Method for identifying urban active area based on enhanced Infomap algorithm

Abstract

The invention provides an optimization method based on an Infomap algorithm and a genetic algorithm, aiming at solving the problem of inaccurate functional area division caused by neglect of node attributes in the existing urban activity area identification method. The method comprises the following steps: (1) carrying out gridding processing on mobile phone signaling data, and constructing a space interaction network fusing node attributes; (2) realizing high-modularity community detection considering node attributes based on an enhanced Infomap algorithm; and (3) modeling and quantitatively analyzing the boundary effect of the active area, and proposing optimization suggestions. The space interaction network is constructed based on the mobile phone signaling data, and an enhanced Infomap algorithm considering node attributes is provided to complete community detection, so that quantitative analysis of the importance of each activity area and the boundary effect of the activity area is implemented, and reference is provided for constructing a more efficient and sustainable urban traffic network.

Description

Technical Field

[0001] This invention relates to the fields of urban planning and traffic management, and in particular to a method and system for identifying urban activity zones based on node attributes. Background Technology

[0002] With the acceleration of urbanization, the scientific and rational delineation of urban activity zones has become an important foundation for urban planning and traffic management. Urban activity zones refer to areas where residents' daily activities are frequent and functions are relatively concentrated. The results of their delineation directly affect the allocation of transportation resources, the layout of infrastructure, and the formulation of urban development strategies.

[0003] Traditional methods for delineating activity zones primarily rely on administrative boundaries or spatial clustering or community detection based solely on travel flow data. For example, some studies employ community detection algorithms such as Louvain, Leiden, or Infomap, constructing networks based on travel data (e.g., subway card swipes, shared bicycle trajectories, signaling data) to identify urban functional zones. However, these methods generally neglect the impact of node attributes on travel behavior, such as key socioeconomic indicators like population density and job-housing ratios. This results in delineation results that fail to accurately reflect urban functional differences, impacting the scientific rigor and relevance of subsequent traffic management and policy formulation.

[0004] Furthermore, the lack of quantitative analysis methods for the boundary effects of activity zones in existing technologies has prevented an effective assessment of the hindering effect of boundaries on travel flow, thus limiting the application value of activity zone delineation results in actual urban governance.

[0005] Therefore, there is an urgent need for a method for identifying urban activity zones that integrates multi-source data and takes into account both node attributes and travel flow, in order to improve the accuracy and interpretability of functional zone division, further quantify the impact of boundaries on travel, and provide technical support for urban traffic planning and management. Summary of the Invention

[0006] Purpose of the invention: To address the shortcomings of existing technologies, this invention provides a method, system, and storage medium for identifying urban activity zones by integrating node attributes and traffic flow. By introducing an enhanced Infomap algorithm and a boundary effect model, it achieves high-precision, interpretable, and practical urban activity zone delineation, and provides a scientific basis for urban transportation planning, public resource allocation, and policy formulation.

[0007] Technical solution:

[0008] (1) Process mobile signaling data into a grid to construct a spatial interaction network that integrates node attributes;

[0009] (2) Implement high-modularity community discovery that considers node attributes based on the enhanced Infomap algorithm;

[0010] (3) Model and quantify the boundary effect of the activity area.

[0011] Furthermore, step 1, which involves meshing mobile signaling data and constructing a spatial interaction network, includes the following steps:

[0012] 1.1 Acquisition and Cleaning of Mobile Signaling Data:

[0013] The system obtains mobile signaling data for the target time period from the operator's side. The data fields must include at least the user ID, timestamp, and base station latitude and longitude. Then, it cleans the raw data by performing drift point removal, ping-pong handover merging, and camp point identification, removing abnormal trajectories, duplicate records, and data with missing key fields.

[0014] 1.2, Mesh mapping and node attribute calculation:

[0015] The urban area is divided into regular square grids (250m × 250m recommended). The grid side length can be adjusted between 100-500m depending on the city size. A mapping relationship between grid numbers and geographic coordinates is established, mapping the origin and destination of each trip record to the corresponding grid, forming a trip flow matrix T between grids. ij , which represents the number of trips from grid i to grid j.

[0016] Using grids as statistical units, node attributes are calculated, including travel intensity s. i Job-to-Household Ratio (cx) i Population density y i and spatial coordinates. Travel intensity s i The total number of trips originating from or ending at grid i within a specified time period; the job-housing ratio cx i The difference between net increase / decrease in users during the morning peak (07:00–09:00) and evening peak (18:00–20:00) represents the employment-residence ratio of the corresponding grid area; population density y i It is expressed as the ratio of the number of users staying at night to the grid area; the spatial coordinates are the latitude and longitude values ​​of the grid center point.

[0017] 1.3, Construction of Spatial Interaction Network:

[0018] Construct a directed weighted graph G = (V, E, W). The set of nodes V corresponds to the centroids of each travel grid, forming the vertices of the network and representing the origin or destination of a trip. The set of edges E corresponds to directional trips between grids. The set of weights W aggregates the travel volume along the link and the attribute differences of the corresponding nodes. ij Calculate using the following formula:

[0019]

[0020] In the formula, Tij For the trip volume from grid i to grid j, dist ij Let a, b, and c be the Euclidean distance between the centroids of grid i and grid j, respectively, and let a, b, and c be the corresponding weights, satisfying a + b + c = 1. The values ​​of a, b, and c are obtained by a genetic algorithm to obtain the optimal weight recombination (a * ,b * ,c * ), and thus determine W in the optimal case. ij .

[0021] Furthermore, step 2, which involves discovering highly modular communities based on the enhanced Infomap algorithm, includes the following steps:

[0022] 2.1 Input graph structure:

[0023] The weighted directed graph G = (V, E, W) constructed in step 1 is used as input, with nodes as grids, edges as travel connections, and weights as values ​​after fusing node attributes and travel intensity.

[0024] 2.2, Run the enhanced Infomap algorithm:

[0025] Based on the traditional Infomap algorithm, edge weights that incorporate node attributes are introduced, and W... ij As the input to Infomap's "page jump probability", the modularity value corresponding to each partition is recorded by running the algorithm independently multiple times and traversing different trial number parameters.

[0026] Iterate through trials from 1 to 20, and output the community partitioning set C = {c k}, each community c k This refers to an urban activity area. The modularity value is used to evaluate the community detection algorithm results; a higher modularity value indicates a more stable structure in the corresponding community detection results. Therefore, the set of community partitions C that achieves the maximum modularity Q is selected. * The community is divided into set C. * The optimal urban community set is used as the final urban activity area division result.

[0027] The specific formula for the modularity Q is as follows:

[0028]

[0029] In the formula, W ij It is the edge weight between grids i and j in step one, γ is the resolution parameter, and k is the edge weight between grids i and j in step one. i It is the sum of the weights of the edges connected to grid i, c i It is the group to which grid i is assigned, if c i =c j ,δ(ci ,c j If the value is 1, then the value is 0; otherwise, the value is 0.

[0030] 2.3, Ranking of Activity Areas by Importance:

[0031] The PageRank algorithm is used to quantitatively assess the importance of each activity zone. The PageRank value is obtained by iteratively calculating the travel connectivity between zones. Core activity zones and secondary activity zones are labeled in descending PageRank order for planning priority determination. The formula for calculating the PageRank value is:

[0032]

[0033] In the formula, d is the damping factor, with a value of 0.85; N is the total number of active zones; B i Let L be the set of activity areas in activity area i that have travel flow; j This represents the number of links outside the active area j.

[0034] Furthermore, step 3, which involves modeling and quantifying the boundary effect of the active area, includes the following steps:

[0035] 3.1 Calculation of the number of boundary crossings:

[0036] To quantify the actual effect of boundary effects on travel as the number of crossings increases, the Floyd-Warshall algorithm is used to determine the shortest path between any grid i→j to determine the number of community boundaries traversed, bor. ij Create a dataset {i, j, T}. ij ,bor ij dist ij y i y j , cx i , cx j}

[0037] 3.2, Boundary Effect Model Construction:

[0038] Further, a boundary effect model was constructed. The model applied Poisson pseudo-maximum likelihood estimation (PPML) to avoid the influence of zero values ​​in the travel flow data on the model. A log-linear regression equation was constructed, and the explanatory variables included the population size, job-to-housing ratio, spatial distance, and the number of activity area boundaries crossed in the travel path between the origin and destination regions.

[0039] lnT ij =α0+α1lny i +α2lny j +α3lncx i +α4lncx j+α5lndist ij +βbor ij +ε ij

[0040] In the formula, T ij For the trip volume from grid i to grid j, y i With y j The population densities of grids i and j are respectively, cx i With cx j The job-housing ratios for grids i and j are respectively, and dist ij Let αi be the Euclidean distance between the centroids of grid i and grid j, α1, α2, α3, α4, and α5 be the corresponding estimated parameters, and β be the number of community boundaries crossed. ij The estimated coefficient, ε ij This is the random error term. The boundary's inhibition rate on travel is expressed as (e...). β -1)×100% is used to explain the average percentage decrease in travel traffic caused by crossing a boundary each time.

[0041] 3.3 Analysis of the regression results of the boundary effect model:

[0042] The impact of each variable on travel volume is analyzed based on the regression results of the model.

[0043] Beneficial Effects: This invention employs an enhanced Infomap algorithm for community detection, combining node attributes with travel flow to identify urban activity zones. This method significantly improves the modularity of community segmentation results, enhancing the accuracy of community detection. By utilizing the PageRank algorithm and constructing a boundary effect model, the importance of each activity zone is evaluated, quantifying the inhibitory effect of activity zone boundaries on travel. This improves the reference value of the activity zones identified in this invention for urban planning decisions, enabling more effective support for traffic organization optimization and urban planning decisions. Attached Figure Description

[0044] Figure 1 This is a flowchart of a method for identifying urban activity areas based on an enhanced Infomap algorithm according to the present invention;

[0045] Figure 2 This is a heat map showing the travel intensity of various networks in Haidian District in October 2023.

[0046] Figure 3 This represents the modularity value of each trial during the traversal process;

[0047] Figure 4 The results of the activity area division;

[0048] Figure 5 This represents the PageRank value for each activity area. Detailed Implementation

[0049] The technical solution of the present invention will be further described below with reference to the accompanying drawings. Figure 1 The diagram shows a flowchart of a method for dividing urban activity areas based on an enhanced Infomap algorithm according to the present invention, which mainly includes the following steps:

[0050] Step (1) involves gridding the signaling data to construct a spatial interaction network that integrates node attributes;

[0051] 1.1 Acquisition and Cleaning of Mobile Signaling Data

[0052] We obtained mobile signaling data from the operator's side for one month in October 2023 in Haidian District, Beijing. The data fields included at least user ID, timestamp, and base station latitude and longitude. Then, we cleaned the raw data by removing drift points, ping-pong handover merging, and stationing point identification, removing abnormal trajectories, duplicate records, and data with missing key fields.

[0053] Table 1 Mobile Signalling Data Field Information

[0054] Fields type content stime timestamp Trip start time etime timestamp End time of the trip mode int mode of transportation start_grid_id bigint Grid number of the starting point of the journey end_grid_id bigint Grid number of the end point of the journey start_zone string The county where the journey begins end_zone string The county where the journey ends uid string User ID gender string User gender age string User age weight decimal(28,8) Weight home_lon double User's home address longitude home_lat double User's home address latitude and longitude centroid_lat double Latitude of grid center point centroid_lon double Longitude of grid center point

[0055] 1.2 Mesh Mapping and Node Attribute Calculation

[0056] The Haidian District of Beijing was divided into 6858 square grids with sides of 250m × 250m. A mapping relationship between grid numbers and geographic coordinates was established, mapping the origin and destination of each travel record to the corresponding grid, forming a travel flow matrix T between grids. ij , which represents the number of trips from grid i to grid j.

[0057] Using grids as statistical units, node attributes are calculated, including travel intensity s. i Job-to-Household Ratio (cx) i Population density y i and spatial coordinates. Travel intensity s i The total number of trips originating from or ending at grid i within a specified time period; the job-housing ratio cx i The difference between net increase / decrease in users during the morning peak (07:00–09:00) and evening peak (18:00–20:00) represents the employment-residence ratio of the corresponding grid area; population density y i The ratio of the number of users staying overnight to the grid area is used; the spatial coordinates are the latitude and longitude values ​​of the grid center point. Figure 2 The processed grid travel intensity.

[0058] 1.3, Construction of Spatial Interaction Network

[0059] Based on this, by completing the gridded processing of mobile signaling data and calculating the required node attributes, a spatial interaction network can be constructed. A directed weighted graph G = (V, E, W) is constructed, where the node set V corresponds to the centroids of each travel grid, forming the vertices of the network and representing the start or end point of a trip; the edge set E corresponds to directional trips between grids; and the weight set W aggregates the travel volume along the link and the attribute differences of the corresponding nodes. ij Calculate using the following formula:

[0060]

[0061] In the formula, T ij For the trip volume from grid i to grid j, dist ij Let a, b, and c be the Euclidean distance between the centroids of grid i and grid j, respectively, and let a, b, and c be the corresponding weights, satisfying a + b + c = 1. The values ​​of a, b, and c are obtained by a genetic algorithm. With the objective of maximizing the modularity Q, (a, b, c) is optimized through 50 generations of evolution with a crossover probability of 0.5 and a mutation probability of 0.2 to obtain the optimal weighted recombination (a...). * ,b * ,c * ), and thus determine W in the optimal case. ij .

[0062] Step (2), high-modularity community detection is achieved based on the enhanced Infomap algorithm:

[0063] 2.1 Input Graph Structure

[0064] The weighted directed graph G = (V, E, W) constructed in step (1) is used as input, with nodes as grids, edges as travel connections, and weights as values ​​after fusing node attributes and travel intensity.

[0065] 2.2 Running the enhanced Infomap algorithm

[0066] Based on the traditional Infomap algorithm, edge weights that incorporate node attributes are introduced, and W... ij As the input to Infomap's "page jump probability", the modularity value corresponding to each partition is recorded by running the algorithm independently multiple times and traversing different trial number parameters.

[0067] Iterate through trials from 1 to 20, and output the community partitioning set C = {c k}, each community c k This refers to an urban activity area. The modularity value is used to evaluate the community detection algorithm results; a higher modularity value indicates a more stable structure in the corresponding community detection results. Therefore, the set of community partitions C that achieves the maximum modularity Q is selected. * The community is divided into set C.* The optimal urban community partitioning set is used as the final urban activity area partitioning result, such as... Figure 3 As shown, the fifth experiment yielded the highest modularity value, reaching 0.574. Therefore, the community division set obtained from the fifth experiment was selected as the final urban activity area division result. The activity area division result is as follows: Figure 4 As shown.

[0068] The specific formula for the modularity Q is as follows:

[0069]

[0070] In the formula, W ij It is the edge weight between grids i and j in step one, γ is the resolution parameter, and k is the edge weight between grids i and j in step one. i It is the sum of the weights of the edges connected to grid i, c i It is the group to which grid i is assigned, if c i =c j ,δ(c i ,c j If the value is 1, then the value is 0; otherwise, the value is 0.

[0071] 2.3 Ranking of Activity Areas by Importance

[0072] The PageRank algorithm is used to quantitatively assess the importance of each activity zone. The PageRank value is obtained by iteratively calculating the travel connectivity between zones. Core activity zones and secondary activity zones are labeled in descending PageRank order for planning priority determination. The formula for calculating the PageRank value is:

[0073]

[0074] In the formula, d is the damping factor, with a value of 0.85; N is the total number of active zones; B i Let L be the set of activity areas in activity area i that have travel flow; j This represents the number of links outside the active region j. The PageRank results are as follows: Figure 5 As shown, communities 2, 4, and 8 have the highest PageRank values, which aligns with the planning of the core area of ​​Zhongguancun Science City and the development trend of the Zhongguancun Avenue high-end innovation cluster corridor in the actual map.

[0075] Step (3), realizing boundary effect quantification and result output, includes the following steps:

[0076] 3.1 Calculation of Boundary Crossing Count

[0077] The future quantification of the boundary effect on travel will increase with the number of crossings, and the shortest path between any grid i→j will be determined based on the Floyd-Warshall algorithm to determine the number of community boundaries traversed. ij Create a dataset {i, j, T}. ij ,bor ij dist ij y i y j , cx i , cx j}

[0078] 3.2, Construction of Boundary Effect Model

[0079] Further, a boundary effect model was constructed. The model applied Poisson pseudo-maximum likelihood estimation (PPML) to avoid the influence of zero values ​​in the travel flow data on the model. A log-linear regression equation was constructed, and the explanatory variables included the population size, job-to-housing ratio, spatial distance, and the number of activity area boundaries crossed in the travel path between the origin and destination regions.

[0080] lnT ij =α0+α1lny i +α2lny j +α3lncx i +α4lncx j +α5lndist ij +βbor ij +εij

[0081] In the formula, T ij For the trip volume from grid i to grid j, y i With y j The population densities of grids i and j are respectively, cx i With cx j The job-housing ratios for grids i and j are respectively, and dist ij Let αi be the Euclidean distance between the centroids of grid i and grid j, α1, α2, α3, α4, and α5 be the corresponding estimated parameters, and β be the number of community boundaries crossed. ij The estimated coefficient, ε ij This is the random error term. The boundary's inhibition rate on travel is expressed as (e...). β The calculation is 1) × 100%, which is used to explain the average percentage decrease in travel flow caused by crossing each boundary. The model regression results are shown in Table 2.

[0082] Table 2. Model Regression Results

[0083]

[0084] The values ​​in parentheses represent robust standard errors. ** Statistical at the 5% level. *** Statistical at the 1% level.

[0085] 3.3 Analysis of the regression results of the boundary effect model:

[0086] Based on the regression results in Table 2, for Model II, a 10% increase in the population size of the origin (destination) results in a 2.737% (2.739%) increase in calculated travel flow. A 10% increase in the absolute value of the employment-to-housing ratio in the origin (destination) region results in a 3.282% (3.291%) increase in calculated travel flow. A 10% increase in travel distance results in a 12.39% decrease in travel flow. Crossing the boundary of an activity area results in a decrease of approximately 14.52% in travel flow, demonstrating the inhibitory effect of activity area boundaries on cross-regional travel.

[0087] Policymakers can prioritize optimizing public transportation and deploying shared mobility resources within the region based on model results. For example, developing targeted services can significantly improve mobility in high-importance areas such as Activity Zones 2, 8, and 4. This includes initiatives such as establishing shuttle bus routes, optimizing the allocation of shared bicycles, and reducing bus intervals. Furthermore, since each crossing of an Activity Zone boundary reduces travel by 14.52%, this highlights the barrier effect of these boundaries. Policymakers can strategically focus on mitigating these barriers to facilitate necessary cross-regional travel. For example, improving infrastructure in detected border areas (such as the Beijing-Urumqi (G7) expressway, located between Activity Zones 11 and 12) can effectively reduce barriers. Integrating these insights can lead to the construction of more efficient and sustainable urban transportation networks.

Claims

1. A method for identifying urban activity areas based on an enhanced Infomap algorithm, characterized in that, Includes the following steps: (1) Process mobile signaling data into a grid to construct a spatial interaction network that integrates node attributes; (2) Implement high-modularity community discovery that considers node attributes based on the enhanced Infomap algorithm; (3) Model and quantify the boundary effect of the activity area.

2. The method for identifying urban activity areas based on the enhanced Infomap algorithm according to claim 1, characterized in that, Step 1, which involves gridding mobile signaling data and constructing a spatial interaction network, includes the following steps: 1.1 Acquisition and Cleaning of Mobile Signaling Data: The mobile signaling data within the target time period is obtained from the operator. The data fields must include at least the user ID, timestamp, and base station latitude and longitude. Then, the original data is cleaned by removing drift points, ping-pong handover merging, and stationing point identification, and abnormal trajectories, duplicate records, and data with missing key fields are removed. 1.2, Mesh mapping and node attribute calculation: The urban area is divided into regular square grids, with grid side lengths adjusted between 100-500m based on the city size. A mapping relationship is established between grid numbers and geographic coordinates, mapping the origin and destination of each trip record to the corresponding grid, forming a trip flow matrix T between grids. ij , used to represent the number of trips from grid i to grid j; Using grids as statistical units, node attributes are calculated, including travel intensity s. i Job-to-Household Ratio (cx) i Population density y i and spatial coordinates; travel intensity s i The total number of trips originating from or ending at grid i within a specified time period; the job-housing ratio cx i The difference between net increase / decrease in users during morning and evening peak hours represents the employment-residence ratio of the area corresponding to the grid; population density y i The ratio of the number of users staying at night to the grid area is used; the spatial coordinates are the latitude and longitude values ​​of the grid center point. 1.3, Construction of Spatial Interaction Network: Construct a directed weighted graph G = (V, E, W), where the set of nodes V corresponds to the centroids of each travel grid, forming the vertices of the network and representing the start or end point of a trip; the set of edges E corresponds to directional trips between grids. The weight set W aggregates the travel traffic volume along the link and the attribute differences of the corresponding nodes. ij Calculate using the following formula: In the formula, T ij For the trip volume from grid i to grid j, dist ij Let a, b, and c be the Euclidean distance between the centroids of grid i and grid j, respectively, and let a, b, and c be the corresponding weights, satisfying a + b + c = 1. The values ​​of a, b, and c are obtained by a genetic algorithm to obtain the optimal weight recombination (a * ,b * ,c * ), and thus determine W in the optimal case. ij .

3. The method for identifying urban activity areas based on the enhanced Infomap algorithm according to claim 2, characterized in that, Step 2, which involves high-modularity community detection based on the enhanced Infomap algorithm, includes the following steps: 2.1 Input graph structure: The weighted directed graph G = (V, E, W) constructed in step 1 is used as input, with nodes as grids, edges as travel connections, and weights as values ​​after fusing node attributes and travel intensity; 2.2, Run the enhanced Infomap algorithm: Based on the traditional Infomap algorithm, edge weights that incorporate node attributes are introduced, and W... ij As the input to Infomap's "page jump probability", the modularity value corresponding to each partition is recorded by running the algorithm independently multiple times and iterating through different trial number parameters. Iterate through trials from 1 to 20, and output the community partitioning set C = {c k }, each community c k This refers to an urban activity area; the modularity value is used to evaluate the results of the community detection algorithm. The larger the modularity value, the more stable the structure of the corresponding community detection results. Therefore, the set of community partitions C that reaches the maximum modularity Q is selected. * The community is divided into set C. * The optimal urban community set is used as the final urban activity area division result; The specific formula for the modularity Q is as follows: In the formula, W ij It is the edge weight between grids i and j in step one, γ is the resolution parameter, and k is the edge weight between grids i and j in step one. i It is the sum of the weights of the edges connected to grid i, c i It is the group to which grid i is assigned, if c i =c j ,δ(c i ,c j If the value is 1, then the value is 0; 2.3, Ranking of Activity Areas by Importance: The PageRank algorithm is used to quantitatively assess the importance of each activity zone. The PageRank value is obtained by iteratively calculating the travel connectivity between zones. Core activity zones and secondary activity zones are labeled in descending PageRank order for planning priority determination. The formula for calculating the PageRank value is: In the formula, d is the damping factor, with a value of 0.85; N is the total number of active zones; B i Let L be the set of activity areas in activity area i that have travel flow; j This represents the number of links outside the active area j.

4. The method for identifying urban activity areas based on the enhanced Infomap algorithm according to claim 1, characterized in that, Step 3, which involves modeling and quantifying the boundary effect of the active region, includes the following steps: 3.1 Calculation of the number of boundary crossings: To quantify the actual effect of boundary effects on travel as the number of crossings increases, the Floyd-Warshall algorithm is used to determine the shortest path between any grid i→j to determine the number of community boundaries traversed, bor. ij ; Create a dataset {i, j, T} ij ,bor ij dist ij y i y j , cx i , cx j }; 3.2, Boundary Effect Model Construction: Further, a boundary effect model was constructed. The model applied Poisson pseudo-maximum likelihood estimation to avoid the influence of zero values ​​in the travel flow data on the model. A log-linear regression equation was constructed, with explanatory variables including population size, job-to-housing ratio, spatial distance, and the number of activity area boundaries crossed in the travel path between the origin and destination regions. lnT ij =α0+α1lny i +α2lny j +α3lncx i +α4lncx j +α5lndist ij +βbor ij +e ij In the formula, T ij For the trip volume from grid i to grid j, y i With y j The population densities of grids i and j are respectively, cx i With cx j The job-housing ratios for grids i and j are respectively, and dist ij Let αi be the Euclidean distance between the centroids of grid i and grid j, α1, α2, α3, α4, and α5 be the corresponding estimated parameters, and β be the number of community boundaries crossed. ij The estimated coefficient, ε ij For the random error term; the boundary inhibition rate of travel is expressed as (e β -1)×100% is used to explain the average percentage decrease in travel flow caused by each boundary crossing; 3.3 Analysis of the regression results of the boundary effect model: The impact of each variable on travel volume is analyzed based on the regression results of the model.

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