Research on influencing factors of financial performance of listed companies based on multiple linear regression and fuzzy logic system

Abstract

The ultimate goal of listed companies is to maximize shareholders’ wealth. With the increasingly fierce market competition, enterprise managers are constantly exploring the key indicators that have an important impact on the financial performance (FP) of enterprises, and achieve the expected FP of shareholders by improving these key indicators. On the basis of the existing enterprise performance measurement system and index research, through expert scoring to determine the secondary indicators, this paper selects 87 small and medium-sized board listed companies which officially announced the implementation of equity incentive from 2009 to 2012 as the sample, takes the financial information disclosed in 2013 as the empirical data, and analyzes the traditional multiple linear regression analysis (MLR) When dealing with big data, especially the data with hierarchical structure, this paper proposes a partial regression coefficient calculation model based on hierarchical data, constructs a multiple nonlinear regression model, and concludes through empirical analysis that there is a nonlinear correlation between equity incentive ratio and corporate performance, and that there is an interval effect between equity incentive ratio and corporate performance. We also present Fuzzy based financial performance prediction of listed companies. Finally, we demonstrate Comparative analysis for financial prediction in term of accuracy between multiple regression model and fuzzy logic system and result deduce that fuzzy logic gives better accuracy than regression model.

Keywords

Multiple linear regression data mining hierarchical data superior company finance;performance influencing factors

1 Introduction

In recent years, with the increasing negative impact of industry competition, raw material prices and inflation and other factors, the profit space of traditional large-scale manufacturing mode is further squeezed [1]. Enterprise managers are faced with how to improve the competitiveness of parts enterprises and better realize the shareholders’ expectation of financial performance (FP). Because the upstream and downstream parts enterprises are affected by uncontrollable factors of raw materials and vehicle factories respectively, if we want to improve the FP of enterprises, we should find a breakthrough from the internal level [2]. Based on the analysis of the existing enterprise performance evaluation index, this paper divides the enterprise performance evaluation index into financial index and non-financial index, finds the important key factors affecting the FP by factor analysis and multiple linear regression, and guides enterprise managers to take effective measures to realize shareholders’ expectation of FP.

In order to achieve the accuracy and objectivity of the research results, the establishment of enterprise performance evaluation index is the premise and foundation. As an important part of enterprise management, enterprise performance evaluation has attracted more and more attention. The production and operation functions of enterprises should be effectively managed by the best evaluation method [3]. At the same time, the management of enterprise performance evaluation should be based on strategy, and ultimately achieve the enterprise level strategic objectives through the achievement of performance evaluation indicators [3]. Both scholars and enterprise practitioners have realized that only by objectively measuring the performance of enterprises can we find effective methods to improve enterprise performance [4]. Therefore, enterprise performance evaluation is considered to be the premise of gaining competitive advantage and continuous improvement. In the 20th century, DuPont company initiated “DuPont financial analysis system", which can clearly reflect the reasons for changes in financial indicators. This system is a great progress for enterprise performance evaluation [5].

In the 1970s, Melnes pointed out that the most commonly used indicator for enterprises is “return on investment". Persen et al. [6] found through the investigation that the performance evaluation indicators of enterprises in this period are net profit rate of sales, earnings per share, cash flow and internal rate of return. Stewart consulting company [7] proposed an enterprise performance evaluation system based on economic value added (EVA) model. It is the balance of the adjusted net operating profit minus the opportunity cost of the economic value of the enterprise’s existing assets, reflecting the cost factor of the investor’s capital investment. With the increasingly fierce market competition, more and more scholars have realized that only focusing on economic indicators will lead to short-term behavior and unable to consider the long-term development of enterprises. Christopher et al. [8] through empirical research, found that under the same conditions, enterprises adopting the performance evaluation balance mode including financial indicators and non-financial indicators have higher satisfaction with performance evaluation and stock market performance than similar enterprises. Kaplan et al. [9] introduced the Balanced Scorecard into the field of performance appraisal, and gradually formed today’s balanced scorecard model. The balanced scorecard is divided into four dimensions: finance, customer, internal process and learning and innovation. It introduces the long-term and short-term factors, financial and non-financial factors, external and internal factors into the enterprise performance evaluation system.

Then, the concept of strategic map is put forward, which extends the Balanced Scorecard naturally and reveals the causality among the objectives of the balanced scorecard system. After the self balanced scorecard performance evaluation system was put forward, some organizations and scholars designed a variety of Balanced Scorecard models according to their own understanding and needs. Kanji et al. [10] proposed that the logical relationship between the four dimensions established by the Balanced Scorecard evaluation model was not clear, and KBS performance evaluation system was proposed after improving it on the original basis; Neely [11] proposed a performance multi prism evaluation system by analyzing the shortcomings of the balanced scorecard, which was based on the satisfaction and contribution of stakeholders To consider the organization’s goals and strategies as well as business process improvement requirements. In addition, sink and is based on the supplier input processing output customer result model Tuttle (SAT) system starts from seven evaluation indexes, namely efficiency (input), effectiveness (achievement), productivity (output / input), profitability, quality (processing), innovation and working environment, to evaluate enterprise performance. Scholars also put forward smart performance evaluation system, performance evaluation matrix and dynamic comprehensive performance evaluation system.

The above-mentioned evaluation indexes and systems have made corresponding contributions to the evaluation of enterprise performance from various aspects, but there are still some deficiencies, including the determination of indicators and the combination of industry and opportunity: the idea of balanced scorecard is scientific and comprehensive [12]. But it only gives the general framework and thinking direction of performance evaluation, but does not give how to select effective indicators how to integrate these indicators; sat system simplifies the complex relationship between various departments of the supply chain, and does not consider the evaluation indicators comprehensively, so it is not detailed enough; the key performance indicator method fails to provide a complete index framework system which has guiding significance for operation, and there is no inevitable internal logical connection among the indicators [13]; SCOR model is compared It is complex and difficult to understand, and it is difficult to operate. This method requires enterprises with relatively strong strength, rich resources and relatively rich experience to drive all other members of the supply chain together. It is too cumbersome for the enterprises studied in this paper, and the capital requirements are too high. Therefore, considering the advantages and disadvantages of each evaluation method, as well as the research object of this paper –listed companies, this paper has no choice to sort out and list the existing enterprise performance evaluation indicators, and select the indicators suitable for the situation of enterprises by experts to achieve objectivity and reference. In this paper we also present Fuzzy based financial performance prediction of listed companies.

2 Establishment of data mining method for multivariate linear regression

2.1 Multi level data model of FP of listed companies

In the big data analysis and processing of listed companies, in order to facilitate data storage, reading, calculation and other operations, most of the data are stored according to a certain topology structure, such as chain structure, mesh structure, ring structure, etc., among which the more commonly used data management structure is hierarchical structure. The data formed by the hierarchical structure is the hierarchical data [14]. The specific relationship of the hierarchical data is shown in Fig. 1.

Fig. 1

Multi level data topology of FP of listed companies.

In hierarchical data, all data points form a hierarchical vertical tree network, and each upper data set has all data members of lower branches. In the actual operation process, for a hierarchical data set that contains a common layer P, all the data sets in the p-layer will be transmitted to the corresponding upper data node of the node, and then the data sets of the P-1 layer will be summarized and transmitted to the corresponding data node of the P-2 layer. Each time the data set is summarized to the upper layer, the summary layer will be empty, and so on until the transmission summary Total to Tier 1 data nodes. Through the hierarchical and structured vertical tree network, the data is transferred and summarized layer by layer [15]. In the actual calculation and analysis, the data can be processed in the current data layer or summarized in the upper layer. This not only can keep the statistical law unchanged, but also realize parallel processing, which increases the flexibility and availability of data. Based on this feature, hierarchical data has a wide range of applicability in banking, finance, health care and other industries. At the same time, in the fields of banking, finance, health care and other industries, the data set often contains the user’s privacy information, so encryption database is often used for storage and transmission.

In the encrypted database, each database only keeps a few external interfaces or encrypts the data. Both encryption methods cause some difficulties in the construction of regression analysis model based on all data. In order to carry out regression analysis on hierarchical data set based on privacy data, this paper proposes a regression data calculation method based on a small number of interface data based on traditional regression analysis:

Step 1 Begin;

Step 2 Initializes P and P to make p=P;

Step 3 Partial regression coefficient BP and the hierarchical matrix QP are calculated from the interface data of the layer P, so that P=P-1;

Step 4 Partial regression coefficient BP and hierarchical matrix QP are used to solve the overall partial regression coefficient B;

Step 5 Judges the value of P, if P>1, turn to step 2, if P=1, turn to step 6;

Step 6 End.

In this algorithm, the parameter p is the counter to calculate the current number of layers, and the parameter p is the total number of layers of hierarchical data. Step 2 of the algorithm is responsible for calculating the partial regression coefficient of the lower layer containing a small amount of interface data, and constructing the MLR model of the small part of the lower structure data under the premise of fully protecting the data privacy. Step 3 is responsible for calculating the partial regression coefficient of the upper layer by using the partial regression coefficient of the lower layer and the hierarchical structure matrix during data transmission. In the calculation process of steps 2 and 3, only a small amount of interface data is needed for the calculation of all partial regression coefficients and hierarchical matrix. Therefore, this algorithm can fully guarantee the privacy of the data while constructing the MLR model of hierarchical data. The specific calculation methods of steps 3 and 4 are as follows.

2.2 Regression modeling of multi-level structure data of FP of listed companies

Considering a set of known hierarchical data, MLR analysis is used to model and calculate the data within the structure. According to the characteristics of hierarchical structure, this paper considers to analyze any upper and lower data subsets. There is a part in the upper layer of the data subset, and the lower layer is composed of K parts. The data between the upper and lower layers meet the hierarchical structure, and the data between the lower levels are independent of each other. On the basis of this data set, this paper considers the construction of the relationship model between the partial regression coefficient of the upper level and the partial regression coefficient of the lower level.

2.2.1 Calculation of partial regression coefficient

The following will specifically describe the solution method of partial regression coefficient of lower level. In order to protect privacy, this method only needs a small amount of interface data to solve the partial regression coefficients of each part of the lower layer, where the interface data includes the sum of the original data, the average value and the product sum of cross terms. In the traditional MLR analysis, using the least square method [16] to solve the partial regression coefficient only needs to calculate: ${\begin{matrix} L_{11} b_{1} + L_{12} b_{2} + . . . + L_{1 N} b_{N} + = L_{10} \\ L_{21} b_{1} + L_{22} b_{2} + . . . + L_{2 N} b_{N} + = L_{20} \\ . . . \\ L_{N 1} b_{1} + L_{N 2} b_{2} + . . . + L_{NN} b_{N} + = L_{N 0} \end{matrix}$ (1) where N is the dimension of the independent variable X in the regression model.

In Equation (1), the coefficient matrix L and L⁰ = (L₁₀, L₂₀, . . . , L_N0) ^T is usually as follows: ${\begin{matrix} L_{ij} = \sum_{n} (x_{ni} - {\bar{x}}_{i}) (x_{nj} - {\bar{x}}_{j}) \\ L_{i 0} = \sum_{n} (x_{ni} - {\bar{x}}_{i}) (y_{n} - \bar{y}) \end{matrix} i, j = 1, 2, . . ., N$ (2) where N is the dimension of the independent variable X in the regression model; n is the sample number of the independent variable in each dimension. In the algorithm of Equation (2), the original values of all independent variables X and dependent variable Y can be calculated and solved. However, in some special cases, the original data is strictly confidential. Therefore, this paper considers construct the coefficient matrix L and constant vector L⁰ of partial regression coefficient equations through the original data sum, average value and cross term product, which are not related to privacy information and can be used for transmission. In this paper, we consider expanding the L_ij in Equation (2) to design a new method for constructing the coefficients of the system of equations. The expanded results are as follows: $L_{ij} = T (x_{i}, x_{j}) - {\bar{x}}_{i} T (x_{j}) = T (x_{i}, x_{j}) - {\bar{x}}_{j} T (x_{i})$ (3)

Secondly, this paper considers the expansion calculation of L_j0: $L_{j 0} = T (x_{i}, y) - \bar{yT} (x_{i})$ (4) where the average value of the i dimension independent variable data is ${\bar{x}}_{i}$ ; the sum of the idimension independent variable data is T (x_i); the sum of the cross products with the j dimension independent variable data is T (x_i, x_j); the average value of the dependent variable data is $\bar{y}$ ; the cross product sum of the dependent variable and the i dimensional independent variable data is T (x_i, y). In this way, the two-part coefficients of partial regression coefficient of lower level and partial regression coefficient of non constant term can be obtained [17]: $b_{i} = {AL}^{0}, i = 1, 2, . . ., N$ (5)

And constant partial regression coefficient: $b_{0} = \bar{y} - \sum_{i = 1}^{N} b_{i} {\bar{x}}_{i}$ (6) where N is the dimension of independent variable; matrix A in Equation (5) is the coefficient inverse matrix constructed by the sum of original data, average value and cross term product, and the specific expression is A = L^-1. The specific expression of L⁰ is L⁰ = (L₁₀, L₂₀, . . . , L_N0) ^T. In Equation (6), where $\bar{y}$ is the average value of dependent variable and ${\bar{x}}_{i}$ is the average value of independent variable in dimension i.

Through the above derivation, the purpose of this paper is to carry out further merging calculation for the solution method of the original regression analysis, and construct the coefficient L in Equation (1) through the sum, average value and cross term product of the original data, so as to solve the partial regression coefficient B = [b₁, b₂, . . . , b_N]. At the same time, the coefficient inverse matrix A is introduced to replace the original L in the process of solving the equations, and the partial regression coefficient solving method is further simplified.

2.2.2 Calculation of overall partial regression coefficient

In this section, we will construct the relationship model between the partial regression coefficient of the upper part and the partial regression coefficient of the lower part [18]. Matrix solving method considering least squares in MLR analysis: $B = {(X^{T} X)}^{- 1} X^{T} Y$ (7)

In the hierarchical data corresponding to the model in this paper, X and Y in Equation (7) contain K data parts, and the data in part k are X^(k) and Y^(k), k = 1, 2, . . . , K. According to the linear additivity of the model, X^TX and X^TY in Equation (7) can be expressed as: ${\begin{matrix} X^{T} X = \sum_{k = 1}^{K} X^{(k) T} X^{(k)} \\ X^{T} Y = \sum_{k = 1}^{K} X^{(k) T} Y^{(k)} \end{matrix}$ (8)

According to the matrix representation of the least square method, X^TY in Equation (8) can be expressed as: $X^{T} Y = (X^{(k) T} X^{(k)}) B_{k}$ (9)

By substituting Equations (8, 9) into Equation (7), the relationship between partial regression coefficient B_k and overall partial regression coefficient B of part k structural data is: $B = {(\sum_{k = 1}^{K} X^{(k) T} X^{(k)})}^{- 1} ((X^{(k) T} X^{(k)}) B_{k})$ (10) where X^(k)TX^(k) is expressed as the hierarchical matrix Q_k, which can be obtained after expansion calculation: $Q_{k} = [\begin{matrix} N & T (X_{1}^{(k)}) & T (X_{2}^{(k)}) & . . . & T (X_{N}^{(k)}) \\ T (X_{1}^{(k)}) & T (X_{1}^{(k)}, X_{1}^{(k)}) & T (X_{1}^{(k)}, X_{2}^{(k)}) & . . . & T (X_{1}^{(k)}, X_{N}^{(k)}) \\ T (X_{2}^{(k)}) & T (X_{1}^{(k)}, X_{2}^{(k)}) & T (X_{2}^{(k)}, X_{2}^{(k)}) & . . . & T (X_{2}^{(k)}, X_{N}^{(k)}) \\ . . . & . . . & . . . & . . . & . . . \\ T (X_{N}^{(k)}) & T (X_{1}^{(k)}, X_{N}^{(k)}) & T (X_{2}^{(k)}, X_{N}^{(k)}) & . . . & T (X_{N}^{(k)}, X_{N}^{(k)}) \end{matrix}]$ (11) where X^(k) is the expansion matrix of the data matrix of the k part, that is, the data in the first column is all 1, and the second column to the last column is the original data; the sum of the i component of the k part data is $T (X_{i}^{(k)})$ , and the sum of squares is $T (X_{i}^{(k)}, X_{i}^{(k)})$ ; the sum of squares with the j component is $T (X_{i}^{(k)}, X_{j}^{(k)})$ . Through the calculation method of Equation (11), Q_k can be obtained by inputting data directly, and the overall partial regression coefficient can be obtained by combining calculation of B_k: $B = {(\sum_{k = 1}^{M} Q_{k})}^{- 1} (\sum_{k = 1}^{M} Q_{k} B_{k})$ (12) where B_k is the partial regression coefficient of the K part of the lower level data; B is the overall partial regression coefficient of all the upper level data.

Based on Equation (12), partial regression coefficient and matrix between hierarchies can be used to calculate the partial regression coefficient between any p level and p - 1 level that satisfies the hierarchical data relationship. When the hierarchical data is transmitted in the way of Fig. 1 from the bottom to the top, the partial regression coefficient model between the upper and lower layers can be constructed for the data satisfying the relationship between any two layers, thus the partial regression coefficient relationship model of the whole hierarchical data can be constructed. This new data processing mode is of great significance for big data processing with hierarchical structure [19]. On the premise of not affecting the rule extraction, on the one hand, the data block processing can effectively protect the privacy of the data; on the other hand, the data can be partitioned processing, which can realize the parallel operation of the computer and improve the ability of big data processing. In addition, through theoretical derivation, it can be seen that the model calculation in this paper is accurate. But in the actual calculation, the calculation tool will lead to truncation error, which does not affect the model results.

2.3 Establishment of secondary evaluation index

According to the principles of scientificity, operability, applicability, relevance and independence, this paper chooses the methods of expert questionnaire survey and interview to determine the secondary indicators of Finance and other than finance [20]. First of all, the classic and latest enterprise performance evaluation literature at home and abroad after 1999 is browsed, and the indicators related to enterprise performance evaluation in these studies are listed out without choice and made into a questionnaire, which is distributed to the enterprise managers and enterprise performance research experts Score the importance of. In the selection of expert samples, we mainly select management researchers and management managers who are engaged in enterprise performance evaluation, which basically cover all aspects of supply chain theoretical research and practical management. A total of 35 questionnaires were distributed and 32 were recovered.

According to the questionnaire survey, the most frequently selected indicators are selected. These indicators not only take into account the actual development of the industry, but also are supported by the literature. They are the evaluation indicators that can effectively evaluate the performance of enterprises. According to the results of index selection, the experts were interviewed to try to understand the basis and reason of index selection.

The selection of financial indicators must be in line with the demands of shareholders. This paper focuses on exploring the main factors that affect the FP of listed companies. Through the improvement of these factors, the FP can be greatly improved, so as to realize the shareholders’ expectation of FP. Therefore, the FP of shareholders should be described as far as possible.

The selection of operational performance indicators should be targeted. The selection of operational indicators which have little impact on FP should be representative and can reflect the main characteristics of listed enterprises.

Evaluation indicators must be easy to understand, operable and measurable. Compared with the previous year, the indicators such as the advantages of software and hardware, information distortion, information integration, advanced strategic concept, management compatibility, enterprise culture compatibility, customer satisfaction and so on were too abstract to be used to measure quantifiable formulas. Therefore, such indexes were not considered in the evaluation system. According to the actual selection results of experts, 14 indexes with frequency above 25 were selected, and the sorting results are shown in Table 1.

Table 1
Index selection results of hybrid supply chain performance evaluation system

Indexes Percentage

Inventory turnover 32

Manufacturing cycle 30

Defect rate of parts supply 32

Procurement cycle 31

Scrap loss rate 32

Market occupancy 32

Customer complaint rate 29

Increase rate of new customers 28

Personnel expense ratio 32

Sales revenue per capita 30

Indexes	Percentage
Inventory turnover	32
Manufacturing cycle	30
Defect rate of parts supply	32
Procurement cycle	31
Scrap loss rate	32
Market occupancy	32
Customer complaint rate	29
Increase rate of new customers	28
Personnel expense ratio	32
Sales revenue per capita	30

3 Fuzzy logic based financial performance prediction of listed companies

In this section, we use fuzzy system to evaluate and predict the financial performance of listed companies. Fuzzy logic system consists of three step: Fuzzification, Fuzzy rule Base Interference engine and Defuzzfication. The overview of work is shown in Fig. 2. In this method we consider five influencing factor in including Equity Incentive Proportion(EIP), Company Size (CS), Financial Leverage(FL), Growth Company(GC), Ownership concentration(OC), Equity Balance(EB) as input attribute to fuzzy system.

Fig. 2

Financial Perfromance Prediction of Listed Companies Using Fuzzy logic System.

3.1 Fuzzification

Fuzzification is the process of converting crisp data input into fuzzy linguistic variable in the form of membership function [8]. Let A be a universal nonempty set, which consider universal discourse A ={ p₁, p₂, … p_n }. A fuzzy set F is defined under universal discourse of nonempty set A ={ p₁, p₂, … p_n } with an ordered pair set represented as: { (p₁, μ_F (p₁)) , (p₂, μ_F (p₂))… (p_n, μ_F (p_n)) } and is characterized by degree of membership function μ_F (A) that maps every element a in A to real number in the interval 0,1. In order to predict the financial perfromnces of listed companies, in this paper we consider five influencing factor in including Equity Incentive Proportion(EIP), Company Size (CS), Financial Leverage(FL), Growth Company(GC), Ownership concentration(OC), Equity Balance(EB) as input attribute to fuzzy system. TO compute fuzzy value of each input attribute in term of membership function using following equation: $μ_{IN} (f, l, m, r) = {\begin{matrix} 0, if f ⩽ l; \\ \frac{f - l}{r - l}, if l < f < r; \\ \frac{m - f}{m - r}, if r < f < m; \\ 0, if f ⩾ m \end{matrix}$ (13)

Where, x represent membership degree and l, m, r represent leftmost, middle and rightmost membership value in triangular fuzzy number,. Each input value of all input variables is converted into fuzzy input sets, define as: μ_IN (f, l, m, r) = {High (H) , Medium (M) , Low (L) , } μ_IN (f, l, m, r) = {High (H) , Medium (M) , Low (L) , }. All input variable is represent based on Gaussian-model membership functions.

3.2 Fuzzy rule base interference engine

This module performs min-max operation over the inputs received. We perform Min-max operation two time during the procedure, first we use service industry parameters and perform min-max operation with Mamdani rule validation [13]. Within fuzzy interference engine we use min-max operation using following equation: $ρ_{j} = \min_{k = 1}^{m} [\max_{X_{k}} (μ_{k}^{'} (x_{k}) \land μ_{jk} (x_{k}))]$ (14)

Where, $μ_{k}^{'} (x_{k})$ represent new autonomous values of input variable. Here, we use Mamdani rule implication that generate individual fuzzy output in the form of membership function [16]. The general format of rule implication is as follows: $\begin{matrix} IF x_{1} is μ_{11} and \dots \dots x_{m} is μ_{1 m} THEN y is {IO}_{1}; \\ IF x_{1} is μ_{m 1} and \dots \dots x_{m} is μ_{nm} THEN y is {IO}_{m}; \end{matrix}$

Where x_k = 1 … m represent input and output sets.

3.3 Defuzzification

The output received is in fuzzy form which is converted into real crisp values using following equation of center of gravity (COG) of defuzzification method: $OUTPUT = \frac{\sum_{x \in X} x . ρ_{j} (x)}{\sum_{x \in X} ρ_{j} (x)}$ (15)

The Fuzzy logic system then finally produce the crisp output [17].

4 Establishment of financial index weight and non-financial index public factor

4.1 Data acquisition

According to the secondary indicators established above, this paper collects the real annual data of 24 representative enterprises in the industry, and carries out factor analysis on all the indicators except FP, so as to summarize the public factors and factor scores except FP, and lay the foundation for the following use of multivariate statistical method to investigate the impact of public factors on FP.

4.2 Data processing

4.2.1 Financial index processing

Invite experts to score the importance of financial related indicators, from 1 to 10 points, and the importance increases with the score. The variance of each index is calculated according to the score of each expert to ensure that the difference between the scores is small enough to process the data by taking the average value. According to the scores of 32 experts, the average value of each index is calculated, and the indexes are sorted according to the importance (the size of the score) and the weight is calculated [21]:

The weight of the n_th nth place $\frac{1}{n} \sum (\frac{1}{1} + \frac{1}{2} + . . . + \frac{1}{N})$ .

where N is the total number of indicator. The results are shown in Table 2.

Table 2
Dimensions of FP indicators

Dimensions Indexes Average scores Weights

Financial affairs Business income 8.428 0.36

Number of working capital turnover 8.103 0.22

Retained profits 7.846 0.18

Net assets income rate 7.619 0.13

Dimensions	Indexes	Average scores	Weights
Financial affairs	Business income	8.428	0.36
	Number of working capital turnover	8.103	0.22
	Retained profits	7.846	0.18
	Net assets income rate	7.619	0.13

Average score weight financial operating income 8.433(0.48) working capital turnover times 8.008(0.24) net profit 7.850(0.16) return on net assets 7.667(0.12).

4.2.2 Treatment of non financial indicators

Kmo test and Bartlett test can be used to measure whether the sample data is suitable for factor analysis. The KMO value of this study is 0.773 (greater than 0.5). The chi square statistical value is 1888.8. The original hypothesis is rejected. The correlation matrix is not the identity matrix, so factor analysis can be carried out. The above KMO test and Bartlett test prove that this study is suitable for factor analysis.

The factor analysis in SPSS17.0 is used to process the data (the original data is omitted), and the factor load matrix is rotated. The rotated factor load matrix is shown in Table 3. After extracting the three common factors, the sum of their eigen-values is accounted for more than 85% of the total variance, which indicates that most of the data have been fully summarized by these three common factors. In this paper, each public factor is named as supply chain factor, human resource factor and marketing factor.

According to the factor score as shown in Table 4, the weights of the secondary indicators under the supply chain, marketing and human resources are given by using the above weight calculation formula, as shown in Table 5.

The original data were normalized. The higher the value, the better the X index (+index) and the lower the better x index (- index), respectively

Table 3
Rotation load matrix of factor analysis

Component

1 2 3

Inventory turnover 0.845 –0.002 0.346

Manufacturing cycle –0.836 0.144 –0.319

Defect rate of parts supply –0.662 0.317 0.068

Procurement cycle –0.651 –0.211 0.294

Scrap loss rate –0.589 0.176 0.443

Market occupancy –0.283 0.873 0.139

Customer complaint rate 0.211 0.733 0.147

Increase rate of new customers –0.235 0.658 0.029

Personnel expense ratio 0.028 –0.084 –0.859

Sales revenue per capita 0.579 0.357 0.615

	Component
Inventory turnover	0.845	–0.002	0.346
Manufacturing cycle	–0.836	0.144	–0.319
Defect rate of parts supply	–0.662	0.317	0.068
Procurement cycle	–0.651	–0.211	0.294
Scrap loss rate	–0.589	0.176	0.443
Market occupancy	–0.283	0.873	0.139
Customer complaint rate	0.211	0.733	0.147
Increase rate of new customers	–0.235	0.658	0.029
Personnel expense ratio	0.028	–0.084	–0.859
Sales revenue per capita	0.579	0.357	0.615

Table 4

Factor score of factor analysis

	Component
	1	2	3
Inventory turnover	0.411	0.045	–0.133
Manufacturing cycle	–0.327	0.019	0.062
Defect rate of parts supply	–0.293	0.016	–0.106
Procurement cycle	–0.266	–0.083	0.055
Scrap loss rate	0.183	–0.015	0.056
Market occupancy	0.007	0.427	–0.051
Customer complaint rate	0.089	–0.411	0.283
Increase rate of new customers	0.053	0.349	0.289
Personnel expense ratio	0.246	0.097	–0.567
Sales revenue per capita	0.028	–0.116	0.358

Table 5

Secondary index weight under common factors

Factors	Secondary index	Weights
Supply chain	Inventory turnover	0.41
	Manufacturing cycle	0.23
	Defect rate of parts supply	0.14
	Procurement cycle	0.13
	Scrap loss rate	0.09
Market	Market occupancy	0.51
	Customer complaint rate	0.26
	Increase rate of new customers	0.19
Human resources	Personnel expense ratio	0.65
	Sales revenue per capita	0.36

$\begin{matrix} x_{ij} = \frac{x_{ij}^{'} - {min}_{j} (x_{ij}^{'})}{{max}_{j} (x_{ij}^{'}) - {min}_{j} (x_{ij}^{'})} \\ x_{ij} = \frac{x_{ij}^{'} - {max}_{j} (x_{ij}^{'})}{{min}_{j} (x_{ij}^{'}) - {max}_{j} (x_{ij}^{'})} \end{matrix}$ (16)

The dependent variable Y, i.e. financial index, is also classified and normalized according to the above-mentioned independent variable X. the higher the value, the better and the lower the better. The normalized data of the four FP indicators are multiplied by the weights in Table 2 and then added together to obtain the comprehensive financial data. According to the weights given above and the normalized data, this paper calculates the scores of finance, supply chain, marketing and human resources for each enterprise, and carries out multiple linear regression, as shown in Table 6 –8.

Table 6

Summary of multivariate linear regression model fitting

Models	R value	R2	Adjusted R2	SD
Model 1	0.8372	0.7228	0.7128	6.2736

Table 7

Multiple linear regression analysis of variance

Models	Methods	Total squares	Df	Regression squares	F	Significance
Model 1	Regression	1988.634	1	1988.635	52.29	0.0
	Residual	810.348	20	40.48
	Total	2799.383	21

Table 8

Multiple linear regression coefficients

Models	Regression coefficient			T	Significance
Model 1		B	SD
	(Constant)	7.4451	2.0129	8.7367	0.0
	supply chain	11.1932	0.3212	3.4225	0.00285
	Human resources	0.3288	0.0357	8.7695	0.0
	Marketing	1.3283	0.3312	4.5293	0.0

The standard error model of R2 after adjustment of R value R2 was 10.8590.7380.7236.2814

It can be seen from Table 6 that R>0.7, so the fitting degree between the model and the data is good. It can be seen from Table 7 that the sum of squares of regression is 1988.687, the sum of residual squares is 810.6, and the total sum of squares is 2799.287. The corresponding value of F statistic is 52.38, and the significance level is less than 0.05. It can be considered that the established regression equation is effective. It can be seen from Table 8 that the regression coefficients of FP on supply chain, human resources and marketing are 11.119, 0.322 and 1.333 respectively; the T values of corresponding significance tests are 3.462, 8.8 and 4.56 respectively, and the significance levels of the three regression coefficients B are less than 0.05, which can be considered as supply chain, human resources and market The three independent variables of marketing have a significant impact on the FP of the dependent variables. The regression equation is:

$Y = 7.436 + 11.119 X_{1} + 0.322 X_{2} + 1.333 X_{3}$ (17)

5 Result Analysis on the influencing factors of FP of listed companies using regression model and fuzzy logic system

5.1 Descriptive statistics

As can be seen from Table 9-10, there is a small gap in the proportion of equity incentive and the size of the sample companies, but there are large differences in corporate performance, financial leverage, growth, equity concentration and equity balance [22]. The maximum value of equity incentive ratio is 9.34, the minimum value is 0.46, and the average value is 3.23. Although its span value is 8.88, the difference is not small from the perspective of proportion, which indicates that different enterprises are in different stages in the implementation of equity incentive. The size of the company is the logarithm of the total assets of the company, and the difference is not big. It can be seen that the company scale of the companies with equity incentive is at a relatively similar level. The biggest difference is the growth index and the growth rate of operating income, the highest is 105.53, the lowest is –49.92, and the span reaches 155.45. Secondly, the degree of equity balance also varies greatly, with the maximum of 128.47, the minimum of 1.66, and the span of 128.47. The degree of equity balance reflects the proportion of the total number of shares held by the second and third largest shareholders in the number of shares held by the first largest shareholder.

Table 9
Variable definition

Types Names Symbols Indicators

Explained variable Company performance ROE Net assets income rate

Explaining variable Equity incentive ratio RATE Incentive shares as a percentage of total equity

Scale of company SIZE Total assets

Financial leverage LEVER Asset-liability ratio

Control variable Growth GROWTH Increase rate of business revenue

Ownership concentration S The shareholding ratio of the largest shareholder

Equity balance degree LNZ Second and third largest to the first largest shareholders

Types	Names	Symbols	Indicators
Explained variable	Company performance	ROE	Net assets income rate
Explaining variable	Equity incentive ratio	RATE	Incentive shares as a percentage of total equity
	Scale of company	SIZE	Total assets
	Financial leverage	LEVER	Asset-liability ratio
Control variable	Growth	GROWTH	Increase rate of business revenue
	Ownership concentration	S	The shareholding ratio of the largest shareholder
	Equity balance degree	LNZ	Second and third largest to the first largest shareholders

Table 10

Descriptive statistical analysis

Names	N	Range	Minimum	Maximum	Mean	SD
Company performance	85	96.67	–61.435	35.29	9.0239	12.1634
Equity incentive ratio	85	8.66	0.51	9.47	3.2348	1.9437
Scale of company	85	5.23	10.84	15.83	12.6347	0.8225
Financial leverage	85	75.67	3.56	79.94	38.9381	19.5113
Growth	85	155.34	–49.45	105.48	16.5834	26.4838
Ownership concentration	85	59.67	11.58	71.56	36.3872	13.4734
Equity balance degree	85	128.56	1.56	130.43	46.3784	31.8347

In addition, the difference between the highest level and the lowest level of return on net assets of the company is 96.24, the maximum value is 35.09, and the minimum value is –61.15. The difference of financial leverage, that is, the asset liability ratio is larger in proportion. The highest asset liability ratio is 79.02, and the lowest is only 3.66. The maximum value of equity concentration ratio is 71.38, and the minimum value is 11.51, which indicates that among the listed companies that choose to implement equity incentive, there are both centralized and decentralized enterprises. These factors will have a certain impact on the effect of equity incentive of sample companies.

5.2 Multiple regression analysis

5.2.1 Significance test of regression equation

According to Table s9-10, F=6.991, Sig=0.000, indicating that the regression equation passed the test at the significance level of 0.01. The adjusted R2=0.358, indicating that the explanatory power of regression equation for dependent variables is 35.8%, which can be considered as significant relationship in the equation. In this model, 35.8% of the independent variables and control variables can explain the reasons for the performance changes of listed companies. This shows that in addition to the factors mentioned in this model, the performance of Listed Companies in the small and medium-sized board of China is also affected by many other factors, such as the relevant policies issued by the relevant departments of the state Laws and regulations and economic environment. The tolerance of explanatory variable tolerance of equity incentive proportion, equity incentive proportion square and equity incentive proportion cubic variable is close to 0.1 or less than 0.1, and the variance expansion factor VIF is far greater than 10, which shows obvious multi-collinearity [23]. In addition, the tolerance and variance expansion factor VIF of other variables are close to 1, indicating that multi-collinearity among explanatory variables is weak, and the model is effective.

5.2.2 Significance test of regression coefficient

Through the t test, we can see that the correlation coefficient between the equity incentive proportion and the company performance is 11.375, which is positive correlation, and can pass the t test, which is more significant; the correlation coefficient between the square of equity incentive proportion and the company performance is –2.566, showing a negative correlation, which can pass the t test, which is more significant; the correlation coefficient between the cube of equity incentive proportion and the company performance The correlation coefficient between the company size and the company performance is 7.607, which is very significant through the t test; the correlation coefficient between the company’s financial leverage and the company’s performance is –0.310, showing a negative correlation, which can pass the t test, which is very significant; the company’s growth and corporate performance have a positive correlation with the company’s performance The correlation coefficient of company performance is 0.111, which is positive correlation, which is more significant through the t test; the correlation coefficient between the company’s equity concentration and the company’s performance is 0.170, which is positive correlation, which is not very significant; the correlation coefficient between the company’s equity balance degree and the company’s performance is 0.008, which is positive correlation, and fails to pass the t-test It’s not very obvious.

5.2.3 Result analysis of regression equation

Through the regression results, we can get the regression equation between return on net assets and equity incentive ratio $\begin{matrix} ROE = β_{0} + β_{1} RATE + β_{2} {RATE}^{2} + β_{3} {RATE}^{3} + β_{4} SIZE \\ + β_{5} LEVER + β_{6} GROWTH + β_{7} S + β_{8} LNZ + ɛ \end{matrix}$ (18)

Based on the above formula, the stagnation points of equity incentive ratio are 3.13% and 7.55%, and the image of company performance and equity incentive level is roughly as follows (as shown in Fig. 3):

Fig. 3

Diagram of regression equation.

Equity incentive proportion: from the regression results, we can see that there is a cubic curve relationship between the equity incentive proportion and the earnings per share of Listed Companies in China. The regression coefficient of equity incentive proportion and equity incentive proportion square has passed the significance test. If the regression coefficient of equity incentive proportion cube passes the significance test at the significance level of 0.01, the hypothesis is that 1. The effect of equity incentive ratio on corporate performance is interval, assuming H1 is tenable [24]. The regression results of financial data of sample companies in 2013 show that equity incentive, as an incentive measure to improve corporate performance, is effective in a certain range. When the proportion of equity incentive is low (less than 3.13%), managers can feel the stimulating effect of equity incentive, make their benefit function and owner’s benefit function tend to be consistent, so as to reduce agency cost and improve company value.

Company size: there is a positive correlation between company size and company performance, with strong significance. Large scale companies are generally mature companies with good capital operation, standardized management mode and stable performance growth. Many small and medium-sized enterprises can achieve good performance through effective and standardized operation and management. For example, high-tech enterprises, although generally small in scale, often have good performance due to the accumulation of human capital, standardized operation and rapid growth.

Financial leverage: there is a significant negative correlation between financial leverage and corporate performance, which indicates that the scale of listed companies on SME board is relatively small, the asset liability ratio is too high, and the operating pressure of the company is too large, which leads to unsatisfactory performance.

Growth company: there is a significant positive correlation between growth and performance. This shows that companies with high growth potential, rapid market expansion and rapid sales growth will drive continuous growth in performance [25]. At the same time, the improvement of the company’s performance will accumulate more effective resources for the company, promote the company’s growth and form a virtuous circle.

Ownership concentration: there is a weak positive correlation between ownership concentration and corporate performance, which is not significant. Generally speaking, according to the principal-agent theory and information asymmetry theory, under the situation of continuous concentration of shares, large shareholders are more likely to infringe on the interests of small and medium-sized shareholders. However, the results obtained in this paper do not show this situation. Most of the small and medium-sized board listed companies are small in scale and relatively concentrated in equity, which is easier to improve the operating efficiency of the company. Moreover, most of the small and medium-sized enterprises are private and have high personnel mobility. The managers of the companies prefer to use short-term incentive rather than long-term equity incentive.

Equity balance: there is a weak positive correlation between the degree of equity balance and corporate performance, but it is not significant. This shows that the proportion of other shareholders holding shares is higher than that of large shareholders, which can indeed reduce the probability of large shareholders’ infringement on the interests of small shareholders in the situation of “one share dominating". The higher shareholding ratio of minority shareholders may stimulate their enthusiasm to supervise the company, reduce agency costs, and thus have a positive incentive effect on corporate performance.

5.2.4 Result analysis of fuzzy logic system

Finally, we demonsatrte the comparative analysis for financial prediction in term of accuracy between multiple regression model and fuzzy logic system in Fig. 4. From Fig. 4 is is clearly depicted that Fuzzy system provide best prediction accuracy as comapred to Multivariant regression Model.

Fig. 4

Comparative analysis for financial prediction in term of accuracy between multivariant regression model and fuzzy logic system.

6 Conclusion

Based on the research of enterprise performance evaluation, this paper selects appropriate indicators, summarizes the public factors except FP by factor analysis, and studies the relationship between these public factors and FP by multiple regression method, which provides basis and suggestions for enterprises to improve decision-making and behavior, improve FP and meet shareholders’ expectations. Finally, we demonstrate Comparative analysis for financial prediction in term of accuracy between multiple regression model and fuzzy logic system and result deduce that fuzzy logic gives better accuracy than regression model. On the basis of the research done in this paper, the research on the establishment of enterprise performance evaluation indicators and the influencing factors of FP of listed companies can be further developed in the following aspects in the future:

This paper discusses the non quantitative indicators of enterprise performance evaluation, such as customer satisfaction, and studies the deep-seated relationship between non quantitative indicators and financial indicators, so as to provide more powerful support for the whole enterprise to improve FP in the future.

The research on enterprise performance and the influencing factors of FP should be extended to the manufacturing industry or service industry outside the enterprise to make it more universal.

In order to improve the accuracy of the evaluation and the credibility of the research, we should select more experts with more abundant knowledge background to evaluate, on the premise of sufficient historical data.

In this paper, we only consider the internal factors of enterprises, but not the external factors such as macro-economic environment and government decision-making.

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