MATLAB 多项式回归模型示例：销售预测

clc\nclear\n% 导入数据\ndata = xlsread('Impression&&CPC.xlsx', 'Sheet7');\nexposure = data(:, 1);\nclicks = data(:, 2);\nsales = data(:, 3);\n% 绘制箱线图剔除异常值\nfigure;\nboxplot(sales, 'Notch', 'on');\ntitle('Sales Boxplot');\nxlabel('Sales');\nylabel('Value');\n% 计算异常值上下限\nq1 = quantile(sales, 0.25);\nq3 = quantile(sales, 0.75);\niqr = q3 - q1;\nlower_limit = q1 - 1.5 * iqr;\nupper_limit = q3 + 1.5 * iqr;\n% 剔除异常值\noutlier_idx = sales < lower_limit | sales > upper_limit;\nexposure = exposure(~outlier_idx);\nclicks = clicks(~outlier_idx);\nsales = sales(~outlier_idx);\n% 构建设计矩阵\nX = [exposure, clicks];\n% 设置多项式阶数\npoly_order = 2;\n% 添加多项式特征\nX_poly = [];\nfor i = 1:poly_order\n X_poly = [X_poly, X.^i];\nend\n% 使用最小二乘法估计参数\nbeta = X_poly \ sales;\n% 进行预测\npredicted_sales = X_poly * beta;\n% 绘制实际销售量和预测销售量的散点图\nfigure;\nscatter(sales, predicted_sales);\nhold on;\nplot([min(sales), max(sales)], [min(sales), max(sales)], 'r--');\ntitle('Actual Sales vs Predicted Sales');\nxlabel('Actual Sales');\nylabel('Predicted Sales');\nlegend('Data', 'Ideal Fit');\n% 计算残差\nresiduals = sales - predicted_sales;\n% 绘制残差图\nfigure;\nscatter(predicted_sales, residuals);\ntitle('Residual Plot');\nxlabel('Predicted Sales');\nylabel('Residuals');\n\n\n根据上述代码输出多项式内容：阶数为2的回归模型。