Municipal Legal Framework (Castro Pozo 2007): The municipal legal base, comprising laws and ordinances, sets the normative context for environmental management. The consistency of these norms ensures a coherent regulatory framework, while their continuous updating reflects adaptability to changing dynamics. The responsible use of resources, as a sub-indicator, underscores the importance of promoting sustainable and environmentally conscious practices. In the realm of ordinances, their effectiveness is measured not only by their existence, but by their actual impact. Citizen participation, deemed a fundamental pillar, is directly linked to the legitimacy and effectiveness of these regulations. Constant updating of ordinances is crucial for staying aligned with environmental dynamics and community needs.

Environmental Education System (Castro Pozo 2007): Environmental culture is built through effective educational programmes that aim not only to impart knowledge, but also to foster an active and conscious relationship with the environment. Institutional collaboration, another key indicator, highlights the importance of partnerships between educational entities and relevant stakeholders to strengthen environmental education. Critical awareness of environmental issues, as a sub-dimension, reflects the commitment to a deep understanding of environmental challenges. Student participation, addressing key topics and the development of collective environmental consciousness are essential aspects of this dimension.

Urban Management Tools (Castro Pozo 2007): Urban planning, as a tool, not only provides information on environmental management, but also addresses urban integration as an integral part of sustainable development. Promotion and development tools consider the environment in projects, aiming not just for economic growth, but also for equity in the distribution of benefits. The redistribution of costs and benefits, through strategic resource allocation, fosters citizen participation and promotes transparency and accountability. These tools constitute a complex network that seeks to balance urban progress with environmental preservation and active community participation.

Social Dimension (UN: WCED 1987, Sen 1999, Chen and Feeley 2014, Bermejo 2014, Miletzki and Broten 2017, Alvarado-Arias 2023): Quality of life, a central aspect of sustainable development, is broken down into various indicators. Urban environmental quality, as a sub-dimension, assesses the physical environment in the district, including green spaces and infrastructure and their contribution to improving the quality of life. Solid waste management, essential for environmental health, becomes a crucial marker of community well-being. Meeting basic needs, focused on access to services and decent and affordable housing, is integrated as an essential component of this dimension. Public policies and development programmes, evaluated for their effectiveness, guide the path towards sustainable and equitable quality of life. Health, as another social dimension, addresses equitable access to health services, the suitability of infrastructure and health education and awareness. These aspects are vital for ensuring the population's health and its ability to contribute to sustainable development.

Economic Dimension (Newman and Jennings 2008): Economic development, a key component of sustainable development, is assessed through public policies and programmes aimed at improving the community's economic situation. The generation of dignified and well-paid jobs, a crucial aspect, intertwines with the promotion of entrepreneurship and the creation of micro-enterprises. Activities and occupations, focused on training and labour formation, corporate social and ethical responsibility and economic contribution to sustainable development, constitute the district's economic fabric. Production with environmental criteria, a subset, ensures that these activities are not only economically viable, but also environmentally responsible.

Environmental-Ecological Dimension (Beatley 2000, Holden et al. 2017, Ilyichev et al. 2018, Bokov 2019): The environmental-ecological dimension stands as an essential pillar of sustainable development. In the face of climate change, the community's knowledge and the effectiveness of measures to mitigate its effects are evaluated, along with effective collaboration between different sectors to tackle this global challenge. Sustainable management of natural resources, as a central element, addresses the responsible use of resources like water and materials. Corporate responsibility and transparency concerning environmental and social impact, along with the promotion of eco-innovation and clean technologies, complete this crucial dimension.

This in-depth analysis highlights the importance of these variables and dimensions in assessing sustainable development in the Lurin District. The interconnection between independent and dependent variables reveals the complexity of factors influencing the path towards sustainable development. This multidimensional approach provides not only a detailed snapshot of the current state, but also serves as a strategic guide for future policies and practices that drive sustainability and improve the quality of life in this region. The detailed analysis of each variable and sub-variable offers a comprehensive understanding that will be crucial for informed decision-making and designing effective strategies for the future sustainable development of the Lurin District.

Deterioration of Natural Resources: Disordered urban expansion has led to the loss of green areas and the degradation of natural ecosystems, affecting biodiversity and environmental quality.

Challenges in Basic Infrastructure: Unplanned growth has put pressure on basic infrastructure, resulting in deficiencies in essential services like water, sanitation and transportation.

Conversion of Agricultural Lands: The transformation of agricultural lands into urban areas not only compromises food security, but also threatens the traditional agricultural practices rooted in the community's history.

Preservation of Cultural and Environmental Heritage: The research aims to highlight the importance of preserving Lurin's cultural and environmental heritage. A detailed understanding of these elements is essential for designing sustainable development strategies that do not compromise the region's unique identity.

Development of Sustainable Solutions: The urgency to propose viable and sustainable solutions to Lurin's identified problems lies in the need to ensure a balance between urban development and environmental conservation. The research acts as a catalyst for creating policies and practices that comprehensively address the existing challenges.

Community Awareness and Participation: The research not only diagnoses problems, but also aims to actively involve the community in identifying solutions. Citizen participation is crucial for ensuring the feasibility and acceptance of proposed measures.

Model for Future Research: The Lurin case study can serve as a valuable model for other regions facing similar challenges in terms of urban development and environmental conservation. The findings and proposed strategies can be extrapolated and adapted to similar contexts, generating impact beyond the geographical confines of Lurin.

The research in the Lurin District presents itself as a critical and timely initiative. Addressing the specific issues of this region, it contributes not only to local improvement, but also to the advancement of knowledge in the field of sustainable urban development, offering valuable perspectives and solutions for a more equitable future in harmony with its natural and cultural environment.

The methodology employed in surveying the inhabitants of Lurin to examine the relationships between the dependent variable and the independent ones, along with their indicators, reflects a rigorous and scientific approach. The questions posed are available in the Supplementary Files section (Suppl. material 1). The selection of a sample size of 180 individuals from a population of 89,195 inhabitants (Instituto Nacional de Estadística e Informática de Perú 2018), as of the year 2017, adheres to the criteria of a simple random sample.

This approach is appropriate for several reasons. Population and Sample Size: For large populations, a sample of 180 individuals is reasonable to generate statistically significant results, given that the sample is representative of the total population. Simple Random Sampling Formula: The formula employed to calculate the sample size is suitable for studies involving large populations; simple random sampling ensures that each member of the population has an equal probability of being selected, which is crucial for ensuring the validity and reliability of the results. Standard Normal Distribution: The assumption of a standard normal distribution is a common premise in many social and demographic research studies. Non-Probabilistic Samples: The utilisation of a sampling method that does not afford every individual in the population a known chance of inclusion. 95% Confidence Level: A standard confidence level in social and demographic research. (Hernández Sampieri et al. 2014).

The responses to the questions have been structured on a Likert scale ranging from 1 to 5, where 1 indicates total disagreement, 2 disagreement, 3 neither disagreement nor agreement, 4 agreement and 5 total agreement.

The outcomes of the survey will furnish valuable data for comprehending the interactions amongst the selected variables and will facilitate the formulation of pertinent conclusions and recommendations for the sustainable development of the district.

To quantify and identify the relationship between the studied variables, the Pearson sample correlation coefficient was used in its form described in Equation 1, where r_xy represents the Pearson coefficient, x_i and y_i represent each of the samples and \(\bar{x}\) and \(\bar{y}\) represent the means of the samples.

(Eq. 1) \(r_{xy} = \left (\sum_{i=1}^{n} (x_{i} - \bar{x})(y_{i} - \bar{y}) \right) \left/ \left (\sqrt{\sum_{i=1}^{n} (x_{i} - \bar{x})^2} \cdot \sqrt{\sum_{i=1}^{n} (y_{i} - \bar{y})^2} \right) \right.\)

Pearson coefficients close to 1 indicate stronger positive correlations than those close to 0, whereas those close to -1 indicate stronger negative correlations (Bisquerra 1987).

To assess the feasibility of using parametric tests, Kolmogorov-Smirnov tests were applied to test the hypothesis of normality. The test statistic is the maximum difference between the sample and population distribution functions, as shown in Equation 2. A significance level of 5% (p = 0.05) was considered. Therefore, the null hypothesis (H₀) will be accepted when p ≥ 0.05 and the alternative (H₁) when p < 0.05.

(Eq. 2). \(D = \max\limits_{1 \leq i \leq n} |F_{n}(x_i) - F_{o}(x_i)|\)

Subsequently, a linear regression analysis was conducted to determine the influence of the independent variables (\(X_{i}\)) on the dependent variable (Y), where \(\beta\) represents the coefficients of adjustment and m denotes the number of independent variables in the system, as shown in Equation 3.

(Eq. 3). \(Y= \beta_{o}+\sum_{i=1}^{m} \beta_{i}X_i\)

Once each of the linear regression models for the different variables has been obtained and calculated, it is interesting to calculate the multiple regression for each dependent variable. This will allow us to obtain an equation as shown in Eq. 4:

(Eq. 4). \(Y= \beta_{o}+\beta_{1}X_1+\beta_{2}X_2+\beta_{3}X_3\)

Additionally, the VIF (Variance Inflation Factor) will be calculated. The VIF measures how much the variance of a coefficient increases due to collinearity. A VIF of 1 indicates no correlation between each combination of independent variables, 1 < VIF < 5 indicates a moderate, but generally acceptable correlation, VIF ≥ 5 indicates a high correlation that may suggest multicollinearity issues and VIF ≥ 10 indicates a very high correlation, which is problematic and generally unacceptable. The VIF helps identify multicollinearity problems amongst the independent variables, guiding us to decide whether to remove variables from the model, combine them or apply other solutions.

For statistical calculations, the Matlab® R2023b (MathWorks, Natick, MA, USA) software package was employed.

In the initial phase of the study, a comparative analysis was conducted between the variables 'Urban Environmental Management System' (UEMS), serving as the independent variable and 'Sustainable Development' (SD), serving as the dependent variable. Subsequently, each of these variables was further decomposed into a series of study dimensions, each encompassing a set of indicators and sub-indicators.

The UEMS variable analyses the dimensions: Municipal legal framework, Environmental education system and Instruments of urban management.

The SD variable analyses the dimensions: Social dimension, Economic dimension and Environmental-ecological dimension.

In Table 3, descriptive statistics for the data obtained for the variable 'Urban Environmental Management System' are presented, concerning each of its respective dimensions. The first row includes the statistics for the consolidated data. Fig. 1 illustrates data through graphical representation.

For the variable Urban Environmental Management Systems (UEMS), when consolidating the data, a standard deviation of 0.4333 is obtained, with a minimum value of 1.857, a maximum of 4.714 and a mean of 2.673. Upon analysing its dimensions independently, 'Municipal legal framework' and 'Urban management instruments' exhibit the highest and lowest standard deviations, with values of 0.6739 and 0.4607, respectively. Additionally, the 'Urban management instruments' dimension showed the highest number of outliers, all close to its maximum value.

With the presented data, it can also be mentioned that respondents consider 'Urban management instruments' to be the least performing, as it has the lowest mean and standard deviation amongst the dimensions studied. This implies unanimity in perceiving it as the most neglected dimension, demanding greater attention from decision-makers. In contrast, the 'Environmental education system' has the highest mean, while displaying an intermediate standard deviation. Consequently, respondents believe this dimension is in the best condition. Nevertheless, it is noteworthy that the difference in means between these two dimensions is 0.725 and the overall mean is 2.673. Thus, respondents agree that the UEMS variable is characteried by low performance.

It is also interesting to study the weight of each indicator on the UEMS variable. Table 3 displays the specific statistics for each indicator. Fig. 2 illustrates data through graphical representation.

The indicator 'Environmental Awareness' has the highest mean (3.311) and the lowest standard deviation (3.311), indicating unanimous agreement amongst respondents that it is the indicator in the best condition. On the contrary, the indicators 'Planning instruments', 'Instruments for Promotion and development' and 'Instruments for Costs and Benefit Redistribution' have the lowest, albeit close, means (2.430, 2.317, 2.333, respectively) and their standard deviations (0.5498, 0.5825, 0.6332, respectively) are also amongst the lowest. Such unanimity illustrates that these three indicators are the least performing and, hence, merit greater attention from decision-makers.

In Table 4, descriptive statistics for the data obtained for the variable 'Sustainable Development' are presented concerning each of its respective dimensions. The first row includes the statistics for the consolidated data. Fig. 3 illustrates data through graphical representation.

For Sustainable Development (SD), when consolidating the data, a standard deviation of 0.5274 is obtained, with a minimum value of 1.458, a maximum of 3.750 and a mean of 2.269. Analysing the three dimensions independently, both means and standard deviations are very close, with relatively low values, indicating that the weights of each dimension contribute similarly to the total variable. Additionally, respondents unanimously consider that all three dimensions face issues.

It is also interesting to study the weight of each indicator on the Sustainable Development (SD) variable. Table 4 displays the specific statistics. Fig. 4 illustrates data through graphical representation.

Upon analysing the indicators independently, it is observed that 'Health' exhibits the poorest performance, having the lowest mean (1.726) and a significant accumulation of data below the score of 2. Following this, 'Satisfaction of Basic Needs' shows the lowest-performing data with a mean of 1.850. Subsequently, the indicators 'Economic income', 'Activities and Occupations', 'Production with Environmental Criteria', 'Climate Change' and 'Natural Resources' all display similar patterns, with most of their data falling between scores 2 and 3. This suggests a widespread dissatisfaction amongst respondents. Nevertheless, it is interesting to note that 'Quality of Life' has a relatively higher mean and accumulation of results compared to other indicators, indicating a potential sense of attachment to the location.

To analyse the use of the Pearson coefficient and linear regression, the Kolmogorov-Smirnov normality test was conducted. A p-value of 0.053 was obtained for the variable UEMS (Urban Environmental Management System) and a p-value of 0.066 for the variable SD (Sustainable Development). Thus, the null hypothesis, which posits that both variables follow a normal distribution, is accepted. Therefore, parametric tests are employed to determine the causal relationship between them.

Due to the presence of a single independent variable, Equation 3 takes the form of Equation 5, with β₀ representing the intercept and β₁ as the slope of the line.

(Eq. 5). \(Y= \beta_{o}+\beta_{1}X\)

Subsequently, we aim to establish the relationships between the independent variable (UEM) and the dependent variable (SD). For this, we will begin with a hypothesis test where: Ho (β₁ = 0) states 'UEMS does not have a positive effect on SD in the Lurin District' and H1 (β₁ ≠ 0) states 'UEMS has a positive effect on SD in the Lurin District', with a significance level of 5%.

Quantifying the correlation and coefficient of determination of the model yields the observed data in Table 5. Thus, it is inferred that there is a high positive correlation (R = 0.656) between the variables studied. Additionally, the predictor variable UEMS explains 43% (R² = 0.430) of the behaviour of the SD variable.

Subsequently, it is important to determine if there is a linear dependency between both variables. To achieve this, an ANOVA is conducted to obtain the F-statistic and assess the significance value (p). If p = 0, it is concluded that there is a linear relationship between the dependent and independent variables. Upon performing the ANOVA analysis, as seen in Table 6, it is concluded that, with a significance value of 0.000, there is indeed a linear relationship between the variables and, therefore, it is appropriate to use the proposed linear regression model.

With this information, the simple linear regression model is performed, as detailed in Table 7, where it is inferred that β₀ = 0.187 and β₁ = 0.798. However, in the case of β₀, having a significance value of 0.469, this coefficient is excluded. Thus, the linear model relating the variables can be observed in Equation 6.

(Eq. 6). \(SD=+0.798*UEMS\)

With this equation, we can conclude that the implementation of a UEMS has a positive impact on SD in the Lurin District. In Fig. 5, the scatter plot of UEMS versus SD is shown, along with a comparison to the linear regression model given by Equation 6. The methodology could be extended to all other relationships between variables and indicators and their respective linear regression model equations, described later.

Following the method explained in the previous paragraphs, we proceeded to relate the variables UEMS and SD from the perspective of their respective indicators. Table 8 provides a summary of the linear regression models' equations, along with their respective coefficients of determination and Pearson correlation.

(Eq. 7). \(DSO=0.721+0.536*OJM\)

(Eq. 8). \(DE=0.824+0.539*OJM\)

(Eq. 9). \(DAE=1.114+0.444*OJM\)

(Eq. 10). \(DSO=0.852+0.432*SEA\)

(Eq. 11). \(DE=1.193+0.357*SEA\)

(Eq. 12). \(DAE=1.781+0.187*SEA\)

(Eq. 13). \(DSO=0.575+0.682*IGU\)

(Eq. 14). \(DE=0.802+0.633*IGU\)

(Eq. 15). \(DAE=1.116+0.526*IGU\)

The summary of the linear regression model equations offers enlightening insights into the intersection between the analysed variables, the uniqueness of the Lurin environment and the challenges it faces on its path towards sustainable development. The combination of the Municipal Legal Framework (OJM), Environmental Education System (SEA) and Urban Management Instruments (IGU) reveals an intricate web of influences shaping the social, economic and environmental-ecological dimensions in this specific region.

The high R² value in the social dimension (37.8%) suggests that the OJM plays a pivotal role in improving quality of life and meeting basic needs in Lurin. This outcome not only reflects the importance of a clear and effective legal framework, but also indicates that municipal policies significantly impact social cohesion and the overall well-being of the population. In the economic dimension, the OJM remains a crucial driving force, with an R² of 37.2%. The positive connection underscores the capacity of the legal framework to foster sustainable economic development in Lurin, highlighting the need for clear regulations that promote economic equity and efficiency. Regarding the environmental-ecological dimension, the R² of 24.2% underscores the MLF's contribution to the sustainable management of natural resources in the district. The positive relationship indicates that a robust legal framework can be a catalyst for more responsible environmental practices and biodiversity preservation.

The analysis of the social dimension reveals that the SEA, with an R² of 14.5%, plays a vital role in enhancing the quality of life and social awareness in Lurin. The positive connection suggests that environmental educational programmes can positively influence perception and social cohesion, albeit more moderately than the OJM. In the economic dimension, the SEA shows a more subtle influence, with an R² of 9.7%. While the positive relationship indicates that environmental education can contribute to economic aspects, its direct impact may be overshadowed by other variables in Lurin's economic context. In the environmental-ecological dimension, the SEA, with an R² of 2.5%, appears to have a limited connection with sustainable practices in the region. Although the relationship is positive, the low R² proportion suggests that additional factors may be more significantly influencing this dimension.

In the social dimension, the IGUs exhibit considerable influence, with an R² of 28.6%. This finding highlights the importance of a comprehensive approach to urban management in improving social cohesion and quality of life in Lurin. The economic dimension reflects a substantial impact on the IGUs, with an R² of 24.0%. This underscores the effectiveness of urban management tools in driving sustainable economic development, advocating for urban projects that are not only efficient, but also equitable. In the environmental-ecological dimension, the IGUs show significant influence, with an R² of 15.9%. This highlights that effective urban management is directly linked to more sustainable practices, pointing towards urban planning that considers environmental impact.

A multiple regression was subsequently performed, as observed in Equation 4, following the same methodology previously explained. The results obtained are shown in Table 9. The obtained equations correspond to Equations 16, 17 and 18.

(Eq. 16). \(DSO= 0.098+0.395 \cdot OJM+0.031 \cdot SEA+0.386 \cdot IGU\)

(Eq. 17). \(DE= 0.460+0.451 \cdot OJM-0.065 \cdot SEA+0.340 \cdot IGU\)

(Eq. 18). \(DAE= 1.096+0.420 \cdot OJM-0.207 \cdot SEA+0.319 \cdot IGU\)

All VIF values are close to 1.5, indicating that there are no significant multicollinearity issues amongst the independent variables in these models. This allows us to assume that the coefficient estimates are reliable and not unduly inflated by strong correlations between the predictor variables.

In Fig. 6, we can observe the graphical representation of the experimentally obtained data versus the data predicted by the regression model for the variable DSO (Eq. 16). In Suppl. materials 2, 3, the graphical representation for DAE and DE variables is shown. A y=x reference line has been added for better understanding.

From the observations in Table 9 for the variable DSO, we can conclude that, since the p-value for Environmental Education Systems (SEA) is 0.681, it is not statistically significant. Therefore, its influence on the Social Dimension (DSO) of Sustainable Development is less than that provided by Urban Management Instruments (IGU) and Municipal Legal Framework (OJM). Consequently, it can be concluded that SEA can be removed from the model without detriment.

Upon closer analysis, it is striking, yet not surprising, that the inhabitants of Lurin consider the investment in education to be of lesser influence compared to investments in urban management and legal framework. The latter yield more visible short-term results, whereas educational investments, although necessary, take longer to show their best outcomes. Considering this and despite the statistical evidence, we believe that other indicators should be taken into account in future studies to reinforce the weight of SEA within the model.

Despite those mentioned earlier, as the p-value of the multivariable model is 8.71x10^-23, thus the model can be considered valid. Additionally, the adjusted R² was chosen because it better represents the accuracy of multivariable models. For DSO, 0.442 is considered acceptable since R² values tend to be relatively low in social perception studies.

For the variable DAE, we observe that OJM and IGU behave similarly to the previous case for DSO. However, for SEA, it is within the 5% significance level in this instance, albeit with a negative trend.

When we analyse the model corresponding to DE, a similar case to that found in DSO arises, as the p-value of SEA is 0.409, making it not statistically significant for the model. However, we emphasise that, since this concerns educational topics, the effects introduced by this variable into the model may become apparent in the long term. Therefore, the current perception is severely diminished or undervalued by the respondents.

In general, for all models, we recommend seeking and including more potentially relevant variables that may help explain greater variability in the model.