MATLAB 多项式回归模型构建与预测 - 销售数据分析

{"title":"MATLAB 多项式回归模型构建与预测 - 销售数据分析","description":"使用 MATLAB 进行多项式回归分析，构建销售预测模型，并可视化结果，包括实际销售和预测销售的散点图以及残差图。","keywords":"MATLAB, 多项式回归, 销售预测, 模型构建, 散点图, 残差图","content":"clc\nclear\n\n% 导入数据\ndata = xlsread('Impression&&CPC.xlsx', 'Sheet7');\nexposure = data(:, 1);\nclicks = data(:, 2);\nsales = data(:, 3);\n\n% 绘制箱线图剔除异常值\nfigure;\nboxplot(sales, 'Notch', 'on');\ntitle('Sales Boxplot');\nxlabel('Sales');\nylabel('Value');\n\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\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\n% 构建设计矩阵\nX = [exposure, clicks];\n\n% 设置多项式阶数\npoly_order = 2;\n\n% 添加多项式特征\nX_poly = [];\nfor i = 1:poly_order\n X_poly = [X_poly, X.^i];\nend\n\n% 使用最小二乘法估计参数\nbeta = X_poly \ sales;\n\n% 进行预测\npredicted_sales = X_poly * beta;\n\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\n% 计算残差\nresiduals = sales - predicted_sales;\n\n% 绘制残差图\nfigure;\nscatter(predicted_sales, residuals);\ntitle('Residual Plot');\nxlabel('Predicted Sales');\nylabel('Residuals');\n&quot