

世界地理研究 ›› 2026, Vol. 35 ›› Issue (4): 60-74.DOI: 10.3969/j.issn.1004-9479.2026.04.20250149
收稿日期:2025-01-30
修回日期:2025-05-11
出版日期:2026-04-15
发布日期:2026-04-29
作者简介:黄立赫(1993—),男,讲师,博士,研究方向为马克思主义政治经济学,E-mail:370299367@qq.com。
基金资助:Received:2025-01-30
Revised:2025-05-11
Online:2026-04-15
Published:2026-04-29
摘要:
随着数字化浪潮席卷全球,其对环境可持续发展的影响引发学术界广泛关注。然而,现有研究缺乏从国别差异视角系统考察数字化对企业环境保护影响的实证证据。本研究基于47个国家、5 015家企业2008—2022年的面板数据,采用固定效应模型考察国家数字化发展与企业环境保护表现的关系。研究结果表明:国家数字化发展与企业环境保护呈现“倒U形”关系,即数字化初期有利于企业环境保护水平提升,但超过阈值后则产生负面影响;国家制度质量对此关系具有正向调节作用,高质量制度环境能够有效延缓数字化对环境的负面影响;上述关系在环境创新、排放管理和资源使用3个维度上存在差异,且在发达国家与发展中国家间表现不同。本研究丰富了数字化环境效应的理论研究体系,为各国制定数字化环境治理政策提供了实证依据。
黄立赫. 国家数字化发展对企业环境保护的影响:倒 U 形关系、制度调节与国别异质性[J]. 世界地理研究, 2026, 35(4): 60-74.
Lihe HUANG. National digital development and corporate environmental protection: Inverted U‑shaped relationship, institutional moderation, and cross‑country heterogeneity[J]. World Regional Studies, 2026, 35(4): 60-74.
| 变量 | 测量 | 来源 | |
|---|---|---|---|
| 因变量 | 环保表现 | 该指数由以下相关指标生成: ① 环境创新;② 排放;③ 资源利用。取值范围从 0(最差)到 100(最好) | Thomson Reuters Eikon |
| 环境创新 | 该变量基于 32 个项目(例如,环境产品、生态设计产品、环境研发支出等)的汇总,取值范围从 0(最差)到 100(最好) | ||
| 排放 | 该变量通过汇总 51 个项目(如排放政策、CO2、VOC、NOx、SOx 以及危险废物等)得到,取值范围从 0到 100 | ||
| 资源使用 | 该变量通过汇总 36 个项目(例如,资源削减政策、节水政策、能源使用总量、购买的电力、生产的电力、水泥能源使用量、取水总量、淡水取水总量和循环水)得到,取值范围从 0~ 100 | ||
| 自变量 | 一国数字化水平 | 该变量涵盖国家数字化的三个主要维度(知识、技术和未来准备),取值范围从 0(低)到 100(高) | IMD 世界数字竞争力数据库 |
| 调节变量 | 本国体制框架 | 该变量通过汇总 15 个国家特定项目,包括法律和监管框架、政府政策的适应性、政府决策、资本成本、中央银行政策和国家信用等级等得到,取值范围从 0(低)到 100(高) | IMD 世界数字竞争力数据库 |
| 控制变量 | 公司规模 | 总营收 | Thomson Reuters Eikon |
| 公司负债 | 定义为总债务与总资产之比的自然对数,用于衡量企业的资本结构与偿债压力 | ||
| 企业行业 | 设置行业虚拟变量控制企业所属行业差异,具体包括工业、通信服务、非必需消费品、必需消费品、金融、能源、医疗保健、信息技术、材料、房地产和公用事业 | ||
| 国内生产总值 | 该变量衡量一国整体经济产出水平。本文使用经购买力平价(PPP)调整的不变国际美元计GDP总量数据 | 世界经济展望数据库 | |
| 环境绩效指数 | 该变量衡量一个国家的环境保护,使用耶鲁大学环境法与政策中心与哥伦比亚大学国际地球科学信息网络中心合作的The Environmental Performance Index(EPI) 数据库 | The Environmental Performance Index数据库(epi.yale.edu) | |
表1 变量列表
Tab. 1 List of variables
| 变量 | 测量 | 来源 | |
|---|---|---|---|
| 因变量 | 环保表现 | 该指数由以下相关指标生成: ① 环境创新;② 排放;③ 资源利用。取值范围从 0(最差)到 100(最好) | Thomson Reuters Eikon |
| 环境创新 | 该变量基于 32 个项目(例如,环境产品、生态设计产品、环境研发支出等)的汇总,取值范围从 0(最差)到 100(最好) | ||
| 排放 | 该变量通过汇总 51 个项目(如排放政策、CO2、VOC、NOx、SOx 以及危险废物等)得到,取值范围从 0到 100 | ||
| 资源使用 | 该变量通过汇总 36 个项目(例如,资源削减政策、节水政策、能源使用总量、购买的电力、生产的电力、水泥能源使用量、取水总量、淡水取水总量和循环水)得到,取值范围从 0~ 100 | ||
| 自变量 | 一国数字化水平 | 该变量涵盖国家数字化的三个主要维度(知识、技术和未来准备),取值范围从 0(低)到 100(高) | IMD 世界数字竞争力数据库 |
| 调节变量 | 本国体制框架 | 该变量通过汇总 15 个国家特定项目,包括法律和监管框架、政府政策的适应性、政府决策、资本成本、中央银行政策和国家信用等级等得到,取值范围从 0(低)到 100(高) | IMD 世界数字竞争力数据库 |
| 控制变量 | 公司规模 | 总营收 | Thomson Reuters Eikon |
| 公司负债 | 定义为总债务与总资产之比的自然对数,用于衡量企业的资本结构与偿债压力 | ||
| 企业行业 | 设置行业虚拟变量控制企业所属行业差异,具体包括工业、通信服务、非必需消费品、必需消费品、金融、能源、医疗保健、信息技术、材料、房地产和公用事业 | ||
| 国内生产总值 | 该变量衡量一国整体经济产出水平。本文使用经购买力平价(PPP)调整的不变国际美元计GDP总量数据 | 世界经济展望数据库 | |
| 环境绩效指数 | 该变量衡量一个国家的环境保护,使用耶鲁大学环境法与政策中心与哥伦比亚大学国际地球科学信息网络中心合作的The Environmental Performance Index(EPI) 数据库 | The Environmental Performance Index数据库(epi.yale.edu) | |
| 序号 | 变量 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 环境保护 | 1 | |||||||||
| 2 | 环境创新 | 0.653*** | 1 | ||||||||
| (0.00) | |||||||||||
| 3 | 排放 | 0.858*** | 0.289*** | 1 | |||||||
| (0.00) | (0.00) | ||||||||||
| 4 | 资源使用 | 0.849*** | 0.322*** | 0.719*** | 1 | ||||||
| (0.00) | (0.00) | (0.00) | |||||||||
| 5 | 本国数字化 | -0.082*** | -0.010 | -0.065*** | -0.017** | 1 | |||||
| (0.00) | (0.25) | (0.00) | (0.024) | ||||||||
| 6 | 体制框架 | 0.013* | 0.013 | -0.009 | 0.021*** | 0.661*** | 1 | ||||
| (0.056) | (0.209) | (0.243) | (0.005) | (0.00) | |||||||
| 7 | 外延指数 | 0.090*** | 0.083*** | 0.094*** | 0.124*** | 0.629*** | 0.313*** | 1 | |||
| (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | ||||||
| 8 | 公司规模(对数) | 0.472*** | 0.204*** | 0.421*** | 0.421*** | 0.082*** | 0.049*** | 0.061*** | 1 | ||
| (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | |||||
| 9 | 公司负债(对数) | 0.053*** | 0.053*** | 0.023*** | 0.027*** | -0.011*** | -0.039*** | -0.027*** | 0.060*** | 1 | |
| (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | ||||
| 10 | 国内生产总值(对数) | -0.098 7*** | -0.064*** | -0.101*** | -0.091*** | -0.465*** | -0.339*** | -0.634*** | -0.056*** | 0.021*** | 1 |
| (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | |||
| 11 | 平均值 | 39.54 | 50.19 | 49.55 | 49.8 | 75.86 | 49.94 | 66.33 | 18.51 | 2.71 | 0.75 |
| 标准差 | 26.61 | 25.44 | 28.87 | 29.18 | 18.51 | 9.52 | 15.33 | 2.23 | 1.58 | 0.91 | |
| 最小 | 0.02 | 0.21 | 0.19 | 0.16 | 23.51 | 10.88 | 29.11 | 13.87 | -15.65 | -4.35 | |
| 最大 | 98.55 | 99.81 | 99.81 | 99.83 | 100 | 80.35 | 90.64 | 26.93 | 9.39 | 3.14 |
表 2 描述性统计和皮尔逊相关
Tab. 2 Descriptive statistics and Pearson Correlation
| 序号 | 变量 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 环境保护 | 1 | |||||||||
| 2 | 环境创新 | 0.653*** | 1 | ||||||||
| (0.00) | |||||||||||
| 3 | 排放 | 0.858*** | 0.289*** | 1 | |||||||
| (0.00) | (0.00) | ||||||||||
| 4 | 资源使用 | 0.849*** | 0.322*** | 0.719*** | 1 | ||||||
| (0.00) | (0.00) | (0.00) | |||||||||
| 5 | 本国数字化 | -0.082*** | -0.010 | -0.065*** | -0.017** | 1 | |||||
| (0.00) | (0.25) | (0.00) | (0.024) | ||||||||
| 6 | 体制框架 | 0.013* | 0.013 | -0.009 | 0.021*** | 0.661*** | 1 | ||||
| (0.056) | (0.209) | (0.243) | (0.005) | (0.00) | |||||||
| 7 | 外延指数 | 0.090*** | 0.083*** | 0.094*** | 0.124*** | 0.629*** | 0.313*** | 1 | |||
| (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | ||||||
| 8 | 公司规模(对数) | 0.472*** | 0.204*** | 0.421*** | 0.421*** | 0.082*** | 0.049*** | 0.061*** | 1 | ||
| (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | |||||
| 9 | 公司负债(对数) | 0.053*** | 0.053*** | 0.023*** | 0.027*** | -0.011*** | -0.039*** | -0.027*** | 0.060*** | 1 | |
| (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | ||||
| 10 | 国内生产总值(对数) | -0.098 7*** | -0.064*** | -0.101*** | -0.091*** | -0.465*** | -0.339*** | -0.634*** | -0.056*** | 0.021*** | 1 |
| (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | (0.00) | |||
| 11 | 平均值 | 39.54 | 50.19 | 49.55 | 49.8 | 75.86 | 49.94 | 66.33 | 18.51 | 2.71 | 0.75 |
| 标准差 | 26.61 | 25.44 | 28.87 | 29.18 | 18.51 | 9.52 | 15.33 | 2.23 | 1.58 | 0.91 | |
| 最小 | 0.02 | 0.21 | 0.19 | 0.16 | 23.51 | 10.88 | 29.11 | 13.87 | -15.65 | -4.35 | |
| 最大 | 98.55 | 99.81 | 99.81 | 99.83 | 100 | 80.35 | 90.64 | 26.93 | 9.39 | 3.14 |
| 变量 | 总计 | 环境创新 | 排放 | 资源使用 |
|---|---|---|---|---|
| 模型1 | 模型1a | 模型1b | 模型1c | |
| 数字化发展 | 1.113*** (0.152) | 1.059*** (0.203) | 1.224*** (0.173) | 0.721** (0.227) |
| 数字化发展(平方) | -0.008*** (0.002) | -0.007** (0.003) | -0.009*** (0.002) | -0.005* (0.002) |
| 外延指数 | 0.137*** (0.039) | 0.047 (0.034) | 0.194*** (0.045) | 0.233*** (0.052) |
| 公司规模(对数) | 6.937*** (0.384) | 3.154*** (0.428) | 7.759*** (0.463) | 7.588*** (0.492) |
| 公司负债(对数) | 0.161 (0.124) | 0.369* (0.178) | -0.048 (0.143) | -0.051 (0.162) |
| 国内生产总值(对数) | -0.192 (0.245) | -0.288 (0.236) | -0.464** (0.197) | 0.020 (0.251) |
| 部门效应 | 是 | 是 | 是 | 是 |
| 年份效应 | 是 | 是 | 是 | 是 |
| 常数 | -163.268*** (12.853) | -65.844*** (14.276) | -176.821*** (15.427) | -163.661*** (16.895) |
| 拐点 | 69.56 | 75.64 | 68 | 72.1 |
| R² | 0.251 | 0.053 | 0.232 | 0.211 |
表 3 随机效应模型结果
Tab. 3 Results of Random Effects Model
| 变量 | 总计 | 环境创新 | 排放 | 资源使用 |
|---|---|---|---|---|
| 模型1 | 模型1a | 模型1b | 模型1c | |
| 数字化发展 | 1.113*** (0.152) | 1.059*** (0.203) | 1.224*** (0.173) | 0.721** (0.227) |
| 数字化发展(平方) | -0.008*** (0.002) | -0.007** (0.003) | -0.009*** (0.002) | -0.005* (0.002) |
| 外延指数 | 0.137*** (0.039) | 0.047 (0.034) | 0.194*** (0.045) | 0.233*** (0.052) |
| 公司规模(对数) | 6.937*** (0.384) | 3.154*** (0.428) | 7.759*** (0.463) | 7.588*** (0.492) |
| 公司负债(对数) | 0.161 (0.124) | 0.369* (0.178) | -0.048 (0.143) | -0.051 (0.162) |
| 国内生产总值(对数) | -0.192 (0.245) | -0.288 (0.236) | -0.464** (0.197) | 0.020 (0.251) |
| 部门效应 | 是 | 是 | 是 | 是 |
| 年份效应 | 是 | 是 | 是 | 是 |
| 常数 | -163.268*** (12.853) | -65.844*** (14.276) | -176.821*** (15.427) | -163.661*** (16.895) |
| 拐点 | 69.56 | 75.64 | 68 | 72.1 |
| R² | 0.251 | 0.053 | 0.232 | 0.211 |
| 变量 | 总计 | 环境 | 排放 | |||||
|---|---|---|---|---|---|---|---|---|
| 模型1 | 模型 | 模型1 | 模型1 | |||||
| 低 | 高 | 低 | 高 | 低 | 高 | 低 | 高 | |
| 0.75 | -0.31 | 0.71 | -0.36 | 0.78 | -0.55 | 0.48 | -0.25 | |
| T | 12.37 | -10.46 | 6.674 | -5.94 | 9.736 | -11.5 | 6.09 | -5.22 |
| P | 0.000 | 0.003 | 0.000 | 0.002 | 0.000 | 0.003 | 0.004 | 0.001 |
| 极点 | 73.593 | 74.164 | 68.316 | 73.712 | ||||
| 总体测试 | 倒U形 | 倒U形 | 倒U形 | 倒U形 | ||||
| T | 10.51 | 5.88 | 9.78 | 5.24 | ||||
| P | 0.002 | 0.000 | 0.003 | 0.001 | ||||
表 4 驼峰关系检验
Tab. 4 Hump relationship test
| 变量 | 总计 | 环境 | 排放 | |||||
|---|---|---|---|---|---|---|---|---|
| 模型1 | 模型 | 模型1 | 模型1 | |||||
| 低 | 高 | 低 | 高 | 低 | 高 | 低 | 高 | |
| 0.75 | -0.31 | 0.71 | -0.36 | 0.78 | -0.55 | 0.48 | -0.25 | |
| T | 12.37 | -10.46 | 6.674 | -5.94 | 9.736 | -11.5 | 6.09 | -5.22 |
| P | 0.000 | 0.003 | 0.000 | 0.002 | 0.000 | 0.003 | 0.004 | 0.001 |
| 极点 | 73.593 | 74.164 | 68.316 | 73.712 | ||||
| 总体测试 | 倒U形 | 倒U形 | 倒U形 | 倒U形 | ||||
| T | 10.51 | 5.88 | 9.78 | 5.24 | ||||
| P | 0.002 | 0.000 | 0.003 | 0.001 | ||||
| 总计 | 环境 | 排放 | 资源 | |
|---|---|---|---|---|
| 模型2 | 模型 | 模型2 | 模型2 | |
7.902 (0.000) | 0.574 (0.933) | 6.563 (0.000) | 6.141 (0.000) | |
| LRF | 9.216 (0.010) | 0.282 (0.868) | 12.971 (0.002) | 6.656 (0.036) |
表 5 模型非线性的测试结果
Tab. 5 Nonlinear test results of the model
| 总计 | 环境 | 排放 | 资源 | |
|---|---|---|---|---|
| 模型2 | 模型 | 模型2 | 模型2 | |
7.902 (0.000) | 0.574 (0.933) | 6.563 (0.000) | 6.141 (0.000) | |
| LRF | 9.216 (0.010) | 0.282 (0.868) | 12.971 (0.002) | 6.656 (0.036) |
| 项目 | 总计 | 环境 | 排放 | |
|---|---|---|---|---|
| 模型2 | 模型 | 模型2 | 模型2 | |
| 低 | ||||
| 本国 | 1.138*** (0.000) | 1.070*** (0.000) | 1.244*** (0.000) | 0.735*** (0.000) |
| 本国 | -0.008*** (0.000) | -0.007*** (0.000) | -0.009*** (0.000) | -0.005*** (0.000) |
| 极值 | 73.331 | 74.188 | 68.079 | 73.051 |
| 高 | ||||
| 本国 | 0.900*** (0.000) | 1.022*** (0.000) | 0.875*** (0.000) | 0.498*** (0.000) |
| 本国 | -0.005*** (0.000) | -0.007*** (0.000) | -0.005*** (0.000) | -0.003* (0.053) |
| 极值 | 87.103 | 76.704 | 84.798 | 98.702 |
| 外延指数 | 0.134**** (0.000) | 0.046 (0.174) | 0.200*** (0.000) | 0.245*** (0.000) |
| 公司 | 6.942*** (0.000) | 3.153*** (0.000) | 7.757*** (0.000) | 7.588*** (0.000) |
0.152 (0.207) | 0.387 (-0.283) | -0.065 (0.745) | -0.051 (0.760) | |
| 国内生产总值( | -0.284* (0.071) | -0.283 (0.257) | -0.633** (0.002) | -0.129 (0.534) |
| 部门 | 是 | 是 | 是 | 是 |
| 是 | 是 | 是 | 是 | |
-164.083*** (0.000) | -66.244*** (0.000) | -177.878*** (0.000) | -164.012*** (0.000) | |
| 阈 | 62.756 | 62.756 | 62.756 | 62.756 |
| 公司 | 5 015 | 2 747 | 4 594 | 4 516 |
| 观察样本 | 16 893 | 8 930 | 15,219 | 15,068 |
表 6 PSTR模型的估计结果
Tab. 6 Estimation results of PSTR model
| 项目 | 总计 | 环境 | 排放 | |
|---|---|---|---|---|
| 模型2 | 模型 | 模型2 | 模型2 | |
| 低 | ||||
| 本国 | 1.138*** (0.000) | 1.070*** (0.000) | 1.244*** (0.000) | 0.735*** (0.000) |
| 本国 | -0.008*** (0.000) | -0.007*** (0.000) | -0.009*** (0.000) | -0.005*** (0.000) |
| 极值 | 73.331 | 74.188 | 68.079 | 73.051 |
| 高 | ||||
| 本国 | 0.900*** (0.000) | 1.022*** (0.000) | 0.875*** (0.000) | 0.498*** (0.000) |
| 本国 | -0.005*** (0.000) | -0.007*** (0.000) | -0.005*** (0.000) | -0.003* (0.053) |
| 极值 | 87.103 | 76.704 | 84.798 | 98.702 |
| 外延指数 | 0.134**** (0.000) | 0.046 (0.174) | 0.200*** (0.000) | 0.245*** (0.000) |
| 公司 | 6.942*** (0.000) | 3.153*** (0.000) | 7.757*** (0.000) | 7.588*** (0.000) |
0.152 (0.207) | 0.387 (-0.283) | -0.065 (0.745) | -0.051 (0.760) | |
| 国内生产总值( | -0.284* (0.071) | -0.283 (0.257) | -0.633** (0.002) | -0.129 (0.534) |
| 部门 | 是 | 是 | 是 | 是 |
| 是 | 是 | 是 | 是 | |
-164.083*** (0.000) | -66.244*** (0.000) | -177.878*** (0.000) | -164.012*** (0.000) | |
| 阈 | 62.756 | 62.756 | 62.756 | 62.756 |
| 公司 | 5 015 | 2 747 | 4 594 | 4 516 |
| 观察样本 | 16 893 | 8 930 | 15,219 | 15,068 |
| 变量 | 大型企业 | 中小企业 | 国有企业 | 民营企业 | 外资企业 |
|---|---|---|---|---|---|
| 数字化发展 | 0.842*** | 1.327*** | 1.176*** | 0.837** | 0.614* |
| (-0.127) | (-0.196) | (-0.204) | (-0.168) | (-0.237) | |
| 数字化发展(平方) | -0.005** | -0.011*** | -0.008*** | -0.005* | -0.003 |
| (-0.002) | (-0.002) | (-0.002) | (-0.002) | (-0.002) | |
| 环境保护指数 | 0.162*** | 0.093* | 0.186*** | 0.124** | 0.078 |
| (-0.035) | (-0.044) | (-0.051) | (-0.039) | (-0.057) | |
| 公司规模(对数) | 5.214*** | 4.837*** | 6.429*** | 5.628*** | 4.519*** |
| (-0.532) | (-0.837) | (-0.734) | (-0.572) | (-0.916) | |
| 公司负债(对数) | 0.237 | -0.196 | 0.483* | 0.092 | -0.347 |
| (-0.163) | (-0.184) | (-0.219) | (-0.174) | (-0.235) | |
| 国内生产总值(对数) | -0.327 | -0.148 | -0.524* | -0.163 | 0.219 |
| (-0.238) | (-0.257) | (-0.241) | (-0.217) | (-0.314) | |
| 行业/年份效应 | 包括 | 包括 | 包括 | 包括 | 包括 |
| 拐点 | 84.2 | 60.3 | 73.5 | 83.7 | 102.3 |
| R² | 0.285 | 0.217 | 0.251 | 0.219 | 0.194 |
| U形检验(p值) | 0.006 | 0 | 0.001 | 0.049 | 0.172 |
表7 按企业特征分组的回归结果
Tab. 7 Regression results grouped by enterprise characteristics
| 变量 | 大型企业 | 中小企业 | 国有企业 | 民营企业 | 外资企业 |
|---|---|---|---|---|---|
| 数字化发展 | 0.842*** | 1.327*** | 1.176*** | 0.837** | 0.614* |
| (-0.127) | (-0.196) | (-0.204) | (-0.168) | (-0.237) | |
| 数字化发展(平方) | -0.005** | -0.011*** | -0.008*** | -0.005* | -0.003 |
| (-0.002) | (-0.002) | (-0.002) | (-0.002) | (-0.002) | |
| 环境保护指数 | 0.162*** | 0.093* | 0.186*** | 0.124** | 0.078 |
| (-0.035) | (-0.044) | (-0.051) | (-0.039) | (-0.057) | |
| 公司规模(对数) | 5.214*** | 4.837*** | 6.429*** | 5.628*** | 4.519*** |
| (-0.532) | (-0.837) | (-0.734) | (-0.572) | (-0.916) | |
| 公司负债(对数) | 0.237 | -0.196 | 0.483* | 0.092 | -0.347 |
| (-0.163) | (-0.184) | (-0.219) | (-0.174) | (-0.235) | |
| 国内生产总值(对数) | -0.327 | -0.148 | -0.524* | -0.163 | 0.219 |
| (-0.238) | (-0.257) | (-0.241) | (-0.217) | (-0.314) | |
| 行业/年份效应 | 包括 | 包括 | 包括 | 包括 | 包括 |
| 拐点 | 84.2 | 60.3 | 73.5 | 83.7 | 102.3 |
| R² | 0.285 | 0.217 | 0.251 | 0.219 | 0.194 |
| U形检验(p值) | 0.006 | 0 | 0.001 | 0.049 | 0.172 |
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