.121931974365),
('s2', 504.70960058378813),
('s3', 157.42034928335502),
('s4', 226.29533600601638),
('s5', 840.7938070846119),
('s6', 34.712225788519554),
('intercept', 152.05314895029233)]
```
###### For question 3, is the output of `predictions_on_test[:10]`?
```console
array([[111.74351759],
[ 98.41335251],
[168.36373195],
[255.05882934],
[168.43764643],
[117.60982186],
[198.86966323],
[126.28961941],
[117.73121787],
[224.83346984]])
```
###### For question 4, is the mse on the **train set** `2888.326888` and the mse on the **test set** `2858.255153`?
---
---
#### Exercise 5: Gradient Descent (Optional)
##### The exercise is validated if all questions of the exercise are validated.
###### +For question 1, does the outputted plot looks like?
![alt text][ex5q1]
[ex5q1]: ../w2_day1_ex5_q1.png "Scatter plot "
###### +For question 2, is the output `11808.867339751561`?
###### +For question 3, is `grid.shape` equal to `(640000,2)`?
###### +For question 4, are the 10 first values of losses the following?
```console
array([158315.41493175, 158001.96852692, 157689.02212209, 157376.57571726,
157064.62931244, 156753.18290761, 156442.23650278, 156131.79009795,
155821.84369312, 155512.39728829])
```
###### +For question 5, does the outputted plot look like the following?
![alt text][ex5q5]
[ex5q5]: ../w2_day1_ex5_q5.png "MSE"
###### +For question 6, is the point returned the following?
`array([42.5, 99. ])`. It means that `a= 42.5` and `b=99`.
###### +For question 7, are the coefficients returned the following?
```console
Coefficients (a): 42.61943031121358
Intercept (b): 99.18581814447936
```
###### +For question 8, is the outputted plot the following?
![alt text][ex5q8]
[ex5q8]: ../w2_day1_ex5_q8.png "MSE + Gradient descent"
###### +For question 9, are the coefficients and intercept returned the following?
```console
Coefficients: [42.61943029]
Intercept: 99.18581817296929
```