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21 code.py

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+import pandas as pd
+import numpy as np
+import matplotlib.pyplot as plt
+from sklearn import metrics
+import statsmodels.api as sm
+import patsy
+
+# data acquisition
+stats = pd.read_table('/Users/wangtianyi/Documents/python_work/regression.csv')
+point = stats.iloc[:,4] / 38
+rating = stats.iloc[:,5]
+
+# linear regression with statsmodels
+rating_add = sm.add_constant(rating)
+est_simple = sm.OLS(point,rating_add).fit()
+linear_error = metrics.mean_squared_error(point, est_simple.fittedvalues)
+
+# polynomial fitting with numpy
+poly_model = np.polyfit(rating, point, 10)
+xx = np.linspace(rating.min(), rating.max(), 100)
+poly_value = np.polyval(poly_model, xx)
+poly_error = metrics.mean_squared_error(point, np.polyval(poly_model, rating))
+
+spline_data = stats.iloc[:,[4,5]]
+# a small pertubation is applied to distinguish identical ratings
+spline_data['Ratings'] = spline_data['Ratings'].map(lambda x: x + np.random.normal(0, 1e-5))
+spline_data['Points'] = spline_data['Points'].map(lambda x: x / 38)
+# ascending sorted data for spline regression
+spline_data = spline_data.sort_values(by=['Ratings']).values
+
+# generating cubic spline with 3 knots at quantiles
+transformed_x = patsy.dmatrix("cr(spline_data[:,1], knots=(6.74,6.88,7.02))")
+# fitting generalised linear model on transformed dataset
+cubicspline = sm.GLM(spline_data[:,0], transformed_x).fit()
+# predicted value for error calculation
+pred = cubicspline.predict(patsy.dmatrix("cr(spline_data[:,1], knots=(6.74,6.88,7.02))"))
+spline_error = metrics.mean_squared_error(point, pred)
+# data for plot
+pred_smooth = cubicspline.predict(patsy.dmatrix("cr(xx, knots=(6.74,6.88,7.02))"))
+
+plt.figure(1)
+plt.plot(rating, est_simple.fittedvalues, c="r", linewidth=4, label = "RMSE = {}".format(linear_error))
+plt.plot(xx, poly_value, c="g", linewidth=4, label = "RMSE = {}".format(poly_error))
+plt.scatter(rating, point, c="b", s=4)
+plt.ylim(0.5, 3)
+plt.xlabel("average rating")
+plt.ylabel("average point per game")
+plt.title("Simple Linear Regression")
+plt.legend()
+
+plt.figure(2)
+plt.plot(rating, est_simple.fittedvalues, c="r", linewidth=4, label = 'Linear')
+plt.plot(xx, pred_smooth, c="g", linewidth=4, label = 'CubicSpline')
+plt.scatter(rating, point, c="b", s=4)
+plt.ylim(0.5, 3)
+plt.xlabel("average rating")
+plt.ylabel("average point per game")
+plt.title("Spline Regression")
+plt.legend()
+
+plt.show()