简单线性回归预测实现

import numpy as np
from .metrics import r2_score


class SimpleLinearRegression:

    def __init__(self):
        """初始化Simple Linear Regression模型"""
        self.a_ = None
        self.b_ = None

    def fit(self, x_train, y_train):
        """根据训练数据集x_train, y_train训练Simple Linear Regression模型"""
        assert x_train.ndim == 1, 
            "Simple Linear Regressor can only solve single feature training data."
        assert len(x_train) == len(y_train), 
            "the size of x_train must be equal to the size of y_train"

        x_mean = np.mean(x_train)
        y_mean = np.mean(y_train)

        self.a_ = (x_train - x_mean).dot(y_train - y_mean) / (x_train - x_mean).dot(x_train - x_mean)#向量化 点乘运算
        self.b_ = y_mean - self.a_ * x_mean

        return self

    def predict(self, x_predict):
        """给定待预测数据集x_predict，返回表示x_predict的结果向量"""
        assert x_predict.ndim == 1, 
            "Simple Linear Regressor can only solve single feature training data."
        assert self.a_ is not None and self.b_ is not None, 
            "must fit before predict!"

        return np.array([self._predict(x) for x in x_predict])

    def _predict(self, x_single):
        """给定单个待预测数据x，返回x的预测结果值"""
        return self.a_ * x_single + self.b_

    def score(self, x_test, y_test):
        """根据测试数据集 x_test 和 y_test 确定当前模型的准确度"""

        y_predict = self.predict(x_test)
        return r2_score(y_test, y_predict)

    def __repr__(self):
        return "SimpleLinearRegression()"

衡量线性回归模型误差的三种方式

def mean_squared_error(y_true, y_predict):
    """计算y_true和y_predict之间的MSE"""
    assert len(y_true) == len(y_predict), 
        "the size of y_true must be equal to the size of y_predict"

    return np.sum((y_true - y_predict)**2) / len(y_true)


def root_mean_squared_error(y_true, y_predict):
    """计算y_true和y_predict之间的RMSE"""

    return sqrt(mean_squared_error(y_true, y_predict))


def mean_absolute_error(y_true, y_predict):
    """计算y_true和y_predict之间的RMSE"""
    assert len(y_true) == len(y_predict), 
        "the size of y_true must be equal to the size of y_predict"

    return np.sum(np.absolute(y_true - y_predict)) / len(y_true)

计算最终模型预测准确度R方

def r2_score(y_true, y_predict):
    """计算y_true和y_predict之间的R Square"""

    return 1 - mean_squared_error(y_true, y_predict)/np.var(y_true)