Stock price analysis based on the research of multiple linear regression macroeconomic variables

The data in this article comes from the Sina Finance Market Center. After excluding companies with insufficient financial data, we selected 8 financial indicators of 14 listed agricultural companies from 2013 to 2019 as sample data.

This article selects a total of 8 financial indicators from 4 aspects of profitability, growth ability, operating ability and solvency: EPS (X₁), central business profit margin (X₂), primary business income growth rate (X₃), net asset growth rate (X₄), Total asset turnover rate (X₅), current asset turnover rate (X₆), quick ratio (X₇) and interest payment multiple (X₈).

The panel data is an X×Y data matrix. What is recorded in the matrix is a particular data index of X objects at Y time nodes. In recent decades, a variety of statistical methods have emerged, including panel data analysis methods. Panel data is generally analysed by Eviews software, so this paper selects Eviews6.0 software for research and analysis. The models used in this article are as follows: (9) Yit=ai+βXit+εit {Y_{it}} = {a_i} + \beta {X_{it}} + {\varepsilon _{it}} i = 1,2, ⋯, 14 indicates the cross-section mark. t = 1, 2, 3, 4, 5 represents the time stamp. Y_it is the dependent variable, which represents the stock price of a company i in year t. a_i is a constant term, and the intercept terms between i individual member equations are not the same. We use it to explain personal effects. That is to say. It is used to explain the effects of variables that are neglected to explain individual differences in the model. X_it is the independent variable, where i represents the company and t represents the time. β is the coefficient of the independent variable and ɛ_it is the bias term, which explains the negligence in the model caused by the changes of individual members and time. Combining the eight independent variables and 1 dependent variable of this study, the model is: (10) Y=ai+β1X1+β2X2+β3X3+β4X4+β5X5+β6X6+β7X7+β8X8+ε Y = {a_i} + {\beta _1}{X_1} + {\beta _2}{X_2} + {\beta _3}{X_3} + {\beta _4}{X_4} + {\beta _5}{X_5} + {\beta _6}{X_6} + {\beta _7}{X_7} + {\beta _8}{X_8} + \varepsilon (11) ∂tF+∂xG=−2aF−〈zx,∇S1(z)χ1+∇S2(z)χ2〉 {\partial _t}F + {\partial _x}G = - 2aF - \left\langle {{z_x},\nabla {S_1}(z){\chi _1} + \nabla {S_2}(z){\chi _2}} \right\rangle Among them F=12〈z,Mzx〉 F = {1 \over 2}\left\langle {z,M{z_x}} \right\rangle and G=S0(z)+12〈zt,Mz〉 G = {S_0}(z) + {1 \over 2}\left\langle {{z_t},Mz} \right\rangle . We use Eq. (11) and z_x as the inner product (12) 〈zx,Mzt〉+〈zx,Kzx〉=〈zx,−aMz〉+〈zx,∇S0(z)〉+〈zx,∇S1(z)χ1〉+〈zx,∇S2(z)χ2〉 \left\langle {{z_x},M{z_t}} \right\rangle + \left\langle {{z_x},K{z_x}} \right\rangle = \left\langle {{z_x}, - aMz} \right\rangle + \left\langle {{z_x},\nabla {S_0}(z)} \right\rangle + \left\langle {{z_x},\nabla {S_1}(z){\chi _1}} \right\rangle + \left\langle {{z_x},\nabla {S_2}(z){\chi _2}} \right\rangle Among them (13) 〈zx,Kzx〉=〈(pxqxvxwx),(00100001−10000−100)(pxqxvxwx)〉=〈(pxqxvxwx),(vxwx−px−qx)〉=〈px,vx〉+〈qx,wx〉+〈vx,−px〉+〈wx,−qx〉=〈px,vx〉+〈qx,wx〉−〈px,vx〉−〈qx,wx〉=0 \matrix{ {\left\langle {{z_x},K{z_x}} \right\rangle } \hfill & { = \left\langle {\left( {\matrix{ {{p_x}} \cr {{q_x}} \cr {{v_x}} \cr {{w_x}} \cr } } \right),\left( {\matrix{ 0 & 0 & 1 & 0 \cr 0 & 0 & 0 & 1 \cr { - 1} & 0 & 0 & 0 \cr 0 & { - 1} & 0 & 0 \cr } } \right)\left( {\matrix{ {{p_x}} \cr {{q_x}} \cr {{v_x}} \cr {{w_x}} \cr } } \right)} \right\rangle = \left\langle {\left( {\matrix{ {{p_x}} \cr {{q_x}} \cr {{v_x}} \cr {{w_x}} \cr } } \right),\left( {\matrix{ {{v_x}} \cr {{w_x}} \cr { - {p_x}} \cr { - {q_x}} \cr } } \right)} \right\rangle } \hfill \cr {} \hfill & { = \left\langle {{p_x},{v_x}} \right\rangle + \left\langle {{q_x},{w_x}} \right\rangle + \left\langle {{v_x}, - {p_x}} \right\rangle + \left\langle {{w_x}, - {q_x}} \right\rangle } \hfill \cr {} \hfill & { = \left\langle {{p_x},{v_x}} \right\rangle + \left\langle {{q_x},{w_x}} \right\rangle - \left\langle {{p_x},{v_x}} \right\rangle - \left\langle {{q_x},{w_x}} \right\rangle } \hfill \cr {} \hfill & { = 0} \hfill \cr } (14) 〈zx,−aMz〉=−a〈zx,Mz〉=−a=〈(pxqxvxwx),(0−100100000000000)(pqvw)〉=−a〈(pxqxvxwx),(−qp00)〉=−a(〈px,−q〉+〈qx,p〉)=a(〈px,q〉+〈−qx,p〉)==a(〈z,Mzx〉) \matrix{ {\left\langle {{z_x}, - aMz} \right\rangle } \hfill & { = - a\left\langle {{z_x},Mz} \right\rangle = - a = \left\langle {\left( {\matrix{ {{p_x}} \cr {{q_x}} \cr {{v_x}} \cr {{w_x}} \cr } } \right),\left( {\matrix{ 0 & { - 1} & 0 & 0 \cr 1 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 \cr } } \right)\left( {\matrix{ p \cr q \cr v \cr w \cr } } \right)} \right\rangle = - a\left\langle {\left( {\matrix{ {{p_x}} \cr {{q_x}} \cr {{v_x}} \cr {{w_x}} \cr } } \right),\left( {\matrix{ { - q} \cr p \cr 0 \cr 0 \cr } } \right)} \right\rangle } \hfill \cr {} \hfill & { = - a\left( {\left\langle {{p_x}, - q} \right\rangle + \left\langle {{q_x},p} \right\rangle } \right)} \hfill \cr {} \hfill & { = a\left( {\left\langle {{p_x},q} \right\rangle + \left\langle { - {q_x},p} \right\rangle } \right)} \hfill \cr {} \hfill & { = = a\left( {\left\langle {z,M{z_x}} \right\rangle } \right)} \hfill \cr } Get (15) 〈zx,∇S0(z)〉−〈zx,Mzt〉=−〈zx,−aMz〉−〈zx,∇S1(z)χ1〉−〈zx,∇S2(z)χ2〉=−a〈zx,Mzx〉−〈zx,∇S1(z)χ1〉−〈zx,∇S2(z)χ2〉=−2aF−〈zx,∇S1(z)χ1+∇S2(z)χ2〉 \matrix{ {\left\langle {{z_x},\nabla {S_0}(z)} \right\rangle - \left\langle {{z_x},M{z_t}} \right\rangle } \hfill & { = - \left\langle {{z_x}, - aMz} \right\rangle - \left\langle {{z_x},\nabla {S_1}(z){\chi _1}} \right\rangle - \left\langle {{z_x},\nabla {S_2}(z){\chi _2}} \right\rangle } \hfill \cr {} \hfill & { = - a\left\langle {{z_x},M{z_x}} \right\rangle - \left\langle {{z_x},\nabla {S_1}(z){\chi _1}} \right\rangle - \left\langle {{z_x},\nabla {S_2}(z){\chi _2}} \right\rangle } \hfill \cr {} \hfill & { = - 2aF - \left\langle {{z_x},\nabla {S_1}(z){\chi _1} + \nabla {S_2}(z){\chi _2}} \right\rangle } \hfill \cr } As well as (16) ∂tF+∂xG=12∂t〈z,Mzx〉+∂x[S0(z)+12〈zt,Mz〉]=12〈zt,Mzx〉+12〈z,Mzxt〉+∂xS0(z)+12〈zxt,Mz〉+12〈zt,Mzx〉=∂xS0(z)+〈zt,Mzx〉+12〈z,Mzxt〉+12〈zxt,Mz〉 \matrix{ {{\partial _t}F + {\partial _x}G} \hfill & { = {1 \over 2}{\partial _t}\left\langle {z,M{z_x}} \right\rangle + {\partial _x}\left[ {{S_0}(z) + {1 \over 2}\left\langle {{z_t},Mz} \right\rangle } \right]} \hfill \cr {} \hfill & { = {1 \over 2}\left\langle {{z_t},M{z_x}} \right\rangle + {1 \over 2}\left\langle {z,M{z_{xt}}} \right\rangle + {\partial _x}{S_0}(z) + {1 \over 2}\left\langle {{z_{xt}},Mz} \right\rangle + {1 \over 2}\left\langle {{z_t},M{z_x}} \right\rangle } \hfill \cr {} \hfill & { = {\partial _x}{S_0}(z) + \left\langle {{z_t},M{z_x}} \right\rangle + {1 \over 2}\left\langle {z,M{z_{xt}}} \right\rangle + {1 \over 2}\left\langle {{z_{xt}},Mz} \right\rangle } \hfill \cr } Because of 〈z_t, Mz_x〉 = −〈z_x, Mz_t〉, 〈z,−Mz_xt〉 = −〈z_xt, Mz〉, so ∂_tF + ∂_xG = ∂_xS₀(z) − 〈z_x, Mz_t〉. We only need to prove ∂_xS₀(z) = 〈z_x, ∇S₀(z)〉, because: (17) ∂xS0(z)=∂x[−λ4(p2+q2)2−12(v2+w2)]=−λ(p2+q2)(ppx+qqx)−(vvx+wwx)〈zx,∇S0(z)〉=−λ(p2+q2)ppx−λ(p2+q2)qqx−vvx−wwx \matrix{ \hfill {{\partial _x}{S_0}(z)} & { = {\partial _x}\left[ { - {\lambda \over 4}{{({p^2} + {q^2})}^2} - {1 \over 2}({v^2} + {w^2})} \right] = - \lambda ({p^2} + {q^2})(p{p_x} + q{q_x}) - (v{v_x} + w{w_x})} \hfill \cr \hfill {\left\langle {{z_x},\nabla {S_0}(z)} \right\rangle }& { = - \lambda ({p^2} + {q^2})p{p_x} - \lambda ({p^2} + {q^2})q{q_x} - v{v_x} - w{w_x}} \hfill \cr } Based on the above formula (18) ∂tF+∂xG=−2aF−〈zx,∇S1(z)χ1+∇S2(z)χ2〉 {\partial _t}F + {\partial _x}G = - 2aF - \left\langle {{z_x},\nabla {S_1}(z){\chi _1} + \nabla {S_2}(z){\chi _2}} \right\rangle

We must analyse whether there are unit roots in a sequence we choose. Once we find that there is a unit root, we call this series a non-stationary time series. Such a sequence will lead to spurious regression when performing regression analysis [11]. Therefore, to ensure the data's stability, we must first perform a unit root test on the selected sequence.

First, we use the obtained P-value to indicate whether the data contain unit roots. When the obtained P-value is <0.05, we think that the data does not have a unit root, proving that the data is stable. Otherwise, it is considered that the data has a unit root, and the data is not stable.

As can be seen from Table 1, the P-value obtained by LLC inspection of the stock prices of 14 agricultural listed companies and eight financial index data from 2013 to 2019 is 0.0045, and that of IPS inspection, Fisher-ADF inspection, and Fisher-PP inspection. The P values are all 0.0000, and the P values of the 4 test methods are all <0.05. The research results show that the data in this paper do not contain unit roots. Therefore, the data in this article are all stable, and we can conduct an empirical analysis on them.

According to the characteristics of this article, we select the variable intercept model as the evaluation method. The Hausman test method is usually used to select a specific model [12]. Assume no correlation between the individual influence and the independent variable in the random influence model. The first step is to do a regression analysis of the original data. Then, we selected and used the random influence variable intercept model on the model, and the estimated results are shown in Table 2.

In the second step, Hausman's test method is used to determine whether the conclusion obtained by the random influence model analysis is appropriate. The results obtained by this method are shown in Table 3.

It can be seen from Table 3 that the model statistic is 17.111761, and the P-value is 0.0290 and <0.05. Therefore, a fixed-effect variable-intercept model should be established. The calculated results of the model are shown in Table 4.

From Table 4, the model equation can be obtained as: V=8.871968+4.86747080281X1+0.140535518671X2−0.00715553983237X3+0.0097928613261X4+ 2.30372560619X5−0.333951126952X6+0.0136045182504X7+0.000126695946192X8+ϵ \matrix{ V \hfill & { = 8.871968 + 4.86747080281{X_1} + 0.140535518671{X_2} - 0.00715553983237{X_3} + 0.0097928613261{X_4}} \hfill \cr {} \hfill & { +\, 2.30372560619{X_5} - 0.333951126952{X_6} + 0.0136045182504{X_7} + 0.000126695946192{X_8} + \varepsilon } \hfill \cr } The F statistic of this model is 24.84466. The results show that the accuracy of this model is high, and the explanation is robust. The corresponding P-value is 0.000000, indicating that all explanatory variables of the model are significant overall. The explanatory variables (selected eight indicators) explain the stock price is feasible. Therefore, the data of the eight indicators we selected from the four aspects of profitability, growth ability, operating ability and solvency are reliable.

The coefficient of determination R2 in the process of the fitness test is 0.669120. This result is still relatively ideal in the time series model. The reason may be that the company's finances are sometimes affected by some uncertain factors, causing the current stock price to fluctuate. However, from the perspective of the degree of fit, these fluctuations have little effect on the test index data, and they can be effectively analysed and studied.

The DW statistic is 0.945865, indicating that the residuals of the model follow a normal distribution. Thus, the data has a solid ability to explain the model.

Among the selected eight financial indicators, the P-value of EPS () is 0.0060, and the P-value of the profit margin of the leading business () is 0.0060. They have passed the significance test, and the regression coefficient is positive, showing a positive correlation with the stock price (V). The test results show that EPS are the most important indicator to measure profitability. When it changes, the stock price will also be affected. EPS have extremely high research significance for analyzing stock prices. The primary business profit rate has a considerable impact on stock prices. EPS and paramount business profitability are the most critical indicators for analysing profitability, which can significantly reflect the company's financial performance fluctuations. Investors’ attention to the company can be more inclined to the strength of profitability, but it must also be combined with other indicators for a comprehensive analysis.

The P-value of the interest payment multiple (X₈) in other indicators is 0.0000, which has passed the significance test. The regression coefficient is positive, showing a positive correlation with the stock price (V). Judging from the test results, the data on interest payment multiples is reliable. This indicator can reflect the size of profitability and reflect the degree of guarantee of profitability to repay the debts due. Therefore, it is an essential indicator of a company's solvency.

In the remaining indicators, the net asset growth rate (X₄), total asset turnover rate (X₅), and quick ratio (X₇) have not passed the significance test, but the correlation coefficient is positive. This shows that it is positively correlated with stock prices. The primary business income growth rate (X₃) and current assets turnover rate (X₆) have not passed the significance test, and the correlation coefficient is negative. Failure to pass the significance test does not mean that it has nothing to do with its stock price, but the impact on the stock price is not as high as other factors. However, these indicators cannot be ignored when analysing the impact of financial performance on the company's stock price. We have to analyse more comprehensively and systematically to bring the best benefits.