Polynomial fit

glr_example_2.py

np.random.seed(10)
x_1=np.linspace(0,10,11)
x_0=np.ones(len(x_1))
y=4*x+1+np.random.normal(0, 5, len(x_1))
data = pd.DataFrame(np.column_stack([x_0,x_1,y]),columns=['x_0','x_1','y'])
 
predictors=['x_0','x_1']
predictors.extend(['x_{}'.format(i) for i in range(2,13)])
for i in range(2,13):
    data['x_{}'.format(i)] = data['x_1']**i
 
col = ['rss','intercept'] + ['coef_x_{}'.format(i) for i in range(1, 16)]
ind = ['alpha_%.2g'%alpha for alpha in alpha_lasso]
coef_matrix_lasso = pd.DataFrame(index=ind, columns=col)
 
graphs = []
models = []
idx = 0
for degree in [1, 2, 4, 6, 8, 10]:
    X = data[predictors[0:degree+1]]
    reg = LinearRegression(fit_intercept=False)
    reg.fit(X, data['y'])
    p=figure(width=300, height=300)
    p.circle(x,y,legend='obseration')
    y_pred = reg.predict(X)
    p.line(x,y_pred, legend='model', color='red')
    p.xaxis.axis_label='x'
    p.yaxis.axis_label='y'
    p.legend.location = "top_left"
    p.title.text='degree {}'.format(degree)
    rss = sum((y_pred-data['y'])**2)
    res = [rss]
    res.extend([model.intercept_])
    res.extend(model.coef_)
    coef_matrix_lasso.iloc[idx,] = res
    graphs.append(p)
    models.append(reg)
    idx += 1
grid = gridplot([[graphs[0], graphs[1]], [graphs[2], graphs[3]], [graphs[4], graphs[5]]])
show(grid);