C语言实现波士顿房价预测

波士顿房价预测是一个经典的机器学习任务，类似于程序员世界的“Hello World”。和大家对房价的普遍认知相同，波士顿地区的房价受诸多因素影响。该数据集统计了13种可能影响房价的因素和该类型房屋的均价，期望构建一个基于13个因素进行房价预测的模型，如 下图所示。

对于预测问题，可以根据预测输出的类型是连续的实数值，还是离散的标签，区分为回归任务和分类任务。因为房价是一个连续值，所以房价预测显然是一个回归任务。下面我们尝试用最简单的线性回归模型解决这个问题，并用神经网络来实现这个模型。

线性回归模型

假设房价和各影响因素之间能够用线性关系来描述：
$$
y = \sum_{j=1}^M w_jx_j + b (公式1)
$$
模型的求解即是通过数据拟合出每个$w_j$和$b$。其中，$w_j$和$b$分别表示该线性模型的权重和偏置。一维情况下，$w_j$ 和 $b$ 是直线的斜率和截距。

线性回归模型使用均方误差作为损失函数（Loss），用以衡量预测房价和真实房价的差异，公式如下（其中$\widehat Y_i$为预测值 $Y_i$为实际值）：
$$
s = \frac{1}{n}\sum_{i=1}^n (\widehat Y_i - Y_i)^2 (公式2)
$$

---

思考：

为什么要以均方误差作为损失函数？即将模型在每个训练样本上的预测误差加和，来衡量整体样本的准确性。这是因为损失函数的设计不仅仅要考虑“合理性”，同样需要考虑“易解性”，这个问题在后面的内容中会详细阐述。

---

神经网络的标准结构中每个神经元由加权和与非线性变换构成，然后将多个神经元分层的摆放并连接形成神经网络。线性回归模型可以认为是神经网络模型的一种极简特例，是一个只有加权和、没有非线性变换的神经元（无需形成网络），如 图2 所示。

以上内容复制自飞桨AI Studio - 人工智能学习与实训社区 (baidu.com)

---

程序编写概要：

1. 编写一个 C 语言程序，基于以往房价影响数据训练出房价预测模型，从而预测以后房价。

2. 使用用户给出的housing.data数据，该数据每份有14项，前13项为房价影响因素，最后一项为同类型房价中位数。对获得数据进行归一化处理，确保步长不影响模型效果。

3. 使用输入层13层，隐藏层2层，输出层1层的简易神经网络。

4. 采用训练集：测试集=8：2。

5. 实现必要的错误检查和处理机制，防止无效的输入和计算。

6. 将程序按照模块化设计原则进行组织，使得代码结构清晰、易于理解和扩展。

7. 使用注释对程序进行说明，包括每个函数的作用、输入输出参数、算法思路等。

8. 程序的函数声明位于.h文件中，函数具体实现位于.c文件中。

9. 进行充分的测试，验证程序在各种情况下的正确性和稳定性。

系统功能分析

1. 系统分为四大块：数据分配模块、模型训练模块、模型质量检验模块、预测模块。

2. 使用如下神经网络架构实现房价预测模型的训练。

   输入层：13

   隐藏层：2

   输出层：1

3. 数据分配模块：应对整体数据按照8：2分类比分配，分别为训练集和测试集。

4. 模型训练模块：载入训练集，对训练集中的数据进行归一化处理后，获取相应数据集和标签集，对模型参数初始化后开始训练，训练的轮次及学习率需在训练前设置，模型训练完成后，导出模型。

5. 模型质量检验模块：导入训练好的模型，依照模型参数，对测试集中的数据进行归一化处理后，依照用户所给标准，检验模型质量。

6. 预测模块：导入训练好的模型，依照模型参数，对用户所给的数据进行归一化处理后，进行房价预测，并给出99%-50%预测下的房价区间。

数据分配源码

#include "global_define.h"
#include <stdio.h>
#include <stdlib.h>

double data[SIZE][LABELS];

int main() {
	printf("请输入数据文件路径：");
	char datafile[101];
	scanf("%s", datafile);
	printf("开始载入数据...\n");
	FILE* fdata = fopen(datafile, "r");
	if (fdata == NULL) {
		printf("文件%s打开失败，程序即将退出..", datafile);
		exit(-11);
	}
	int ysize = 0;
	while (!feof(fdata)) {
		//按着每行14份数据为一组进行分割
		for (int i = 0; i < LABELS; i++) {
			//fscanf_s(fdata, "%lf", &data[ysize][i]);
			fscanf(fdata, "%lf", &data[ysize][i]);
		}
		ysize++;
	}
	fclose(fdata);

	printf("开始分配训练数据...\n");
	FILE* train = fopen("train.data", "w");
	for (int i = 0; i < TRAIN_SIZE; i++) {
		if (i)fprintf(train, "\n");
		for (int j = 0; j < LABELS; j++) {
			fprintf(train, "%lf ", data[i][j]);
		}
	}
	printf("训练数据分配完毕！.\n");
	fclose(train);

	printf("开始分配测试数据...\n");
	FILE* eval = fopen("eval.data", "w");
	for (int i = 0; i < EVAL_SIZE; i++) {
		if(i)fprintf(eval, "\n");
		for (int j = 0; j < LABELS; j++) {
			fprintf(eval, "%lf ", data[i + TRAIN_SIZE][j]);
		}
	}
	printf("测试数据分配完毕！\n");
	fclose(eval);
	printf("数据处理完成！\n");
	system("pause");
	return 0;
}

---

训练源码

#include "global_define.h"
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define M_PI 3.14159265358979323846

double normal_random() {
	double u1 = rand() / (RAND_MAX + 1.0);
	double u2 = rand() / (RAND_MAX + 1.0);
	double z = sqrt(-2.0 * log(u1)) * sin(2.0 * M_PI * u2);
	return z;
}
struct Pair {
	double* first;
	double second;
};

typedef struct Pair Pair;
const int iterations = 40000;
const int log_step = 50;
double learningrate = 0.00125;
double data[SIZE][LABELS];
double train_data[TRAIN_SIZE][LABELS];
double maximums[LABELS] = { 0.0 };
double minimums[LABELS] = { 0.0 };
double avgs[LABELS] = { 0.0 };
int init = 0;
double w[DATA_SIZE] = {
	1.76405235,
	0.40015721,
	0.97873798,
	2.2408932,
	1.86755799,
	-0.97727788,
	0.95008842,
	-0.15135721,
	-0.10321885,
	0.4105985,
	0.14404357,
	1.45427351,
	0.76103773, };
double b = 0;
////////////////////////////
#include "array.h"
#include "dataprocess.h"
#include "Network.h"
#include "vectorcomputation.h"
////////////////////////////

int main() {
	printhello(1);
	load_data();
	//数据集 TRAIN_SIZE * SIZE
	double x[TRAIN_SIZE][DATA_SIZE];
	//double** x = (double**)malloc(sizeof(double*) * TRAIN_SIZE);
	//for (int i = 0; i < TRAIN_SIZE; i++) {
	//	x[i] = (double*)malloc(SIZE * sizeof(double));
	//}
	for (int i = 0; i < TRAIN_SIZE; i++) {
		for (int j = 0; j < DATA_SIZE; j++) {
			x[i][j] = train_data[i][j];
		}
	}

	//标签集 TRAIN_SIZE * 1
	double y[TRAIN_SIZE];
	//double* y = (double*)malloc(sizeof(double) * TRAIN_SIZE);
	for (int i = 0; i < TRAIN_SIZE; i++) {
		y[i] = train_data[i][DATA_SIZE];
	}
	__init__();
	printf("按下任意按键以开始训练...\n");
	system("pause");

	train(x, y);

	return 0;
}


/////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////////////////////////////////////////////
////////////////////////////////__ARRAY_H__//////////////////////////////////

double getsum(const double* arr, const int size) {
	double ans = 0;
	for (int i = 0; i < size; i++) {
		ans += arr[i];
	}
	return ans;
}

double getavg(const double* arr, const int size) {
	return getsum(arr, size) / (double)size;
}

double getmax_col(const double arr[TRAIN_SIZE][LABELS], const int col) {
	double ans = -23333;
	for (int i = 0; i < TRAIN_SIZE; i++) {
		if (arr[i][col] > ans) {
			ans = arr[i][col];
		}
	}

	return ans;
}

double getmin_col(const double arr[TRAIN_SIZE][LABELS], const int col) {
	double ans = 23333;

	for (int i = 0; i < TRAIN_SIZE; i++) {
		if (arr[i][col] < ans) {
			ans = arr[i][col];
		}
	}

	return ans;
}

double getsum_row(const double arr[TRAIN_SIZE][LABELS], const int col) {
	double ans = 0;
	for (int i = 0; i < TRAIN_SIZE; i++) {
		ans += arr[i][col];
	}
	return ans;
}

double getavg_col(const double arr[TRAIN_SIZE][LABELS], const int col) {
	return getsum_row(arr, col) / (double)TRAIN_SIZE;
}

/////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////////////////////////////////////////////
/////////////////////////////__DATAPROCESS_H__///////////////////////////////
void load_data() {
	printf("开始载入数据...\n");
	const char* datafile = "train.data";
	FILE* fdata = fopen(datafile, "r");
	if (fdata == NULL) {
		printf("文件%s打开失败，程序即将退出..", datafile);
		exit(-11);
	}
	int ysize = 0;
	while (!feof(fdata)) {
		//按着每行14份数据为一组进行分割
		for (int i = 0; i < LABELS; i++) {
			fscanf(fdata, "%lf", &data[ysize][i]);
		}
		ysize++;
	}

	fclose(fdata);

	//	copy(data, data_slice, 0, 0, TRAIN_SIZE, LABELS);
	for (int i = 0; i < TRAIN_SIZE; i++) {
		for (int j = 0; j < LABELS; j++) {
			train_data[i][j] = data[i][j];
		}
	}

	//for (int i = 0; i < TRAIN_SIZE * LABELS; i++) {
	//	printf("%lf ", train_data[i / 14][i % 14]);
	//	if (i % 14 == 0)printf("\n");
	//}

	for (int i = 0; i < LABELS; i++) {
		maximums[i] = getmax_col(train_data, i);
		minimums[i] = getmin_col(train_data, i);
		avgs[i] = getavg_col(train_data, i);
		//printf("%lf %lf %lf\n", maximums[i], minimums[i], avgs[i]);
	}
	
	//归一化
	for (int x = 0; x < TRAIN_SIZE; x++) {
		for (int y = 0; y < DATA_SIZE; y++) {
			if (maximums[y] - minimums[y] == 0)continue;
			data[x][y] = (data[x][y] - minimums[y]) / (maximums[y] - minimums[y]);
		}
	}

	/*for (int y = 0; y < TRAIN_SIZE; y++) {
		printf("%.5lf ", data[y][0]);
	}
	printf("\n");*/

	for (int i = 0; i < TRAIN_SIZE; i++) {
		for (int j = 0; j < LABELS; j++) {
			train_data[i][j] = data[i][j];
		}
	}
	printf("数据载入完成\n");
}

/////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////////////////////////////////////////////
///////////////////////////////__NETWORK_H__/////////////////////////////////
/// <summary>
/// 初始化
/// </summary>
void __init__() {
	init = 1;
	printf("***w***\n");
	for (int i = 0; i < DATA_SIZE; i++) {
		//w[i] = 1.0 * normal_random();
		printf("%.2lf ", w[i]);
	}
	printf("\n");
	b = 0.0;
	printf("初始化完成\n");
}

/// <summary>
/// 前向计算
/// </summary>
/// <param name="x">数据集，大小为TRAIN_SIZE * DATA_SIZE</param>
/// <param name="z">用于接受返回值的数组，其值为基于当前w b计算得来的预测值</param>
void forward(const double x[TRAIN_SIZE][DATA_SIZE], double z[TRAIN_SIZE]) {
	if (!init) {
		printf("网络未进行初始化！--forward 错误代码：-1");
		exit(-1);
	}

	for (int i = 0; i < TRAIN_SIZE; i++) {
		z[i] = vectordot(x[i], w) + b;
		//printf("%lf\n",z[i]);
	}
}

/// <summary>
/// 计算损失
/// </summary>
/// <param name="z">当前w b下的预测值[将用于与标签值比较]，大小为TRAIN_SIZE</param>
/// <param name="y">标签值，大小为TRAIN_SIZE</param>
/// <returns>一个double，代表预测值与实际值的误差，误差越小，返回值越小</returns>
double loss(double z[TRAIN_SIZE],const double y[TRAIN_SIZE]) {
	if (!init) {
		printf("网络未进行初始化！--loss 错误代码：-2");
		exit(-2);
	}
	//printf("::vectorsub ");
	double error[TRAIN_SIZE];
	vectorsub(z, y, error);
	/*for (int i = 0; i < TRAIN_SIZE; i++) {
		printf("%lf ", z[i]);
	}
	printf("\n");*/

	//printf("::vectormultiply  ");
	double cost[TRAIN_SIZE];
	vectormultiply(error, error, cost);
	
	/*for (int i = 0; i < TRAIN_SIZE; i++) {
		printf("%.3lf ", cost[i]);
	}
	printf("\n***********************************\n");*/
	
	double dcost = getavg(cost, TRAIN_SIZE);

	return dcost;
}

/// <summary>
/// 梯度计算
/// </summary>
/// <param name="x">数据集，大小为TRAIN_SIZE * DATA_SIZE</param>
/// <param name="y">标签集，大小为TRAIN_SIZE</param>
/// <returns>返回Pair 第一项为梯度w 第二项为梯度b</returns>
Pair gradient(const double x[TRAIN_SIZE][DATA_SIZE], const double y[TRAIN_SIZE]) {
	if (!init) {
		printf("网络未进行初始化！--gradient 错误代码：-3");
		exit(-3);
	}
	//printf("gradient::forward\n");
	//z : 404 * 1
	//y : 404 * 1
	//x : 404 * 13
	double z[TRAIN_SIZE];
	forward(x, z);
	/*for (int i = 0; i < TRAIN_SIZE; i++) {
		printf("%.3lf ", z[i]);
	}
	printf("\n");*/


	//printf("gradient::sub\n");
	double tgradient_b[TRAIN_SIZE];

	vectorsub(z, y, tgradient_b);

	/*for (int i = 0; i < TRAIN_SIZE; i++) {
		printf("%lf %d\n", tgradient_b[i], i);
	}*/

	//printf("gradient::multiply2\n");
	
	double tgradient_w[TRAIN_SIZE][DATA_SIZE];
	for (int i = 0; i < TRAIN_SIZE; i++) {
		for (int j = 0; j < DATA_SIZE; j++) {
			tgradient_w[i][j] = tgradient_b[i] * x[i][j];
			//printf("%.2lf ", tgradient_w[i][j]);
		}
		//printf("\n");
	}

	//for (int i = 0; i < TRAIN_SIZE; i++) {
	//	vectormultiply(tgradient_b, x[i], tgradient_w[i]);
	//}

	//printf("end multiply\n");

	double gradient_w[DATA_SIZE];
	//列均值
	for (int i = 0; i < DATA_SIZE; i++) {
		double sum = 0.0;
		for (int x = 0; x < TRAIN_SIZE; x++) {
			sum += tgradient_w[x][i];
			//printf("::gra%lf %d\n", tgradient_w[x][i], i);
		}
		gradient_w[i] = sum / (double)TRAIN_SIZE;
	}
	//printf("end avg\n");

	double gradient_b = getavg(tgradient_b, TRAIN_SIZE);
	/*for (int i = 0; i < TRAIN_SIZE; i++) {
		free(tgradient_w[i]);
	}
	free(tgradient_w);
	free(tgradient_b);
	free(z);*/
	//printf("%lf\n", gradient_b);
	return (Pair) { gradient_w, gradient_b };
}

/// <summary>
/// 更新权重w, b
/// </summary>
/// <param name="gradient_w">线性的回归的斜率</param>
/// <param name="gradient_b">线性回归的坐标轴位移</param>
void update(const double gradient_w[DATA_SIZE], const double gradient_b) {
	if (!init) {
		printf("网络未进行初始化！--update 错误代码：-4");
		exit(-4);
	}
	for (int i = 0; i < DATA_SIZE; i++) {
		w[i] -= learningrate * gradient_w[i];
	}
	b -= learningrate * gradient_b;
}

/// <summary>
/// 训练主体
/// </summary>
/// <param name="x">数据集，大小为TRAIN_SIZE * DATA_SIZE</param>
/// <param name="y">标签集，大小为TRAIN_SIZE</param>
void train(const double x[TRAIN_SIZE][DATA_SIZE], const double y[TRAIN_SIZE]) {
	if (!init) {
		printf("网络未进行初始化！--train 错误代码：-5");
		exit(-5);
	}
	
	printf("开始训练\n");
	double L = -1;
	for (int i = 0; i < iterations; i++) {
		if (i == iterations * 0.3) {
			learningrate /= 2;
		}
		if (i == iterations * 0.5) {
			learningrate /= 2;
		}
		if (i == iterations * 0.8) {
			learningrate /= 2;
		}
		//printf("进行forward \n");
		double z[TRAIN_SIZE];
		forward(x, z);
		//printf("计算loss \n");
		L = loss(z, y)/100;
		/*for (int i = 0; i < TRAIN_SIZE; i++) {
			printf("%lf %lf\n", z[i], y[i]);
		}*/

		//printf("开始gradient \n");
		Pair pair = gradient(x, y);
		double* gradient_w = pair.first;
		double gradient_b = pair.second;
		//printf("进行更新\n");
		update(gradient_w, gradient_b);
		if ((i + 1) % log_step == 0) {
			printf(">  iter %d, loss %.10lf lr %lf\n", i, L, learningrate);
		}
	}
	printf("训练完成，共训练轮次：%d轮 最终得到的参数为：\n", iterations);
	//printf("************gradient_w************\n");
	printgradientw();
	for (int i = 0; i < DATA_SIZE; i++) {
		printf("\033[36mw[%2d] = %64.60lf\033[m\n", i, w[i]);
	}
	//printf("\n************gradient_b************:\n");
	printgradientb();
	printf("\033[36m  b   = %64.60lf\033[m\n\n", b);
	printf("基于该参数的模型预测损失为：%lf\n", L);
	
	printf("正在导出模型...\n");
	FILE* fout = fopen("train_finish.luoy", "w");
	if (fout == NULL) {
		printf("模型导出错误，程序即将退出");
		system("pause");
		exit(-12);
	}
	for (int i = 0; i < DATA_SIZE; i++) {
		fprintf(fout, "%.60lf ", w[i]);
	}
	fprintf(fout, "\n");
	fprintf(fout, "%.60lf", b);
	for (int i = 0; i < LABELS; i++) {
		fprintf(fout,"\n%lf %lf %lf", maximums[i], minimums[i], avgs[i]);
	}
	fclose(fout);
	printf("模型导出完成！\n");
	
	printbye(1);
	printhello(1);
	printf("按任意键退出...\n");
	system("pause");
}

/////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////////////////////////////////////////////
/////////////////////////////////////////////////////////////////////////////
///////////////////////////__VECTORCOMPUTATION_H__///////////////////////////
//add, subtract, multiply and divide
/// <summary>
/// 两个DATA_SIZE大小的一纬向量相乘，返回一个两个向量每项乘积之和
/// </summary>
/// <param name="x">向量1</param>
/// <param name="arr">向量2</param>
/// <returns></returns>
double vectordot(const double x[DATA_SIZE], const double arr[DATA_SIZE]) {
	double ans = 0;

	for (int i = 0; i < DATA_SIZE; i++) {
		ans += x[i] * arr[i];
	}
	return ans;
}

/// <summary>
/// 两个一维向量相减，返回一维向量
/// </summary>
/// <param name="x">减数</param>
/// <param name="y">被减数</param>
/// <param name="ans">用于接收返回值的数组</param>
/// <returns></returns>
void vectorsub(const double x[TRAIN_SIZE], const double y[TRAIN_SIZE], double ans[TRAIN_SIZE]) {
	for (int i = 0; i < TRAIN_SIZE; i++) {
		ans[i] = x[i] - y[i];
	}
}

/// <summary>
/// 两个一维向量相乘
/// </summary>
/// <param name="x">向量1</param>
/// <param name="y">向量2</param>
/// <param name="ans">用于接收返回值的数组</param>
void vectormultiply(const double x[TRAIN_SIZE], const double y[TRAIN_SIZE], double ans[TRAIN_SIZE]) {
	for (int i = 0; i < TRAIN_SIZE; i++) {
		ans[i] = x[i] * y[i];
	}
}

---

预测部分：

载入模型数据

获取用于预测的数据

基于模型参数对获取到的数据进行归一化处理

获取预测结果（这里采用了写死的方式，没有进行复杂的操作）

预测源码

#include "global_define.h"
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

struct Model {
	double w[DATA_SIZE];
	double b;
}model;

const char* label_list[LABELS] = {
	"CRIM","ZN","INDUS","CHAS","NOX","RM",
	"AGE","DIS","RAD","TAX","PTRATIO","B","LSTAT","MEDV"
};
double maximums[LABELS] = { 0.0 };
double minimums[LABELS] = { 0.0 };
double avgs[LABELS] = { 0.0 };
double predict_data[DATA_SIZE];

void get_data();
void load_model(const char* file_path);
void predict();

int main() {
	char model[100];
	printhello(2);
	printf("请输入要使用的模型(可以不带模型后缀,默认为train_finish.luoy)：");
	gets_s(model, 100);
	if (strstr(model, ".luoy") == NULL) {
		strcat(model, ".luoy");
	}
	if (strcmp(model, "")) {
		strcpy(model, "train_finish.luoy");
	}
	load_model(model);
	get_data();
	predict();
	system("pause");

	return 0;
}

void get_data() {
	printf("请输入要预测的数据...\n");
	for (int i = 0; i < DATA_SIZE; i++) {
		printf("请输入%s：", label_list[i]);
		scanf("%lf", &predict_data[i]);
	}
	
	//归一化
	for (int y = 0; y < DATA_SIZE; y++) {
		if (maximums[y] - minimums[y] == 0)continue;
		predict_data[y] = (predict_data[y] - minimums[y]) / (maximums[y] - minimums[y]);
	}
	printf("数据获取完成\n");
}

void load_model(const char* file_path) {
	FILE* file = fopen(file_path, "r");
	printf("加载模型%s\n", file_path);
	if (file == NULL) {
		printf("未找到模型%s\n", file_path);
		system("pause");
		exit(1);
	}

	for (int i = 0; i < DATA_SIZE; i++) {
		fscanf(file, "%lf", &model.w[i]);
	}
	fscanf(file, "%lf", &model.b);
	for (int i = 0; i < LABELS; i++) {
		fscanf(file, "%lf%lf%lf", &maximums[i], &minimums[i], &avgs[i]);
	}
	fclose(file);
	printf("模型加载完成\n");
}

void predict() {
	double ans = 0.0;
	for (int i = 0; i < DATA_SIZE; i++) {
		ans += predict_data[i] * model.w[i];
	}
	ans += model.b;
	printf("根据所给参数：\n");
    //这里采用了写死的方式，没有进行复杂的操作
    //后面的+ -参数为当前训练数据的最优参数。
	printf("\033[36m>>>基于99%%概率预测，该地区房价范围为(%9lf,%10lf)\033[m\n", ans - 7.2, ans + 7.2);
	printf("\033[36m>>>基于98%%概率预测，该地区房价范围为(%9lf,%10lf)\033[m\n", ans - 6.04, ans + 6.04);
	printf("\033[36m>>>基于97%%概率预测，该地区房价范围为(%9lf,%10lf)\033[m\n", ans - 5.77, ans + 5.77);
	printf("\033[36m>>>基于94%%概率预测，该地区房价范围为(%9lf,%10lf)\033[m\n", ans - 5.1, ans + 5.1);
	printf("\033[36m>>>基于91%%概率预测，该地区房价范围为(%9lf,%10lf)\033[m\n", ans - 4.59, ans + 4.59);
	printf("\033[36m>>>基于89%%概率预测，该地区房价范围为(%9lf,%10lf)\033[m\n", ans - 4.2, ans + 4.2);
	printf("\033[36m>>>基于83%%概率预测，该地区房价范围为(%9lf,%10lf)\033[m\n", ans - 3.9, ans + 3.9);
	printf("\033[36m>>>基于76%%概率预测，该地区房价范围为(%9lf,%10lf)\033[m\n", ans - 3.6, ans + 3.6);
	printf("\033[36m>>>基于67%%概率预测，该地区房价范围为(%9lf,%10lf)\033[m\n", ans - 3, ans + 3);
	printf("\033[36m>>>基于60%%概率预测，该地区房价范围为(%9lf,%10lf)\033[m\n", ans - 2.6, ans + 2.6);
	printf("\033[36m>>>基于50%%概率预测，该地区房价范围为(%9lf,%10lf)\033[m\n", ans - 2.08, ans + 2.08);
	printf("\033[36m>>>该地区房价可能为%10lf\033[m\n",ans);
	printbye(2);
	printhello(2);
}

训练数据housing.data

41.529200 0.000000 18.100000 0.000000 0.693000 5.531000 85.400000 1.607400 24.000000 666.000000 20.200000 329.460000 27.380000 6.375000 
67.920800 0.000000 18.100000 0.000000 0.693000 5.683000 100.000000 1.425400 24.000000 666.000000 20.200000 384.970000 22.980000 3.750000 
20.716200 0.000000 18.100000 0.000000 0.659000 4.138000 100.000000 1.178100 24.000000 666.000000 20.200000 370.220000 23.340000 8.925000 
11.951100 0.000000 18.100000 0.000000 0.659000 5.608000 100.000000 1.285200 24.000000 666.000000 20.200000 332.090000 12.130000 20.925000 
7.403890 0.000000 18.100000 0.000000 0.597000 5.617000 97.900000 1.454700 24.000000 666.000000 20.200000 314.640000 26.400000 12.900000 
14.438300 0.000000 18.100000 0.000000 0.597000 6.852000 100.000000 1.465500 24.000000 666.000000 20.200000 179.360000 19.780000 20.625000 
51.135800 0.000000 18.100000 0.000000 0.597000 5.757000 100.000000 1.413000 24.000000 666.000000 20.200000 2.600000 10.110000 11.250000 
14.050700 0.000000 18.100000 0.000000 0.597000 6.657000 100.000000 1.527500 24.000000 666.000000 20.200000 35.050000 21.220000 12.900000 
18.811000 0.000000 18.100000 0.000000 0.597000 4.628000 100.000000 1.553900 24.000000 666.000000 20.200000 28.790000 34.370000 13.425000 
28.655800 0.000000 18.100000 0.000000 0.597000 5.155000 100.000000 1.589400 24.000000 666.000000 20.200000 210.970000 20.080000 12.225000 
45.746100 0.000000 18.100000 0.000000 0.693000 4.519000 100.000000 1.658200 24.000000 666.000000 20.200000 88.270000 36.980000 5.250000 
18.084600 0.000000 18.100000 0.000000 0.679000 6.434000 100.000000 1.834700 24.000000 666.000000 20.200000 27.250000 29.050000 5.400000 
10.834200 0.000000 18.100000 0.000000 0.679000 6.782000 90.800000 1.819500 24.000000 666.000000 20.200000 21.570000 25.790000 5.625000 
25.940600 0.000000 18.100000 0.000000 0.679000 5.304000 89.100000 1.647500 24.000000 666.000000 20.200000 127.360000 26.640000 7.800000 
73.534100 0.000000 18.100000 0.000000 0.679000 5.957000 100.000000 1.802600 24.000000 666.000000 20.200000 16.450000 20.620000 6.600000 
11.812300 0.000000 18.100000 0.000000 0.718000 6.824000 76.500000 1.794000 24.000000 666.000000 20.200000 48.450000 22.740000 6.300000 
11.087400 0.000000 18.100000 0.000000 0.718000 6.411000 100.000000 1.858900 24.000000 666.000000 20.200000 318.750000 15.020000 12.525000 
7.022590 0.000000 18.100000 0.000000 0.718000 6.006000 95.300000 1.874600 24.000000 666.000000 20.200000 319.980000 15.700000 10.650000 
12.048200 0.000000 18.100000 0.000000 0.614000 5.648000 87.600000 1.951200 24.000000 666.000000 20.200000 291.550000 14.100000 15.600000 
7.050420 0.000000 18.100000 0.000000 0.614000 6.103000 85.100000 2.021800 24.000000 666.000000 20.200000 2.520000 23.290000 10.050000 
8.792120 0.000000 18.100000 0.000000 0.584000 5.565000 70.600000 2.063500 24.000000 666.000000 20.200000 3.650000 17.160000 8.775000 
15.860300 0.000000 18.100000 0.000000 0.679000 5.896000 95.400000 1.909600 24.000000 666.000000 20.200000 7.680000 24.390000 6.225000 
12.247200 0.000000 18.100000 0.000000 0.584000 5.837000 59.700000 1.997600 24.000000 666.000000 20.200000 24.650000 15.690000 7.650000 
37.661900 0.000000 18.100000 0.000000 0.679000 6.202000 78.700000 1.862900 24.000000 666.000000 20.200000 18.820000 14.520000 8.175000 
7.367110 0.000000 18.100000 0.000000 0.679000 6.193000 78.100000 1.935600 24.000000 666.000000 20.200000 96.730000 21.520000 8.250000 
9.338890 0.000000 18.100000 0.000000 0.679000 6.380000 95.600000 1.968200 24.000000 666.000000 20.200000 60.720000 24.080000 7.125000 
8.492130 0.000000 18.100000 0.000000 0.584000 6.348000 86.100000 2.052700 24.000000 666.000000 20.200000 83.450000 17.640000 10.875000 
10.062300 0.000000 18.100000 0.000000 0.584000 6.833000 94.300000 2.088200 24.000000 666.000000 20.200000 81.330000 19.690000 10.575000 
6.444050 0.000000 18.100000 0.000000 0.584000 6.425000 74.800000 2.200400 24.000000 666.000000 20.200000 97.950000 12.030000 12.075000 
5.581070 0.000000 18.100000 0.000000 0.713000 6.436000 87.900000 2.315800 24.000000 666.000000 20.200000 100.190000 16.220000 10.725000 
13.913400 0.000000 18.100000 0.000000 0.713000 6.208000 95.000000 2.222200 24.000000 666.000000 20.200000 100.630000 15.170000 8.775000 
11.160400 0.000000 18.100000 0.000000 0.740000 6.629000 94.600000 2.124700 24.000000 666.000000 20.200000 109.850000 23.270000 10.050000 
14.420800 0.000000 18.100000 0.000000 0.740000 6.461000 93.300000 2.002600 24.000000 666.000000 20.200000 27.490000 18.050000 7.200000 
15.177200 0.000000 18.100000 0.000000 0.740000 6.152000 100.000000 1.914200 24.000000 666.000000 20.200000 9.320000 26.450000 6.525000 
13.678100 0.000000 18.100000 0.000000 0.740000 5.935000 87.900000 1.820600 24.000000 666.000000 20.200000 68.950000 34.020000 6.300000 
9.390630 0.000000 18.100000 0.000000 0.740000 5.627000 93.900000 1.817200 24.000000 666.000000 20.200000 396.900000 22.880000 9.600000 
22.051100 0.000000 18.100000 0.000000 0.740000 5.818000 92.400000 1.866200 24.000000 666.000000 20.200000 391.450000 22.110000 7.875000 
9.724180 0.000000 18.100000 0.000000 0.740000 6.406000 97.200000 2.065100 24.000000 666.000000 20.200000 385.960000 19.520000 12.825000 
5.666370 0.000000 18.100000 0.000000 0.740000 6.219000 100.000000 2.004800 24.000000 666.000000 20.200000 395.690000 16.590000 13.800000 
9.966540 0.000000 18.100000 0.000000 0.740000 6.485000 100.000000 1.978400 24.000000 666.000000 20.200000 386.730000 18.850000 11.550000 
12.802300 0.000000 18.100000 0.000000 0.740000 5.854000 96.600000 1.895600 24.000000 666.000000 20.200000 240.520000 23.790000 8.100000 
10.671800 0.000000 18.100000 0.000000 0.740000 6.459000 94.800000 1.987900 24.000000 666.000000 20.200000 43.060000 23.980000 8.850000 
6.288070 0.000000 18.100000 0.000000 0.740000 6.341000 96.400000 2.072000 24.000000 666.000000 20.200000 318.010000 17.790000 11.175000 
9.924850 0.000000 18.100000 0.000000 0.740000 6.251000 96.600000 2.198000 24.000000 666.000000 20.200000 388.520000 16.440000 9.450000 
9.329090 0.000000 18.100000 0.000000 0.713000 6.185000 98.700000 2.261600 24.000000 666.000000 20.200000 396.900000 18.130000 10.575000 
7.526010 0.000000 18.100000 0.000000 0.713000 6.417000 98.300000 2.185000 24.000000 666.000000 20.200000 304.210000 19.310000 9.750000 
6.717720 0.000000 18.100000 0.000000 0.713000 6.749000 92.600000 2.323600 24.000000 666.000000 20.200000 0.320000 17.440000 10.050000 
5.441140 0.000000 18.100000 0.000000 0.713000 6.655000 98.200000 2.355200 24.000000 666.000000 20.200000 355.290000 17.730000 11.400000 
5.090170 0.000000 18.100000 0.000000 0.713000 6.297000 91.800000 2.368200 24.000000 666.000000 20.200000 385.090000 17.270000 12.075000 
8.248090 0.000000 18.100000 0.000000 0.713000 7.393000 99.300000 2.452700 24.000000 666.000000 20.200000 375.870000 16.740000 13.350000 
9.513630 0.000000 18.100000 0.000000 0.713000 6.728000 94.100000 2.496100 24.000000 666.000000 20.200000 6.680000 18.710000 11.175000 
4.752370 0.000000 18.100000 0.000000 0.713000 6.525000 86.500000 2.435800 24.000000 666.000000 20.200000 50.920000 18.130000 10.575000 
4.668830 0.000000 18.100000 0.000000 0.713000 5.976000 87.900000 2.580600 24.000000 666.000000 20.200000 10.480000 19.010000 9.525000 
8.200580 0.000000 18.100000 0.000000 0.713000 5.936000 80.300000 2.779200 24.000000 666.000000 20.200000 3.500000 16.940000 10.125000 
7.752230 0.000000 18.100000 0.000000 0.713000 6.301000 83.700000 2.783100 24.000000 666.000000 20.200000 272.210000 16.230000 11.175000 
6.801170 0.000000 18.100000 0.000000 0.713000 6.081000 84.400000 2.717500 24.000000 666.000000 20.200000 396.900000 14.700000 15.000000 
4.812130 0.000000 18.100000 0.000000 0.713000 6.701000 90.000000 2.597500 24.000000 666.000000 20.200000 255.230000 16.420000 12.300000 
3.693110 0.000000 18.100000 0.000000 0.713000 6.376000 88.400000 2.567100 24.000000 666.000000 20.200000 391.430000 14.650000 13.275000 
6.654920 0.000000 18.100000 0.000000 0.713000 6.317000 83.000000 2.734400 24.000000 666.000000 20.200000 396.900000 13.990000 14.625000 
5.821150 0.000000 18.100000 0.000000 0.713000 6.513000 89.900000 2.801600 24.000000 666.000000 20.200000 393.820000 10.290000 15.150000 
7.839320 0.000000 18.100000 0.000000 0.655000 6.209000 65.400000 2.963400 24.000000 666.000000 20.200000 396.900000 13.220000 16.050000 
3.163600 0.000000 18.100000 0.000000 0.655000 5.759000 48.200000 3.066500 24.000000 666.000000 20.200000 334.400000 14.130000 14.925000 
3.774980 0.000000 18.100000 0.000000 0.655000 5.952000 84.700000 2.871500 24.000000 666.000000 20.200000 22.010000 17.150000 14.250000 
4.422280 0.000000 18.100000 0.000000 0.584000 6.003000 94.500000 2.540300 24.000000 666.000000 20.200000 331.290000 21.320000 14.325000 
15.575700 0.000000 18.100000 0.000000 0.580000 5.926000 71.000000 2.908400 24.000000 666.000000 20.200000 368.740000 18.130000 14.325000 
13.075100 0.000000 18.100000 0.000000 0.580000 5.713000 56.700000 2.823700 24.000000 666.000000 20.200000 396.900000 14.760000 15.075000 
4.348790 0.000000 18.100000 0.000000 0.580000 6.167000 84.000000 3.033400 24.000000 666.000000 20.200000 396.900000 16.290000 14.925000 
4.038410 0.000000 18.100000 0.000000 0.532000 6.229000 90.700000 3.099300 24.000000 666.000000 20.200000 395.330000 12.870000 14.700000 
3.568680 0.000000 18.100000 0.000000 0.580000 6.437000 75.000000 2.896500 24.000000 666.000000 20.200000 393.370000 14.360000 17.400000 
4.646890 0.000000 18.100000 0.000000 0.614000 6.980000 67.600000 2.532900 24.000000 666.000000 20.200000 374.680000 11.660000 22.350000 
8.055790 0.000000 18.100000 0.000000 0.584000 5.427000 95.400000 2.429800 24.000000 666.000000 20.200000 352.580000 18.140000 10.350000 
6.393120 0.000000 18.100000 0.000000 0.584000 6.162000 97.400000 2.206000 24.000000 666.000000 20.200000 302.760000 24.100000 9.975000 
4.871410 0.000000 18.100000 0.000000 0.614000 6.484000 93.600000 2.305300 24.000000 666.000000 20.200000 396.210000 18.680000 12.525000 
15.023400 0.000000 18.100000 0.000000 0.614000 5.304000 97.300000 2.100700 24.000000 666.000000 20.200000 349.480000 24.910000 9.000000 
10.233000 0.000000 18.100000 0.000000 0.614000 6.185000 96.700000 2.170500 24.000000 666.000000 20.200000 379.700000 18.030000 10.950000 
14.333700 0.000000 18.100000 0.000000 0.614000 6.229000 88.000000 1.951200 24.000000 666.000000 20.200000 383.320000 13.110000 16.050000 
5.824010 0.000000 18.100000 0.000000 0.532000 6.242000 64.700000 3.424200 24.000000 666.000000 20.200000 396.900000 10.740000 17.250000 
5.708180 0.000000 18.100000 0.000000 0.532000 6.750000 74.900000 3.331700 24.000000 666.000000 20.200000 393.070000 7.740000 17.775000 
5.731160 0.000000 18.100000 0.000000 0.532000 7.061000 77.000000 3.410600 24.000000 666.000000 20.200000 395.280000 7.010000 18.750000 
2.818380 0.000000 18.100000 0.000000 0.532000 5.762000 40.300000 4.098300 24.000000 666.000000 20.200000 392.920000 10.420000 16.350000 
2.378570 0.000000 18.100000 0.000000 0.583000 5.871000 41.900000 3.724000 24.000000 666.000000 20.200000 370.730000 13.340000 15.450000 
3.673670 0.000000 18.100000 0.000000 0.583000 6.312000 51.900000 3.991700 24.000000 666.000000 20.200000 388.620000 10.580000 15.900000 
5.691750 0.000000 18.100000 0.000000 0.583000 6.114000 79.800000 3.545900 24.000000 666.000000 20.200000 392.680000 14.980000 14.325000 
4.835670 0.000000 18.100000 0.000000 0.583000 5.905000 53.200000 3.152300 24.000000 666.000000 20.200000 388.220000 11.450000 15.450000 
0.150860 0.000000 27.740000 0.000000 0.609000 5.454000 92.700000 1.820900 4.000000 711.000000 20.100000 395.090000 18.060000 11.400000 
0.183370 0.000000 27.740000 0.000000 0.609000 5.414000 98.300000 1.755400 4.000000 711.000000 20.100000 344.050000 23.970000 5.250000 
0.207460 0.000000 27.740000 0.000000 0.609000 5.093000 98.000000 1.822600 4.000000 711.000000 20.100000 318.430000 29.680000 6.075000 
0.105740 0.000000 27.740000 0.000000 0.609000 5.983000 98.800000 1.868100 4.000000 711.000000 20.100000 390.110000 18.070000 10.200000 
0.111320 0.000000 27.740000 0.000000 0.609000 5.983000 83.500000 2.109900 4.000000 711.000000 20.100000 396.900000 13.350000 15.075000 
0.173310 0.000000 9.690000 0.000000 0.585000 5.707000 54.000000 2.381700 6.000000 391.000000 19.200000 396.900000 12.010000 16.350000 
0.279570 0.000000 9.690000 0.000000 0.585000 5.926000 42.600000 2.381700 6.000000 391.000000 19.200000 396.900000 13.590000 18.375000 
0.178990 0.000000 9.690000 0.000000 0.585000 5.670000 28.800000 2.798600 6.000000 391.000000 19.200000 393.290000 17.600000 17.325000 
0.289600 0.000000 9.690000 0.000000 0.585000 5.390000 72.900000 2.798600 6.000000 391.000000 19.200000 396.900000 21.140000 14.775000 
0.268380 0.000000 9.690000 0.000000 0.585000 5.794000 70.600000 2.892700 6.000000 391.000000 19.200000 396.900000 14.100000 13.725000 
0.239120 0.000000 9.690000 0.000000 0.585000 6.019000 65.300000 2.409100 6.000000 391.000000 19.200000 396.900000 12.920000 15.900000 
0.177830 0.000000 9.690000 0.000000 0.585000 5.569000 73.500000 2.399900 6.000000 391.000000 19.200000 395.770000 15.100000 13.125000 
0.224380 0.000000 9.690000 0.000000 0.585000 6.027000 79.700000 2.498200 6.000000 391.000000 19.200000 396.900000 14.330000 12.600000 
0.062630 0.000000 11.930000 0.000000 0.573000 6.593000 69.100000 2.478600 1.000000 273.000000 21.000000 391.990000 9.670000 16.800000 
0.045270 0.000000 11.930000 0.000000 0.573000 6.120000 76.700000 2.287500 1.000000 273.000000 21.000000 396.900000 9.080000 15.450000 
0.060760 0.000000 11.930000 0.000000 0.573000 6.976000 91.000000 2.167500 1.000000 273.000000 21.000000 396.900000 5.640000 17.925000 
0.109590 0.000000 11.930000 0.000000 0.573000 6.794000 89.300000 2.388900 1.000000 273.000000 21.000000 393.450000 6.480000 16.500000 
0.047410 0.000000 11.930000 0.000000 0.573000 6.030000 80.800000 2.505000 1.000000 273.000000 21.000000 396.900000 7.880000 8.925000 
0.228760 0.000000 8.560000 0.000000 0.520000 6.405000 85.400000 2.714700 5.000000 384.000000 20.900000 70.800000 10.630000 13.950000 
0.211610 0.000000 8.560000 0.000000 0.520000 6.137000 87.400000 2.714700 5.000000 384.000000 20.900000 394.470000 13.440000 14.475000 
0.139600 0.000000 8.560000 0.000000 0.520000 6.167000 90.000000 2.421000 5.000000 384.000000 20.900000 392.690000 12.330000 15.075000 
0.132620 0.000000 8.560000 0.000000 0.520000 5.851000 96.700000 2.106900 5.000000 384.000000 20.900000 394.050000 16.470000 14.625000 
0.171200 0.000000 8.560000 0.000000 0.520000 5.836000 91.900000 2.211000 5.000000 384.000000 20.900000 395.670000 18.660000 14.625000 
0.131170 0.000000 8.560000 0.000000 0.520000 6.127000 85.200000 2.122400 5.000000 384.000000 20.900000 387.690000 14.090000 15.300000 
0.128020 0.000000 8.560000 0.000000 0.520000 6.474000 97.100000 2.432900 5.000000 384.000000 20.900000 395.240000 12.270000 14.850000 
0.263630 0.000000 8.560000 0.000000 0.520000 6.229000 91.200000 2.545100 5.000000 384.000000 20.900000 391.230000 15.550000 14.550000 
0.107930 0.000000 8.560000 0.000000 0.520000 6.195000 54.400000 2.777800 5.000000 384.000000 20.900000 393.490000 13.000000 16.275000 
0.100840 0.000000 10.010000 0.000000 0.547000 6.715000 81.600000 2.677500 6.000000 432.000000 17.800000 395.590000 10.160000 17.100000 
0.123290 0.000000 10.010000 0.000000 0.547000 5.913000 92.900000 2.353400 6.000000 432.000000 17.800000 394.950000 16.210000 14.100000 
0.222120 0.000000 10.010000 0.000000 0.547000 6.092000 95.400000 2.548000 6.000000 432.000000 17.800000 396.900000 17.090000 14.025000 
0.142310 0.000000 10.010000 0.000000 0.547000 6.254000 84.200000 2.256500 6.000000 432.000000 17.800000 388.740000 10.450000 13.875000 
0.171340 0.000000 10.010000 0.000000 0.547000 5.928000 88.200000 2.463100 6.000000 432.000000 17.800000 344.910000 15.760000 13.725000 
0.131580 0.000000 10.010000 0.000000 0.547000 6.176000 72.500000 2.730100 6.000000 432.000000 17.800000 393.300000 12.040000 15.900000 
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