With the continuous innovation of scientific research, technological level and social and economic development, the technological innovation of enterprises in the continuous management is also facing a new breakthrough and upgrade. Especially for enterprises in the era of big data, in order to better respond to the new demands of the development of the new era, enterprise managers should make effective technological innovation from the global economic growth trend on the basis of clarifying their own development advantages. Therefore, on the basis of understanding the multiple linear regression model and its construction conditions, this paper analyses the influencing variables in the actual development according to the current management technology and innovation of enterprises, and obtains the clear results of the model research.

#### Keywords

- multivariate linearity
- regression model
- enterprise management
- technology
- innovation
- F test
- T test

#### MSC 2010

- 93A30

In order to better study the real relationship between enterprise management technology and innovation under the influence of multiple factors, this paper will make a comprehensive exploration based on multiple linear regression model.

It is assumed that enterprise management technology and innovation as the dependent variable Y1 will be affected by multiple factors. K, and y1 not being a linear function of XTJ, are the parameters _{0} and _{i}

In this case, _{t}_{0} +_{1}_{t}_{1} +_{2}_{t}_{2} +...+_{k}x_{tk}

_{0} _{1} _{2}......

In clear samples (YT, XT1, XT2..., XTK), t= 1,2... Under the condition of n, the above model can be expressed as:

_{i} and U1 are unknown, so the corresponding matrix expression formula is:

_{i} and U1 are unknown, so the corresponding matrix expression formula is:

The above formula can be simplified to

In order to obtain the best estimator in the model research, the model constructed must meet the following conditions: first, the mean value of the random error term is 0, and the variance _{2} it has consistent and finite characteristics. Second, the random error terms are independent of each other and have no correlation. Third, the explanatory variable XTJ, j = 1,2,3... There is no linear relationship between k and k. Fourth, in the explanatory variable XTJ, j= 1,2,3..., K is the explicit variable, and the error terms are independent of each other. Fifth, the explanatory variable belongs to the non-random variable, and under the condition of T→ ∞, T-1X ’X→ Q, where Q refers to a finite number of non-singular matrix. Sixth, the random error term obeys the normal distribution. Seventh, the regression model is properly designed.

First, the least square method. According to this principle, the above regression model can be transformed into a sample regression model with the specific formula of

Second, minimum sample size. In the research of enterprise management technology and innovation based on multiple linear regression model, the sample size compiled must exceed the number of explanatory variables of the model; in other words, it must conform to this formula.

Third, basic requirements. Generally speaking, only under the condition of n≥ 30 or n≥ 3 (k+1) can the demand estimated by the expected model be reached.

In the practice test analysis, the statistical quantity is the determination coefficient, and the model constructed at this time is the multiple regression, so the sample determination coefficient R^{2} is called the multiple determination coefficient. Based on the analysis of multiple linear regression model, the decomposition formula of the sum of squares of the total deviation of a single linear regression model is still valid, as will be discussed in the succeeding sections of the article. In this case, the degree of freedom of TSS is n-1, where n represents the sample size.

Combined with the model application analysis, it can be seen that if a new explanatory variable is added to the model, R^{2} will continue to rise, which proves that the square of residual will decrease with the increase of explanatory variable. At the same time, since the goodness of fit of the multiple linear regression model needs to be studied, R^{2} must be adjusted.

On the basis of clear sample size, increasing explanatory variables will inevitably reduce the degree of freedom. In this case, the adjustment operation should make the sum of squares of residuals and total deviations in their own degrees of freedom, respectively, so as to take advantage of the influence of the number of variables corresponding to the goodness of fit. At this point, the formula of multivariate determination coefficient is as follows:

As the independent variable in the model study continues to rise, if RSS/(n-k-1) decreases, then R^{2} will increase. At this time, it can be considered that the independent variable has an impact on the dependent variable and needs to be put into the model; otherwise, it needs to be discarded.

^{2}=0.1,

In practical research and analysis, it is found that no matter whether the
^{2} continues to increase, the actual fitting effect will be better and better. However, this standard is not the only one to evaluate the merits of the model, so it cannot be analysed and judged only according to the size of or R^{2}. Therefore, the judgement can be made by combining Akakike Information Criteria (AIC) and Schwartz Information Criteria (SC), as follows:

In order to conveniently estimate the parameters of the model, the following basic assumptions are made for Model 1. Explanatory variable x, x, is a deterministic variable, not a random variable, and rank(x)=p+1.

For the matrix form of multiple linear regression, this condition can be expressed as:

From the above assumption and the properties of multivariate normal distribution, it can be known that the random vector y still obeys the n-dimensional normal distribution.

Expectation vector of regression model (2–3):

According to the new development trend of social and economic development and technological innovation in recent years, it is necessary to start with the factors as shown in the figure for research and exploration when studying the technological innovation of enterprise management [1]. In front of the building model analysis in this paper, in order to better grasp the enterprise management technology and the development trend and hotspot in the research of the atmosphere of ‘innovation’ and the frontier, with Chinese knowledge resource pool hownet CNKI (China) as the literature information retrieval platform, bibliometrics analysis was carried out with literature data from Chinese academic periodical CNKI database. The retrieval conditions of the journal were as follows: the retrieval of the subject word ‘innovation atmosphere’ OR ‘innovation atmosphere’, the time span from 1999 to 2020, the publication time from 1 January 1999 to 31 December 2020; all journals were selected by source category and a total of 1873 literatures were obtained through retrieval. A total of 576 articles were published in core journals and CSSCI journals. We filtered the required data according to the analysis of the literature in order to ensure the authenticity and reliability of data sources; this paper only analyses the core journal and journal literature from CSSC by browsing through the paper title, abstract and key words on the initial literature with artificial screening and washing sample data, to eliminate repetition and invalid sample documents. A total of 452 search results were obtained. Through the data transformation of Citesspacev (5.7R^{2} version) software, the time span was set as 1999–2020, the time slice was set as 1 year and the time slice threshold was set as 50. The correlation analysis was conducted on the distribution of research institutions, the distribution of research authors, the research hot spots and the research frontier trends. The required variables for this study are shown in Table 1, and the expected efficiency relationship between actual enterprise management and technological innovation is shown in Table 2.

Study variables and explanations

The explained variable | Investment in technological innovation | R&D | R&D investment/business investment |

Explanatory variable | Technological innovation efficiency | D-1 | Development investment/R&D investment |

Concentration of ownership | Cr3 | The sum of the shareholding ratio of the top three shareholders | |

Nature of the largest shareholder | ney | State ownership is marked as 1, otherwise marked as 0 | |

Proportion of independent directors | idr | Number of independent directors/total number of board members | |

Chairman and general manager | lst | The combination of two jobs is marked as 1, otherwise as 0 | |

Two jobs in one | |||

The Board of Supervisors holds shares | bss | Number of shares held by members of the Board of Supervisors/total share capital | |

Executive equity incentives | mit | Number of shares held by managers/total share capital | |

Debt to asset ratio | debt | Total liabilities/total assets | |

Suppliers rely on | spe | Top 5 Supplier Product Amount/Total Product Value | |

Control variables | Company size | size | The natural logarithm of assets in tens of millions |

Corporate performance | roe | Net profit/total assets | |

Industry characteristics | ich | For high-tech enterprises, it is 1, otherwise it is 0 |

The efficiency expectation relationship between enterprise management and technological innovation

Concentration of ownership | + | + |

The nature of the state-owned shareholding | − | − |

Proportion of independent directors | + | + |

Two jobs in one | + | − |

The Board of Supervisors holds shares | + | + |

Executive equity incentives | + | + |

Debt to asset ratio | − | − |

Suppliers rely on | − | + |

In order to study various influencing factors of enterprise management technology and innovation from an overall perspective, the original hypothesis tested can be clearly identified as _{0} : _{1} = _{2} = ... = _{k}_{1} : _{j}

This refers to the F distribution with K, N-K-1 degree of freedom. After the pre-provided significant level A is defined, the exact corresponding degree of freedom can be shown by combining the F distribution.

Assuming that the test level is A, the following two test principles need to be met: First, if _{a}_{a}

At this point, the formula for the relationship between F and

Combined with the formula analysis, it can be seen that F and R^{2} belong to a direct proportional relationship, and the value of F increases with the increase of R^{2}. In this process, the overall F test will also become more significant, and the corresponding R^{2} value will continue to rise. At this time, the fitting degree of the regression equation will also become better and better. Therefore, this test can be regarded as a test of goodness of fit.

In order to eliminate the explanatory variables that have no significant influence on the explained variables in the regression model research, it is necessary to build a simpler multiple linear regression model. Assuming that the explanatory variable Xtj is not significant for the explained variable, then the corresponding regression coefficient _{j} is 0. In this case, we only need to verify whether the regression coefficient _{j} of the explanatory variable Xtj is 0 to get the answer. First of all, we put forward the hypothesis of _{0} : _{j}_{1} : _{j}

And the alternative hypothesis should be accepted under the condition of By (1) and (3).

According to the data collected from the integrated research, the descriptive statistical results of management technology and innovation of an enterprise are shown in Table 3, and the Pearson coefficient test results in the actual multicollinearity analysis are shown in Table 4. Therefore, it can be clearly recognised that there is no multicollinearity problem among the variables.

Analysis of descriptive statistical results

R&D investment (R&D) | 0.0727 | 0.0778 | 0 | 0.9839 |

Technological innovation efficiency (D_1) | 0.1223 | 0.4972 | 0 | 15.51 |

Equity concentration (CR3) | 0.5154 | 0.1299 | 0.0445 | 0.9412 |

State-owned Equity (NEY) | 0.0423 | 0.2016 | 0 | 1 |

Independent Director (IDR) | 0.3743 | 0.0561 | 0.333 | 0.667 |

Two Shares in One (LST) | 0.4256 | 0.4946 | 0 | 1 |

Board of Supervisors shareholding (BSS) | 0.5052 | 0.5002 | 1 | 1 |

Executive ownership [MIT] | 0.1940 | 0.1973 | 0 | 0.8968 |

Pearson coefficient test results analysis

Cr3 | 1.0000 | −0.0614 | 0.0152 | 0.0813 | −0.2384 | 0.1403 | −0.0807 | 0.0866 |

ney | −0.0614 | 1.0000 | −0.1152 | −0.1637 | −0.0838 | −0.1689 | 0.0397 | −0.0365 |

idr | 0.0152 | −0.1152 | 1.0000 | −0.0015 | −0.0323 | 0.1417 | −0.0553 | −0.0853 |

lst | 0.0813 | −0.1637 | −0.0015 | 1.0000 | −0.0054 | 0.6012 | −0.0276 | 0.0803 |

bss | −0.2384 | −0.0838 | −0.0323 | −0.0054 | 1.0000 | 0.0655 | −0.1309 | 0.0362 |

mit | 0.1403 | −0.1689 | 0.1417 | 0.6012 | 0.0655 | 1.0000 | −0.1150 | 0.0960 |

debt | −0.0807 | 0.0397 | −0.0553 | −0.0276 | −0.1309 | −0.1150 | 1.0000 | −0.1799 |

spe | 0.0866 | −0.0365 | −0.0853 | 0.0803 | 0.0362 | 0.0960 | −0.1799 | 1.0000 |

At the same time, combined with the following Table 5 analysis shows that governance and technical innovation investment between inside and outside the enterprise impact is mainly manifested in the following: first, the enterprise technological innovation under the 5% level and equity concentration showed positive correlation, prove that a certain degree of equity concentration can further strengthen the enterprise's technological innovation, the enterprise will also increase with big shareholder holding status. In the long run, controlling shareholders can consider investment decisions from the perspective of long-term development, and then accelerate the pace of technological innovation of enterprises. Second, leadership structure is negatively correlated with technological innovation at the 5% level, which proves that the management model combining the two powers limits the technological innovation of enterprises. Third, the board of supervisors stake to under 5% level, which proves that the increase of the proportion with the members of the board of enterprise technology innovation investment will be continuously heightened; the use of this form to increase the board of supervisors and the correlation of corporate interests help in the comprehensive regulatory management; and the board at the same time is empowered to reduce investment risk faced by technology innovation [3].

Regression analysis

Cr3 | + | 0.210^{***} |
0.134 | 2.97 | 0.003 |

ney | − | −0.130^{***} |
0.086 | −2.11 | 0.010 |

idr | + | 0.447 | 0.307 | 0.75 | 0.410 |

lst | − | 0.033^{**} |
0.042 | 1.77 | 0.044 |

bss | + | 0.026^{***} |
0.035 | 2.14 | 0.009 |

mit | + | 0.074 | 0.109 | 0.68 | 0.499 |

debt | − | −0.111^{***} |
0.119 | −2.78 | 0.005 |

spe | + | −0.036 | 0.090 | −0.4 | 0.687 |

size | + | 0.001 | 0.027 | 0.03 | 0.974 |

roe | − | −0.013^{***} |
0.022 | −4.00 | 0.000^{***} |

ich | − | 0.002 | 0.145 | 0.11 | 0.916 |

Note:

means significant at 1% level,

means significant at 5% level,

means significant at 10% level

From the perspective of technological innovation efficiency, its influence on the internal and external governance of enterprises is mainly reflected in the following points: First, ownership structure. Under the influence of modern enterprise system, the ownership and management rights of enterprises should be adjusted appropriately, and the concentration of ownership should be paid attention to, which can help to reduce the agency cost of enterprise innovation and improve the output efficiency of technological innovation while strengthening supervision. Second, in the development of technology-intensive enterprises, it is very important to put forward a scientific incentive mechanism. In the era of big data, talents are the core resources of enterprise technological innovation, and only a systematic and effective incentive mechanism can fully mobilise employees’ enthusiasm for work. Therefore, based on the multiple linear regression model and impact analysis proposed in this paper, in order to fully show the advantages of enterprise technological innovation, it is necessary to build a systematic talent management system, and put forward diversified incentive models and motivation guarantee for their medium and long term development. For example, different material and spiritual incentives can be designed according to talents at different stages of the core layer, backbone layer and potential layer, so as to provide a better development platform for talents at other levels while building a competitive and fair incentive system. Third, the system of the board of supervisors. According to the analysis of agency cost theory and power balance theory, as the basic content of guiding the orderly development of the enterprise board of supervisors system, under the condition of insider control, the decision-making problems of the innovation subject will inevitably affect the benefits obtained from the overall operation and limit the pace of technological innovation and development of the enterprise. On the contrary, the reasonable operation and comprehensive incentive of the Board of Supervisors system can help to further supervise whether the Board of Supervisors can perform tasks in strict accordance with regulations and requirements, and bring about a positive impact on the practice of technological innovation activities [4].

To sum up, therefore, under the background of the era of big data, in order to better cope with the changing market environment, improve the efficiency of enterprise's internal and external management levels and technical innovation, the ownership structure must be optimally constituted, a board of supervisors system featuring talent development with multi-angle in-depth thinking must be ensured and with these must be combined previous development experience on management optimisation. At the same time, we should start from the current internal and external management environment, and strengthen the supervision and restraint of various departments, so as to reduce the impact of internal and external pressure on technological innovation on the basis of realising the maximum value of the enterprise. In addition, from the perspective of technological innovation, from the enterprise's own development trend and research on scientific research innovation results, the use of multiple linear regression model in-depth discussion of the future development of enterprise management and the main direction of technological innovation, and then combined with practice cases for verification and analysis, finally get clear research results. This can not only provide the basis for enterprise management optimisation, but also help leaders and managers to make clear the importance of technological innovation.

#### Analysis of descriptive statistical results

R&D investment (R&D) | 0.0727 | 0.0778 | 0 | 0.9839 |

Technological innovation efficiency (D_1) | 0.1223 | 0.4972 | 0 | 15.51 |

Equity concentration (CR3) | 0.5154 | 0.1299 | 0.0445 | 0.9412 |

State-owned Equity (NEY) | 0.0423 | 0.2016 | 0 | 1 |

Independent Director (IDR) | 0.3743 | 0.0561 | 0.333 | 0.667 |

Two Shares in One (LST) | 0.4256 | 0.4946 | 0 | 1 |

Board of Supervisors shareholding (BSS) | 0.5052 | 0.5002 | 1 | 1 |

Executive ownership [MIT] | 0.1940 | 0.1973 | 0 | 0.8968 |

#### The efficiency expectation relationship between enterprise management and technological innovation

Concentration of ownership | + | + |

The nature of the state-owned shareholding | − | − |

Proportion of independent directors | + | + |

Two jobs in one | + | − |

The Board of Supervisors holds shares | + | + |

Executive equity incentives | + | + |

Debt to asset ratio | − | − |

Suppliers rely on | − | + |

#### Study variables and explanations

The explained variable | Investment in technological innovation | R&D | R&D investment/business investment |

Explanatory variable | Technological innovation efficiency | D-1 | Development investment/R&D investment |

Concentration of ownership | Cr3 | The sum of the shareholding ratio of the top three shareholders | |

Nature of the largest shareholder | ney | State ownership is marked as 1, otherwise marked as 0 | |

Proportion of independent directors | idr | Number of independent directors/total number of board members | |

Chairman and general manager | lst | The combination of two jobs is marked as 1, otherwise as 0 | |

Two jobs in one | |||

The Board of Supervisors holds shares | bss | Number of shares held by members of the Board of Supervisors/total share capital | |

Executive equity incentives | mit | Number of shares held by managers/total share capital | |

Debt to asset ratio | debt | Total liabilities/total assets | |

Suppliers rely on | spe | Top 5 Supplier Product Amount/Total Product Value | |

Control variables | Company size | size | The natural logarithm of assets in tens of millions |

Corporate performance | roe | Net profit/total assets | |

Industry characteristics | ich | For high-tech enterprises, it is 1, otherwise it is 0 |

#### Pearson coefficient test results analysis

Cr3 | 1.0000 | −0.0614 | 0.0152 | 0.0813 | −0.2384 | 0.1403 | −0.0807 | 0.0866 |

ney | −0.0614 | 1.0000 | −0.1152 | −0.1637 | −0.0838 | −0.1689 | 0.0397 | −0.0365 |

idr | 0.0152 | −0.1152 | 1.0000 | −0.0015 | −0.0323 | 0.1417 | −0.0553 | −0.0853 |

lst | 0.0813 | −0.1637 | −0.0015 | 1.0000 | −0.0054 | 0.6012 | −0.0276 | 0.0803 |

bss | −0.2384 | −0.0838 | −0.0323 | −0.0054 | 1.0000 | 0.0655 | −0.1309 | 0.0362 |

mit | 0.1403 | −0.1689 | 0.1417 | 0.6012 | 0.0655 | 1.0000 | −0.1150 | 0.0960 |

debt | −0.0807 | 0.0397 | −0.0553 | −0.0276 | −0.1309 | −0.1150 | 1.0000 | −0.1799 |

spe | 0.0866 | −0.0365 | −0.0853 | 0.0803 | 0.0362 | 0.0960 | −0.1799 | 1.0000 |

#### Regression analysis

Cr3 | + | 0.210^{***} |
0.134 | 2.97 | 0.003 |

ney | − | −0.130^{***} |
0.086 | −2.11 | 0.010 |

idr | + | 0.447 | 0.307 | 0.75 | 0.410 |

lst | − | 0.033^{**} |
0.042 | 1.77 | 0.044 |

bss | + | 0.026^{***} |
0.035 | 2.14 | 0.009 |

mit | + | 0.074 | 0.109 | 0.68 | 0.499 |

debt | − | −0.111^{***} |
0.119 | −2.78 | 0.005 |

spe | + | −0.036 | 0.090 | −0.4 | 0.687 |

size | + | 0.001 | 0.027 | 0.03 | 0.974 |

roe | − | −0.013^{***} |
0.022 | −4.00 | 0.000^{***} |

ich | − | 0.002 | 0.145 | 0.11 | 0.916 |

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Estate Company Spin-off Property Service Company Listing Selection by differential mortality rates Digital model creation and image meticulous processing based on variational partial differential equation Dichotomy model based on the finite element differential equation in the educational informatisation teaching reform model Nonlinear Dissipative System Mathematical Equations in the Multi-regression Model of Information-based Teaching The modelling and implementation of the virtual 3D animation scene based on the geometric centre-of-mass algorithm The policy efficiency evaluation of the Beijing–Tianjin–Hebei regional government guidance fund based on the entropy method The transfer of stylised artistic images in eye movement experiments based on fuzzy differential equations Research on behavioural differences in the processing of tenant listing information: An eye-movement experiment A review of the treatment techniques of VOC Some classes of complete permutation polynomials in the form of ( x ^{pm}−x +δ )^{s}+ax ^{pm}+bx overF _{p2m}The consistency method of linguistic information and other four preference information in group decision-making Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development A mathematical model of the fractional differential method for structural design dynamics simulation of lower limb force movement step structure based on Sanda movement Fractal structure of magnetic island in tokamak plasma Numerical calculation and study of differential equations of muscle movement velocity based on martial articulation body ligament tension Study on the maximum value of flight distance based on the fractional differential equation for calculating the best path of shot put Sports intensity and energy consumption based on fractional linear regression equation Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Study on Establishment and Improvement Strategy of Aviation Equipment Research on Financial Risk Early Warning of Listed Companies Based on Stochastic Effect Mode Characteristics of Mathematical Statistics Model of Student Emotion in College Physical Education Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Nonlinear strategic human resource management based on organisational mathematical model Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Fractional Differential Equations in Sports Training in Universities Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model