lr_scipy.py

boston = datasets.load_boston()
y = boston.target
X = pd.DataFrame(boston.data, columns = boston.feature_names)

ss = StandardScaler()
Xs = ss.fit_transform(X)
Xs = pd.DataFrame(Xs, columns=boston.feature_names)
Xs['const'] = 1

# calculate y
def calc_y(weights):
    yc = 0
    for i in range(Xs.shape[1]):
        yc = yc + weights[i]*Xs.iloc[:,i]
    return yc

# define objective
def objective(weights):
    return np.mean(((calc_y(weights)-y))**2)

# initial guesses
x0 = np.zeros(Xs.shape[1])

# show initial objective
print('Initial SSE Objective: ' + str(objective(x0)))

# optimize
# bounds on variables
b = (-100, 100)
bnds = [(b)]*Xs.shape[1]
solution = minimize(objective,x0,method='SLSQP',bounds=bnds)
weights = solution.x
y_pred = calc_y(weights)

# show final objective
print('Final SSE Objective: ' + str(objective(weights)))