public/subjects/ai/linear-regression/audit

Linear regression with Scikit Learn

Exercise 0: Environment and libraries

The exercice is validated is all questions of the exercice 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

Does import jupyter, import numpy, import pandas, import matplotlib and import sklearn run without any error ?

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Exercise 1: Scikit-learn estimator

The question 1 is validated if the output is:

    array([[3.96013289]])

The question 2 is validated if the output is:

    Coefficients:  [[0.99667774]]
    Intercept:  [-0.02657807]
    Score:  0.9966777408637874

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Exercise 2: Linear regression in 1D

The exercise is validated is all questions of the exercise are validated

The question 1 is validated if the plot looks like:

The question 2 is validated if the equation of the fitted line is: y = 42.619430291366946 * x + 99.18581817296929

The question 3 is validated if the plot looks like:

The question 4 is validated if the outputted prediction for the first 10 values are:

array([ 83.86186727, 140.80961751, 116.3333897 ,  64.52998689,
        61.34889539, 118.10301628,  57.5347917 , 117.44107847,
       108.06237908,  85.90762675])

The question 5 is validated if the MSE returned is 114.17148616819485

The question 6 is validated if the MSE returned is 2854.2871542048706

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Exercise 3: Train test split

The question 1 is validated if X_train, y_train, X_test, y_test match this output:

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]

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Exercise 4: Forecast diabetes progression

The exercice is validated is all questions of the exercice are validated

The question 1 is validated if the output of y_train.values[:10] and y_test.values[:10]are:

    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.]]

The question 2 is validated if the coefficients and the intercept are:

    [('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)]

The question 3 is validated if the output of predictions_on_test[:10] is:

    array([[111.74351759],
        [ 98.41335251],
        [168.36373195],
        [255.05882934],
        [168.43764643],
        [117.60982186],
        [198.86966323],
        [126.28961941],
        [117.73121787],
        [224.83346984]])

The question 4 is validated if the mse on the train set is 2888.326888 and the mse on the test set is 2858.255153.

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Exercise 5: Gradient Descent (Optional)

The exercise is validated if all questions of the exercise are validated.

+The question 1 is validated if the outputted plot looks like:

+The question 2 is validated if the output is: 11808.867339751561

+The question 3 is validated if grid.shape is (640000,2).

+The question 4 is validated if the 10 first values of losses are:

array([158315.41493175, 158001.96852692, 157689.02212209, 157376.57571726,
    157064.62931244, 156753.18290761, 156442.23650278, 156131.79009795,
    155821.84369312, 155512.39728829])

+The question 5 is validated if the outputted plot looks like

+The question 6 is validated if the point returned is:

array([42.5, 99. ]). It means that a= 42.5 and b=99.

+The question 7 is validated if the coefficients returned are:

Coefficients (a): 42.61943031121358
Intercept (b): 99.18581814447936

+The question 8 is validated if the outputted plot is:

+The question 9 is validated if the coefficients and intercept returned are:

Coefficients:  [42.61943029]
Intercept:  99.18581817296929