使用MATLAB拟合竞价与曝光次数关系模型

{ "title": "使用MATLAB拟合竞价与曝光次数关系模型", "description": "本文介绍了如何使用MATLAB从Excel文件中读取竞价和曝光次数数据，并利用非线性回归模型拟合两者的关系。代码中包含了数据预处理、模型定义、参数估计、模型评价等步骤，并绘制了散点图和拟合曲线。", "keywords": "MATLAB, 竞价, 曝光次数, 非线性回归, 模型拟合, 数据分析", "content": ""% 读取Excel数据\n"data = xlsread("Impression&&CPC.xlsx", "Sheet1", "A2:B212"); % 假设数据在Sheet1中，曝光次数在第一列，竞价在第二列\n\n"impressions = data(:, 1); % 曝光次数数据\n"bid = data(:, 2); % 竞价数据\n\n"% 找到空位置的索引\n"missing_idx = isnan(impressions) | isnan(bid);\n\n"% 将空位置填充为中位数\n"impressions(missing_idx) = median(impressions(~missing_idx));\n"bid(missing_idx) = median(bid(~missing_idx));\n\n"% 画出散点图\n"scatter(bid, impressions);\n"xlabel("竞价");\n"ylabel("曝光次数");\n"title("竞价与曝光次数关系散点图");\n\n"% 定义模型函数\n"model = @(x, bid) x(1) * exp(x(2) * (x(3) * bid + x(4))) .* sin(2pix(5)bid);\n\n"% 定义误差函数（最小二乘法）\n"errorFunc = @(x) sum((model(x, bid) - impressions).^2);\n\n"% 初始参数值\n"x0 = [1, 0.1, 0.1, 0.1, 0.1];\n\n"% 使用fminsearch函数进行参数估计\n"x = fminsearch(errorFunc, x0);\n\n"% 输出估计的参数值\n"a = x(1);\n"b = x(2);\n"c = x(3);\n"d = x(4);\n"T = x(5);\n\n"% 打印参数值\n"fprintf("估计的参数值：\n");\n"fprintf("a = %.2f\n", a);\n"fprintf("b = %.2f\n", b);\n"fprintf("c = %.2f\n", c);\n"fprintf("d = %.2f\n", d);\n"fprintf("T = %.2f\n", T);\n\n"% 代入参数绘制曲线图（包括剔除填充数据后的散点图）\n"x_vals = linspace(min(bid), max(bid), 100); % 生成横坐标数据\n"y_vals = model(x, x_vals); % 计算纵坐标数据\n\n"figure; % 创建新的图形窗口\n"scatter(bid, impressions); % 绘制原始数据的散点图\n"hold on;\n"scatter(bid(~missing_idx), impressions(~missing_idx), "filled", "MarkerFaceColor", "r"); % 绘制剔除填充数据后的散点图\n"plot(x_vals, y_vals, "g--", "LineWidth", 2); % 绘制拟合曲线\n\n"xlabel("竞价");\n"ylabel("曝光次数");\n"title("竞价与曝光次数关系散点图及拟合曲线");\n"legend("原始数据", "剔除填充数据后的数据", "拟合曲线");\n\n"% 随机选取80%的数据作为训练集，20%的数据作为测试集\n"n = size(data, 1);\n"train_idx = randperm(n, round(0.8n)); % 随机选取80%的索引作为训练集\n"test_idx = setdiff(1:n, train_idx); % 剩余的索引作为测试集\n\n"train_data = data(train_idx, :);\n"test_data = data(test_idx, :);\n\n"train_impressions = train_data(:, 1);\n"train_bid = train_data(:, 2);\n\n"test_impressions = test_data(:, 1);\n"test_bid = test_data(:, 2);\n\n"% 重新进行参数估计\n"train_missing_idx = isnan(train_impressions) | isnan(train_bid);\n"train_impressions(train_missing_idx) = median(train_impressions(~train_missing_idx));\n"train_bid(train_missing_idx) = median(train_bid(~train_missing_idx));\n\n"x = fminsearch(@(x) sum((model(x, train_bid) - train_impressions).^2), x0);\n\n"% 使用训练集的参数进行预测\n"train_predictions = model(x, train_bid);\n"test_predictions = model(x, test_bid);\n\n"% 计算训练集和测试集的均方误差\n"train_mse = sum((train_predictions - train_impressions).^2) / length(train_impressions);\n"test_mse = sum((test_predictions - test_impressions).^2) / length(test_impressions);\n\n"fprintf("训练集均方误差：%.2f\n", train_mse);\n"fprintf("测试集均方误差：%.2f\n", test_mse);\n"??? Error using ==> randperm\n"Too many input arguments.\n"上述代码出错怎么改内容：这个错误是由于randperm函数的使用方式不正确导致的。randperm函数只接受一个输入参数，表示生成随机排列的长度。在上述代码中，应该将随机排列的长度n作为randperm函数的输入参数。所以，将以下代码：\n"train_idx = randperm(n, round(0.8n));\n"改为：\n"train_idx = randperm(n, round(0.8n));\n"}