In [3]:
plt.figure(figsize = (6, 4), dpi = 100)
sns.scatterplot(x = 'x', y = 'y', data = train)
Out[3]:
<AxesSubplot:xlabel='x', ylabel='y'>
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
import seaborn as sns
train = pd.read_csv('train.csv')
train
| x | y | |
|---|---|---|
| 0 | 7.127868 | 4.695017 |
| 1 | -1.427134 | 1.184627 |
| 2 | 7.168831 | 4.671386 |
| 3 | -4.940390 | 1.758916 |
| 4 | -5.792271 | 2.064704 |
| 5 | 0.255292 | 0.624571 |
| 6 | -0.744530 | 0.971312 |
| 7 | 9.070997 | 7.444385 |
| 8 | -3.064917 | 1.483040 |
| 9 | 1.959275 | 1.423652 |
plt.figure(figsize = (6, 4), dpi = 100)
sns.scatterplot(x = 'x', y = 'y', data = train)
<AxesSubplot:xlabel='x', ylabel='y'>
from sklearn.linear_model import LinearRegression
def polynomial_design_matrix(X, n):
polynomial_features = np.empty(shape = (X.shape[0], n))
for i in range(1, n + 1):
polynomial_features[:, i - 1] = X**i
return polynomial_features
polynomial_design_matrix(train['x'], 2)
array([[ 7.12786780e+00, 5.08064994e+01],
[-1.42713404e+00, 2.03671157e+00],
[ 7.16883095e+00, 5.13921372e+01],
[-4.94038991e+00, 2.44074524e+01],
[-5.79227110e+00, 3.35504045e+01],
[ 2.55292364e-01, 6.51741910e-02],
[-7.44529526e-01, 5.54324215e-01],
[ 9.07099700e+00, 8.22829865e+01],
[-3.06491740e+00, 9.39371865e+00],
[ 1.95927485e+00, 3.83875794e+00]])
plt.figure(figsize = (6, 4), dpi = 100)
ax = sns.scatterplot(x = 'x', y = 'y', data = train)
n = 9
model = LinearRegression(fit_intercept = True)
X_poly = polynomial_design_matrix(train['x'], n)
model.fit(X_poly, train['y'])
rmse = np.sqrt(np.mean((model.predict(X_poly) - train['y'])**2))
x_to_plot = np.arange(-10, 10.1, .1)
x_to_plot_poly = polynomial_design_matrix(x_to_plot, n)
fitted_line = x_to_plot_poly @ model.coef_ + model.intercept_
ax = sns.lineplot(x = x_to_plot, y = fitted_line, ax = ax, lw = 2/3)
ax.set_ylim(0, 9)
ax.set_xlim(-10, 10);
rmse
6.1024160027378645e-09
rmses = []
for n in range(1, 10):
model = LinearRegression(fit_intercept = True)
X_poly = polynomial_design_matrix(train['x'], n)
model.fit(X_poly, train['y'])
rmse = np.sqrt(np.mean((model.predict(X_poly) - train['y'])**2))
print(n, rmse)
rmses.append(rmse)
1 1.2506895836230856 2 0.25538584218499394 3 0.1470270907185259 4 0.14614304364333902 5 0.13854530489262495 6 0.07189482017386775 7 0.02014778411746299 8 0.014700396694077873 9 6.1024160027378645e-09
test = pd.read_csv('test.csv')
test.head()
| x | y | |
|---|---|---|
| 0 | 0.868099 | 1.026507 |
| 1 | -4.432612 | 1.655747 |
| 2 | -1.509648 | 1.256400 |
| 3 | 6.895523 | 4.313916 |
| 4 | -9.905623 | 2.784235 |
plt.figure(figsize = (6,4), dpi = 100)
ax = sns.scatterplot(x = train['x'], y = train['y'], s = 10, color = 'red', zorder = 10)
ax = sns.scatterplot(x = test['x'], y = test['y'], s = 3, zorder = 1)
n = 9
model = LinearRegression(fit_intercept = True)
X_poly = polynomial_design_matrix(train['x'], n)
model.fit(X_poly, train['y'])
x_to_plot_poly = polynomial_design_matrix(x_to_plot, n)
fitted_line = x_to_plot_poly @ model.coef_ + model.intercept_
ax = sns.lineplot(x = x_to_plot, y = fitted_line, lw = 2/3, color = 'green')
ax.set_xlim(-10, 10)
ax.set_ylim(0, 9)
X_test_poly = polynomial_design_matrix(test['x'], n)
test_rmse = np.sqrt(np.mean((model.predict(X_test_poly) - test['y'])**2))
test_rmse
110.77107676950251
test_rmses = []
for n in range(1, 10):
model = LinearRegression(fit_intercept = True)
X_poly = polynomial_design_matrix(train['x'], n)
model.fit(X_poly, train['y'])
X_test_poly = polynomial_design_matrix(test['x'], n)
test_rmse = np.sqrt(np.mean((model.predict(X_test_poly) - test['y'])**2))
print(n, test_rmse)
test_rmses.append(test_rmse)
1 1.8585554486548226 2 0.7713562614108714 3 0.1691290033322484 4 0.20723955870789773 5 1.2974799641183905 6 8.775129060776468 7 13.649732852088503 8 27.666588565625528 9 110.77107676950251