MATLAB 多项式回归分析：从数据预处理到模型评估

clc\u000a clear\u000a\u000a % 导入数据\u000a data = xlsread('Impression&&CPC.xlsx', 'Sheet7');\u000a exposure = data(:, 1);\u000a clicks = data(:, 2);\u000a sales = data(:, 3);\u000a\u000a % 绘制箱线图剔除异常值\u000a figure;\u000a boxplot(sales, 'Notch', 'on');\u000a title('Sales Boxplot');\u000a xlabel('Sales');\u000a ylabel('Value');\u000a\u000a % 计算异常值上下限\u000a q1 = quantile(sales, 0.25);\u000a q3 = quantile(sales, 0.75);\u000a iqr = q3 - q1;\u000a lower_limit = q1 - 1.5 * iqr;\u000a upper_limit = q3 + 1.5 * iqr;\u000a\u000a % 剔除异常值\u000a outlier_idx = sales < lower_limit | sales > upper_limit;\u000a exposure = exposure(~outlier_idx);\u000a clicks = clicks(~outlier_idx);\u000a sales = sales(~outlier_idx);\u000a\u000a % 构建设计矩阵\u000a X = [exposure, clicks];\u000a\u000a % 设置多项式阶数\u000a poly_order = 3; % 设置为3表示使用三次多项式\u000a\u000a % 添加多项式特征\u000a X_poly = [];\u000a for i = 1:poly_order\u000a X_poly = [X_poly, X.^i];\u000a end\u000a\u000a % 使用最小二乘法估计参数\u000a beta = X_poly \ sales;\u000a\u000a % 进行预测\u000a predicted_sales = X_poly * beta;\u000a\u000a % 绘制实际销售量和预测销售量的散点图\u000a figure;\u000a scatter(sales, predicted_sales);\u000a hold on;\u000a plot([min(sales), max(sales)], [min(sales), max(sales)], 'r--');\u000a title('Actual Sales vs Predicted Sales');\u000a xlabel('Actual Sales');\u000a ylabel('Predicted Sales');\u000a legend('Data', 'Ideal Fit');\u000a\u000a % 计算残差\u000a residuals = sales - predicted_sales;\u000a\u000a % 绘制残差图\u000a figure;\u000a scatter(predicted_sales, residuals);\u000a title('Residual Plot');\u000a xlabel('Predicted Sales');\u000a ylabel('Residuals');