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boston['MEDV'] = boston_dataset.target

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boston = pd.DataFrame(boston_dataset.data, columns=boston_dataset.feature_names)
boston.head()

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import numpy as np
import matplotlib.pyplot as plt 

import pandas as pd  
import seaborn as sns 

%matplotlib inline

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from sklearn.datasets import load_boston
boston_dataset = load_boston()

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import operator

import numpy as np
import matplotlib.pyplot as plt

from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error, r2_score
from sklearn.preprocessing import PolynomialFeatures

np.random.seed(0)

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import numpy as np
import matplotlib.pyplot as plt

from sklearn.linear_model import LinearRegression

np.random.seed(0)
x = 2 - 3 * np.random.normal(0, 1, 20)
y = x - 2 * (x ** 2) + 0.5 * (x ** 3) + np.random.normal(-3, 3, 20)

# transforming the data to include another axis

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import numpy as np
import matplotlib.pyplot as plt

np.random.seed(0)
x = 2 - 3 * np.random.normal(0, 1, 20)
y = x - 2 * (x ** 2) + 0.5 * (x ** 3) + np.random.normal(-3, 3, 20)
plt.scatter(x,y, s=10)
plt.show()

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# sum of square of residuals
ssr = np.sum((y_pred - y_actual)**2)

#  total sum of squares
sst = np.sum((y_actual - np.mean(y_actual))**2)

# R2 score
r2_score = 1 - (ssr/sst)

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# mean squared error
mse = np.sum((y_pred - y_actual)**2)

# root mean squared error
# m is the number of training examples
rmse = np.sqrt(mse/m)

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# imports
import numpy as np


class LinearRegressionUsingGD:
    """Linear Regression Using Gradient Descent.

    Parameters
    ----------
    eta : float