Research on the Matching Mechanism between Career Planning Education and Job Market from the Perspective of Educational Administrators

This paper takes college students career planning education as the independent variable and employability as the dependent variable. The research model of career planning education and employability is shown in Figure 1. Among them, career education planning includes three dimensions such as internship practice, mentor guidance, and curriculum design. The employment ability influenced by career planning education includes five dimensions such as analytical thinking, career identity, professional ability, interpersonal influence, and personal conduct.

Figure 1.

Research model of career planning education and employment ability

In order to verify that college students career planning education can improve college students employability, the relevant hypotheses are proposed through the research form of questionnaire, three dimensions of college students career planning education and five dimensions of college students employability are selected for correlation analysis, and the following research hypotheses are proposed:

H1: There is a positive correlation between career planning education on college students employability.

A multiple linear regression model is interpreted as having a linear relationship between variable Y and multiple explanatory variables X₁,X₂,⋯,X_k. The assumption that there is a linear relationship between the explained variable Y and multiple explanatory variables X₁,X₂,⋯,X_k is a multiple linear function of the explanatory variables and is called a multiple linear regression model. I.e: (1) Y=β0+β1X1+β2X2+⋯+βkXk+μ where Y is the explained variable (dependent variable), X_j(j = 1,2,⋯,k) is the k explanatory variable (independent variable), β_j(j = 0,1,2,⋯,k) is the k+1 unknown parameter, which is the regression coefficient, and μ is the random error, also known as the residual, which is usually assumed to be μ~N(0,σ²).

The linear equation between the expected value of the explained variable Y and the explanatory variable X₁,X₂,⋯,X_k is: (2) E(Y)=β6+β1X1+β2X2+⋯+βkXk

It is called the multivariate overall linear regression equation, or overall regression equation for short.

For n set of observations Y_i,X_1i,X_2i,⋯,X_ki(i = 1,2,⋯,n), the system of equations takes the form: (3) Yi=β0+β1X1i+β2X2i+⋯+βkXki+μi,(i=1,2,⋯,n)

To wit: (4) { Y1=β0+β1X11+β2X21+⋯+βkXk1+μ1Y2=β0+β1X12+β2X22+⋯+βkXk2+μ2⋯⋯Yn=β0+β1X1n+β2X2n+⋯+βkXkn+μn

Its matrix form is: (5) [ Y1Y2⋮Yn]=[ 1X11X21⋯Xk11X12X22⋯Xk2⋮⋮⋮⋮⋮1X1nX2n⋯Xkn ][ β0β1β2⋮βk]+[ μ1μ2⋮μn]

To wit: (6) Y=Xβ+μ where Yn×1=[ Y1Y2⋮Yn ] is the vector of observations of the explanatory variables, Xn×(k+1)=[ 1X11X21⋯Xk11X12X22⋯Xk2⋮⋮⋮⋮⋮1X1nX2n⋯Xkn ] is the matrix of observations of the explanatory variables, β(k+1)×1=[ β0β1β2⋮βk ] is the vector of overall regression parameters, and μn×1=[ μ1μ2⋮μn ] is the vector of random error terms.

The overall regression equation is expressed as: (7) E(Y)=Xβ

Multiple linear regression analysis is the process of estimating each parameter in the model based on the observed samples, and performing statistical tests on the estimated parameters and regression equations so that the regression model can be utilized for size prediction and analysis. The multiple linear regression model contains multiple explanatory variables, and multiple explanatory variables act on the explanatory variable Y at the same time. To examine the effect of one of the explanatory variables on Y, it is necessary to analyze the model by assuming that the other explanatory variables remain unchanged. Therefore, the regression coefficients in the multiple linear regression model are partial regression coefficients, i.e., they reflect the mean effect of one of the explanatory variables on the dependent variable Y when the other variables in the model are held constant.

Since the parameters β₀,β₁,β₂,⋯β_k are all unknown, they can be estimated using the sample observations (X_1i,X_2i,⋯X_ki;Y_i). If the calculated parameter estimates are β^0,β^1,β^2,⋯,β^k , and the parameter estimates are used to replace the unknown parameters β₀,β₁,β₂,⋯,β_k of the overall regression function, the multiple linear sample regression equation is obtained: (8) Y^i=β^0+β^1X1i+β^2X2i+⋯+β^kXkn where β^i(j=0,1,2,⋯,k) is the parameter estimate and Ŷ_i(i = 1,2,⋯,n) is the sample regression value or sample fit, sample estimate of Y_i.

Its matrix expression is in the form: (9) Y=Xβ where Yn×1=[ Y^1Y^2⋮Y^n ] is the column vector of n×1rd-order fitted values for the vector of sample observations of the explanatory variables Y, Xn×(k+1)=[ 1X11X21⋯Xk11X12X22⋯Xk2⋮⋮⋮⋮⋮1X1nX2n⋯Xkn ] is the n×(k+1) th-order matrix of sample observations of the explanatory variables X, and β^(k+1)×1=[ β^0β^1β^2⋮β^k ] is the column vector of (k+1)×1 th-order estimates of the vector of unknown parameters β.

The deviation between the estimated value of the explanatory variable Ŷ_i obtained from the sample regression equation and the actual observed value Y_i is called the residual e_i: (10) ei=Yi−Y^i=Yi−(β^b+β^1X1i+β^2i+⋯+β^iiXki)

The following assumptions must be met when the multiple linear regression model utilizes ordinary least squares (OLS) to estimate the parameters:

Zero mean assumption: E(μ_i) = 0, i = 1,2,⋯,n, i.e.: (11) E(μ)=E[ μ1μ2⋮μn ]=[ E(μ1)E(μ2)⋮E(μn) ]=0

Same variance assumption (variance of μ is the same constant): (12) Var(μi)=E(μi2)=σ2,(i=1,2,⋯,n)

No self-relevance: (13) Cov(μi,μj)=E(μjμj)=0,(i≠j,i,j=1,2,⋯,n) (14) E(μμ′)=[ E[ μ1μ2⋮μn ](μ1,μ2,⋯,μn) ]=E[ μ12μ1μ2⋯μ1μnμ2μ1μ22⋯μ2μn⋮⋮⋮⋮μnμ1μnμ2⋯μn2 ]=[ E(μ12)E(μ1μ2)⋯E(μ1μn)E(μ2μ1)E(μ22)⋯E(μ2μn)⋮⋮⋮⋮E(μnμ1)E(μnμ2)⋯E(μn2) ]=[ σμ20⋯00σμ2⋯0⋮⋮⋮⋮00⋯σμ2 ]=σu2In

Random error term μ is uncorrelated with explanatory variable X (this assumption holds automatically): (15) Cov(Xji,μi)=0,(j=1,2,⋯,k,i=1,2,⋯,n)

The random error term μ follows a normal distribution with mean zero and variance σ²: (16) μ9∼N(0,σμ2In)

There is no multicollinearity between the explanatory variables: (17) rank(X)=k+1≤n

That is, the sample observations of each explanatory variable are linearly independent of each other, and the seconds of the matrix of sample observations of explanatory variables X are the number of parameters k+1, thus ensuring a unique estimate of parameter β₀,β₁,β₂,⋯,β_k.

For a multiple linear regression model containing k explanatory variables: (18) Yi=β0+β1X1i+β2X2i+⋯+βkXki+μi(i=1,2,⋯,n)

Setting β^0,β^1,⋯,β^k as the estimator of parameter β₀,β₁,⋯,β_k, respectively, yields the sample regression equation: (19) Y^i=β^0+β^1X1i+β^2X2i+⋯+β^kXki

The residuals e_i of observation Y_i and regression Y_i are: (20) ei=Yi−Y^i=Yi−(β^0+β^1X1i+β^2i+⋯+β^kiXki)

By the method of least squares β^0,β^1,⋯,β^k should minimize the sum of the squares of the residuals e_i of all observations Y_i and regressions Ŷ_i, even though: (21) Q(β^0,β^1,β^2,⋯,β^k)=∑ ei2=∑ (Yi−Y^i)2=∑ (Yi−β^0−β^1X1i−β^2X2i−⋯−β^kXki)2

Obtain the minimum value. According to the extremum principle for multivariate functions, Q takes the first order partial derivative of β^0,β^1,⋯,β^k respectively and makes it equal to zero, denoted as: (22) ∂Q∂β^j=0,(j=1,2,⋯,k)

Unfolding as: (23) { ∂Q∂β^0=2∑ (Yi−β^0−β^1X1i−β^2X2i−⋯−β^kXki)(−1)=0∂Q∂β^1=2∑ (Yi−β^0−β^1X1i−β^2X2i−⋯−β^kXki)(−X1i)=0⋯⋯∂Q∂β^k=∑ (Yi−β^0−β^1X1i−β^2X2i−⋯−β^kXki)(−Xki)=0

Simplify to obtain the following system of equations: (24) { nβ^0+β^1∑ X1i+β^2∑ X2i+⋯+β^k∑ Xki=∑ Yiβ^0∑ X1i+β^1∑ X1i2+β^2∑ X2iX1i+⋯+β^k∑ XkiX1i=∑ X1iYi⋯⋯β^0∑ Xki+β^1∑ X1iXki+β^2∑ X2iXki+⋯+β^k∑ Xki2=∑ XkiYi

The above (k+1) equation is called the regular equation and its matrix form is: (25) [ n∑ X1i∑ X2i⋯∑ Xki∑ X1i∑ X1i2∑ X2iX1i⋯∑ XkiX1i⋮⋮⋮⋮⋮∑ Xki∑ X1iXki∑ X2iXki⋯∑ Xki2 ][ β^0β^1β^2⋮β^k]=[ ∑ Yi∑ X1iYi⋮∑ XkiYi]

Because: (26) [ n∑ X1i∑ X2i⋯∑ Xki∑ X1i∑ X1i2∑ X2iX1i⋯∑ XkiX1i⋮⋮⋮⋮⋮∑ Xki∑ X1iXki∑ X2iXki⋯∑ Xki2 ]=[ 11⋯1X11X12⋯X1nX21X22⋯X2n⋮⋮⋮⋮Xk1Xk2⋯Xkn ][ 1X11X21⋯Xk11X12X22⋯Xk2⋮⋮⋮⋮⋮1X1nX2n⋯Xkn ]=X′X[ ∑ Yi∑ X1ijYi⋮∑ XkiYi ]=[ 11⋯1X11X12⋯X1nX21X22⋯X2n⋮⋮⋮⋮Xk1Xk2⋯Xkn ][ Y1Y2⋮Yn ]=X′Y

Let β^=[ β^0β^1β^2⋮β^k ] be the vector of estimates and the sample regression model Y = Xβ+e with both sides multiplied by the transpose matrix X′ of the matrix of sample observations X, then we have: (27) X′Y=X′Xβ+X′e to obtain a regular system of equations: (28) X′Y=X′Xβ

From the absence of multicollinearity between the explanatory variables it follows that R(X) = k+1, X′X are square matrices of order (k+1), so that X′X is full rank and the inverse matrix (X′X)⁻¹ of X′X exists. Thus: (29) β=(X′X)−1X′Y is the 0LS estimate of vector β.

The regression analysis of the three dimensions of college students career planning education on the dimension of analytical thinking is shown in Table 1. In the regression analysis of the three dimensions of college students career planning education on the dimension of “analytical thinking” in college students employability, the model P-value: <1.8e-15, indicating that the model is significant at 95% confidence level. From the perspective of the significance of each dimension, internship practice, mentoring and course design have a significant positive relationship with the dimension of analytical thinking in employability (P<0.05). It shows that college students career planning education is conducive to improving the ability of “analytical thinking” in college students employability, and hypothesis H2a, hypothesis H3a and hypothesis H4a are true.

The regression analysis of the dimensions of college students vocational education on the dimension of career identity is shown in Table 2. The model presents significant at 95% confidence level with its P-value: <2.3e-15. Internship practice, mentoring and curriculum design in college students career planning education all have positive correlations on career identity in college students employability (P < 0.01). Hypothesis H2b, hypothesis H3b and hypothesis H4b passed the test.

The results of the above analysis show that all three dimensions of career planning education have a significant positive effect on the dimension of vocational identity in college students employability, which is conducive to improving college students ability in the dimension of vocational identity such as career awareness, career planning and employment expectations.

The regression analysis of the dimensions of college students career education on the dimension of professional competence is shown in Table 3. All three dimensions of college students career planning education can improve college students professional competence in their employability (P < 0.01), which is conducive to the improvement of college students professional knowledge and competence, professionalism, computers and English and other professional knowledge dimensions, and hypotheses H2c, hypotheses H3c and hypotheses H4c are valid.

The regression analysis of the dimensions of college students vocational education on the interpersonal influence dimension is shown in Table 4. There is a significant positive correlation between internship practice, mentor guidance and curriculum design in career planning education and interpersonal influence dimension in employability, the corresponding regression coefficients are 0.459, 0.564 and 0.396 respectively, with a significance level of 1%. Meanwhile, the P-value:<1.7e-13 of the model indicates that internship practice, mentor guidance and curriculum design can enhance the interpersonal influence ability in the employability of college students, and hypothesis H2d, hypothesis H3d and hypothesis H4d are valid.

Table 5 shows the regression analysis of the dimensions of college students vocational education on the dimension of personal conduct. There is a positive correlation between the three dimensions of career planning education on the personal conduct of college students employability at the 5% level, in which the influence of mentor guidance is the largest, with a regression coefficient of 0.583, indicating that the hypothesis H2e, hypothesis H3e, and hypothesis H4e pass the test. College students career planning education is conducive to improving college students sense of responsibility, enterprise, work initiative, dedication, so that college students are more diligent, down-to-earth and conscientious, emotionally stable, and other personal conduct dimensions of the ability to work.

The above analysis shows that the three dimensions of internship practice, mentor guidance, and curriculum design of college students career planning education have a positive effect on the five dimensions of personal conduct dimension, career identity dimension, and professional knowledge ability to enhance college students employability, which verifies the hypotheses H1~H4 that career planning education in colleges and universities can promote the enhancement of college students employability, and realize the docking with the job market.

The current status of the employability skills that college students self-assessed having is shown in Figure 2. The proportion of professional knowledge B1 and professional skills B2 that college students themselves think they possess is the highest, 86.96% and 83.35% respectively, indicating that college students spend most of their time on learning professional knowledge and skills during their four-year college life.

Figure 2.

Status quo of self-evaluation of college students

This is followed by college students communication ability B3, analyzing and decision-making ability B5, stress-resistant ability B9, interpersonal ability B12, continuous learning ability B14 and dedication B16, with the proportion ranging from 42.55% to 59.23%. It indicates that by getting along with people in the process of growing up, living independently in college, and bearing the pressure of coursework will exercise the employment ability of undergraduates.

The proportion of adaptability B6, comprehensive knowledge B7, information gathering ability B8, teamwork ability B10, organization and coordination ability B11 and career planning ability B17 among undergraduates employability ranges from 28.86% to 36.25%, which indicates that some undergraduates employability in these aspects is still weak and is neglected in the overall training program.

Compared with the above abilities, undergraduates think that their practical ability B4, innovation ability B13 and scientific research ability B15 are very insufficient, which are 11.8%, 12.25% and 10.41% respectively.

Based on the statistics of the questionnaires recovered from social employers, from which we analyze what competencies undergraduates should have when social employers consider them in recruiting undergraduates at present. The current situation of the employment ability of undergraduates needed by the job market is shown in Figure 3. From the results of the survey, it can be seen that most of the enterprises in the recruitment of undergraduate graduates pay most attention to undergraduates practical ability B4 and communication ability B3, accounting for 85.03% and 83.74% of the proportion of the survey.

Figure 3.

The status quo of the employment capacity of college students in the job market

Secondly, employers generally value undergraduates interpersonal skills B12, professionalism B16, professional skills B2, professional knowledge B1 and adaptability B6, which accounted for 70.48% to 72.82% of the survey. Undergraduates analytical decision-making ability B5, stress-resistant ability B9, teamwork ability B10, organizational and coordination ability B11, and continuous learning ability B14 are also the abilities to be comprehensively examined by employers, and the survey results show that they accounted for 40.38%~53.65% of the weight respectively. For undergraduate innovation ability B13 and scientific research ability B15 only a small number of units on such employment ability is more important, accounting for 26.29% and 17.84% of the total survey sample.

According to the questionnaire feedback of undergraduates employment ability status and the current situation of undergraduates employment ability needed by social employers for comparison, the correspondence between the employment ability of undergraduates and the employment market demand is shown in Figure 4. It is not difficult to see that there is a big gap between the expectations of the unit and the actual employment ability status of undergraduates in terms of practical ability B4 (-73.25%), and undergraduates have obvious deficiencies in practical ability. At the same time, the needs of enterprises in terms of adaptability B6 (-38.26%), professionalism B16 (-29.40%) and communication ability B3 (-24.51%) are also much higher than the actual ability level of undergraduates. In terms of professional knowledge B1, professional skills B2, analytical decision-making ability B5 and continuous learning ability B14, the current status of undergraduates abilities and the needs of social employers can basically reach a match.

Figure 4.

The comparison between the employment ability of students and the market demand