public/subjects/ai/linear-regression/audit

Linear regression with Scikit Learn

Exercise 0: Environment and libraries

The exercise is validated if 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?

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Exercise 1: Scikit-learn estimator

For question 1, is the output the following?

    array([[3.96013289]])

For question 2, is the output the following?

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

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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?

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?

For question 4, is the outputted prediction for the first 10 values the following?

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?

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Exercise 3: Train test split

For question 1, do 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 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?

    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?

    [('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]?

    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?

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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?

+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?

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?

+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?

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

+For question 8, is the outputted plot the following?

+For question 9, are the coefficients and intercept returned the following?

Coefficients:  [42.61943029]
Intercept:  99.18581817296929