多远线性算法预测房价
2021/11/5 14:10:55
本文主要是介绍多远线性算法预测房价,对大家解决编程问题具有一定的参考价值,需要的程序猿们随着小编来一起学习吧!
一、基于统计分析库statsmodels
1.数据读取
import pandas as pd import numpy as np import seaborn as sns import matplotlib.pyplot as plt df = pd.read_csv('C:\house_prices.csv')
2.数据清洗
def outlier_test(data, column, method=None, z=2): if method == None: print(f'以 {column} 列为依据,使用 上下截断点法(iqr) 检测异常值...') print('=' * 70) column_iqr = np.quantile(data[column], 0.75) - np.quantile(data[column], 0.25) (q1, q3) = np.quantile(data[column], 0.25), np.quantile(data[column], 0.75) upper, lower = (q3 + 1.5 * column_iqr), (q1 - 1.5 * column_iqr) outlier = data[(data[column] <= lower) | (data[column] >= upper)] print(f'第一分位数: {q1}, 第三分位数:{q3}, 四分位极差:{column_iqr}') print(f"上截断点:{upper}, 下截断点:{lower}") return outlier, upper, lower if method == 'z': print(f'以 {column} 列为依据,使用 Z 分数法,z 分位数取 {z} 来检测异常值...') print('=' * 70) mean, std = np.mean(data[column]), np.std(data[column]) upper, lower = (mean + z * std), (mean - z * std) print(f"取 {z} 个 Z分数:大于 {upper} 或小于 {lower} 的即可被视为异常值。") print('=' * 70) outlier = data[(data[column] <= lower) | (data[column] >= upper)] return outlier, upper, lower outlier, upper, lower = outlier_test(data=df, column='price', method='z') outlier.info(); outlier.sample(5) df.drop(index=outlier.index, inplace=True)
3.数据分析
def heatmap(data, method='pearson', camp='RdYlGn', figsize=(10 ,8)): plt.figure(figsize=figsize, dpi= 80) sns.heatmap(data.corr(method=method), xticklabels=data.corr(method=method).columns, yticklabels=data.corr(method=method).columns, cmap=camp, center=0, annot=True) heatmap(data=df, figsize=(6,5))
4.拟合及模型优化
import statsmodels.api as sm from statsmodels.formula.api import ols from statsmodels.stats.anova import anova_lm from statsmodels.formula.api import ols from statsmodels.formula.api import ols lm = ols('price ~ area + bedrooms + bathrooms', data=df).fit() lm.summary()
nominal_data = df['neighborhood'] dummies = pd.get_dummies(nominal_data) dummies.sample() dummies.drop(columns=['C'], inplace=True) dummies.sample() results = pd.concat(objs=[df, dummies], axis='columns') results.sample(3) lm = ols('price ~ area + bedrooms + bathrooms + A + B', data=results).fit() lm.summary()
结果
自定义方差膨胀因子的检测公式:
def vif(df, col_i): """ df: 整份数据 col_i:被检测的列名 """ cols = list(df.columns) cols.remove(col_i) cols_noti = cols formula = col_i + '~' + '+'.join(cols_noti) r2 = ols(formula, df).fit().rsquared return 1. / (1. - r2) test_data = results[['area', 'bedrooms', 'bathrooms', 'A', 'B']] for i in test_data.columns: print(i, '\t', vif(df=test_data, col_i=i)) lm = ols(formula='price ~ area + bathrooms + A + B', data=results).fit() lm.summary()
结果:
二、Excel重做多元线性回归
选择数据分析功能,选择回归选项
接着选择xy的值域
x的值是area、bedroom和bathroom y值为price
点击确定
最终结果price=10072.1+345.911 area-2925.8bedroom+7345.39*bathroom
三、机器学习库Sklearn库重做多元线性回归
1.直接求解
import pandas as pd import numpy as np import math import matplotlib.pyplot as plt from sklearn import linear_model data = pd.read_csv('C:\house_prices.csv') data.head() new_data=data.iloc[:,1:] new_data.head() new_data.corr() x_data = new_data.iloc[:, 1:4] y_data = new_data.iloc[:, -1] print(x_data, y_data, len(x_data)) print("回归系数:", model.coef_) print("截距:", model.intercept_) print('回归方程: price=',model.coef_[0],'*area +',model.coef_[1],'*bedrooms +',model.coef_[2],'*bathromms +',model.intercept_)
2.数据清洗求解
new_data_Z=new_data.iloc[:,0:] new_data_IQR=new_data.iloc[:,0:] def outlier_test(data, column, method=None, z=2): if method == None: print(f'以 {column} 列为依据,使用 上下截断点法(iqr) 检测异常值...') print('=' * 70) column_iqr = np.quantile(data[column], 0.75) - np.quantile(data[column], 0.25) (q1, q3) = np.quantile(data[column], 0.25), np.quantile(data[column], 0.75) upper, lower = (q3 + 1.5 * column_iqr), (q1 - 1.5 * column_iqr) outlier = data[(data[column] <= lower) | (data[column] >= upper)] print(f'第一分位数: {q1}, 第三分位数:{q3}, 四分位极差:{column_iqr}') print(f"上截断点:{upper}, 下截断点:{lower}") return outlier, upper, lower if method == 'z': print(f'以 {column} 列为依据,使用 Z 分数法,z 分位数取 {z} 来检测异常值...') print('=' * 70) mean, std = np.mean(data[column]), np.std(data[column]) upper, lower = (mean + z * std), (mean - z * std) print(f"取 {z} 个 Z分数:大于 {upper} 或小于 {lower} 的即可被视为异常值。") print('=' * 70) outlier = data[(data[column] <= lower) | (data[column] >= upper)] return outlier, upper, lower outlier, upper, lower = outlier_test(data=new_data_Z, column='price', method='z') outlier.info(); outlier.sample(5) new_data_Z.drop(index=outlier.index, inplace=True) print("原数据相关性矩阵") new_data.corr() print("Z方法处理的数据相关性矩阵") new_data_Z.corr() print("IQR方法处理的数据相关性矩阵") new_data_IQR.corr() x_data = new_data_Z.iloc[:, 1:4] y_data = new_data_Z.iloc[:, -1] model = linear_model.LinearRegression() model.fit(x_data, y_data) print("回归系数:", model.coef_) print("截距:", model.intercept_) print('回归方程: price=',model.coef_[0],'*area +',model.coef_[1],'*bedrooms +',model.coef_[2],'*bathromms +',model.intercept_) x_data = new_data_IQR.iloc[:, 1:4] y_data = new_data_IQR.iloc[:, -1] model = linear_model.LinearRegression() model.fit(x_data, y_data) print("回归系数:", model.coef_) print("截距:", model.intercept_) print('回归方程: price=',model.coef_[0],'*area +',model.coef_[1],'*bedrooms +',model.coef_[2],'*bathromms +',model.intercept_)
3.结果对比
不作处理的数据求解的结果为:
price= 345.911018840024 *area + -2925.806324666705 *bedrooms + 7345.391713693825 *bathromms + 10072.107046726742
采用Z方式清洗数据的求解结果为:
price= 226.4211697383351 *area + 49931.50311720713 *bedrooms + -12224.71724496588 *bathromms + 64356.04135007458
采用IQR放心清洗数据的求解结果为:
price= 242.6111551782956 *area + 41547.43068790577 *bedrooms + -6415.78250090158 *bathromms + 58018.13845504692
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