多项式拟合曲线

 

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# import pandas as pd # import numpy as np # from sklearn.preprocessing import PolynomialFeatures # from sklearn.linear_model import LinearRegression # import matplotlib.pyplot as plt   # # Read the data from the Excel file # data = pd.read_excel(r'E:\\孙晓宇\\测试钞A1~E7共62开\\测试钞_磁扫特征统计结果\\combine.xlsx')   # # print(data.iloc[0])   # # Define the dependent variable # y= data['平均值']   # # Define the independent variables # X = data[['油墨类型','BLOCK_width', 'width_ratio', 'BLOCK_depth','BLOCK_carval','BLOCK_angle','类型']]     # # generate polynomial features of degree 2 # poly = PolynomialFeatures(degree=2, include_bias=True) # X_poly = poly.fit_transform(X)   # # fit a linear regression model on the polynomial features # model = LinearRegression().fit(X_poly, y)     # # use the model to make predictions for the new set of independent variables # predictions = model.predict(X_poly)   # # print the predicted values # print(predictions)         import pandas as pd import numpy as np from sklearn.preprocessing import PolynomialFeatures from sklearn.linear_model import LinearRegression import matplotlib.pyplot as plt   # Read the data from the Excel file data = pd.read_excel(r'E:\\孙晓宇\\测试钞A1~E7共62开\\测试钞_磁扫特征统计结果\\combine.xlsx')   # print(data.iloc[0])   # Define the dependent variable y= data['标准差']   # Define the independent variables X = data[['油墨类型','BLOCK_width', 'width_ratio', 'BLOCK_depth','BLOCK_carval','BLOCK_angle','类型']]     # generate polynomial features of degree 2 poly = PolynomialFeatures(degree=10, include_bias=True) X_poly = poly.fit_transform(X)   # fit a linear regression model on the polynomial features model = LinearRegression().fit(X_poly, y)       # use the model to make predictions for the new set of independent variables predictions = model.predict(X_poly)     # print the predicted values print(predictions)       # calculate the residual errors residuals = y - predictions   # plot the predicted values against the actual values plt.scatter(y, predictions)   # plot a horizontal line at y=0 to show the line of perfect prediction plt.plot([min(y), max(y)], [min(y), max(y)], 'k--', lw=2)   # plot the residual errors as a scatter plot plt.scatter(y, residuals, c='r', s=10, alpha=0.5)   # add axis labels and a title plt.xlabel('Actual values') plt.ylabel('Predicted values') plt.title('Prediction error')   # show the plot plt.show()