Study on the Path of Ideological and Political Education Content Diversification Construction in Colleges and Universities under New Media Technology Support

In practical problems, it is often necessary to study the relationship between a phenomenon and the most important factors affecting it. A one-way linear regression model can be a good way to reveal the non-deterministic relationship between two variables. The usual practice is to first write two variables as Y and X, corresponding to the actual observations in the plane coordinate system to make the scatter plot of Y and X, when the scatter plot falls roughly on a straight line, indicating that the two variables have a strong linear relationship, at this point can be used to continue to study the intrinsic relationship of the one-dimensional linear regression. This method of constructing a straight line to fit the observations is known as the least squares method. According to this method, the line should minimize the sum of the squares of the vertical deviations between all actual values observed on the line.

Consider any straight line y = β₀ + β₁x, where constants β₀ and β₁ are to be determined. When x = x_i, the corresponding vertical coordinate on this line is β₀ + β₁x_i. Thus, the perpendicular distance between point (x_i,y_i) and this line is |y_i – (β₀ + β₁x_i)|. Suppose that n points are to be fit by this line, such that Q denotes the sum of the squares of the perpendicular distances | of these n points. Then: (1) Q=∑i=1n[ yi−(β0+β1xi) ]2 \[Q=\sum\limits_{i=1}^{n}{{{\left[ {{y}_{i}}-\left( {{\beta }_{0}}+{{\beta }_{1}}{{x}_{i}} \right) \right]}^{2}}}\]

Use least squares to determine the values of β₀ and β₁ that must be chosen to minimize the value of Q.

It is not difficult to minimize the value of 4 by considering β₀ and β₁. Then: (2) ∂Q∂β0=−2∑i=1n(yi−β0−β1xi) \[\frac{\partial Q}{\partial {{\beta }_{0}}}=-2\sum\limits_{i=1}^{n}{\left( {{y}_{i}}-{{\beta }_{0}}-{{\beta }_{1}}{{x}_{i}} \right)}\] and: (3) ∂Q∂β0=−2∑i=1n(yi−β0−β1xi)xi \[\frac{\partial Q}{\partial {{\beta }_{0}}}=-2\sum\limits_{i=1}^{n}{\left( {{y}_{i}}-{{\beta }_{0}}-{{\beta }_{1}}{{x}_{i}} \right)}{{x}_{i}}\]

The following pair of equations is obtained by making the partial derivatives of the above two equations equal to zero: (4) β0n+β1∑i=1nxi=∑i=1nyiβ0∑i=1nxi+β1∑i=1nxi2=∑i=1nxiyi \[\begin{matrix} {{\beta }_{0}}n+{{\beta }_{1}}\sum\limits_{i=1}^{n}{{{x}_{i}}}=\sum\limits_{i=1}^{n}{{{y}_{i}}} \\ {{\beta }_{0}}\sum\limits_{i=1}^{n}{{{x}_{i}}}+{{\beta }_{1}}\sum\limits_{i=1}^{n}{x_{i}^{2}}=\sum\limits_{i=1}^{n}{{{x}_{i}}}{{y}_{i}} \\ \end{matrix}\]

Call equation (4) the regular equation for β₀ and β₁. By considering the second order partial derivatives of Q, it can be shown that the values of β₀ and β₁ that satisfy the regular equation are the values that minimize the sum of squares Q in equation (2). If these values are represented by β^0${{\hat{\beta }}_{0}}$ and β^1${{\hat{\beta }}_{1}}$, then the equation of the line obtained by least squares will be y=β^0+β^1x$y={{\hat{\beta }}_{0}}+{{\hat{\beta }}_{1}}x$. The line is called the least squares line.

Typically, let x¯n=(1/n)∑i=1nxi\[{{\bar{x}}_{n}}=\left( {1}/{n}\; \right)\sum\limits_{i=1}^{n}{{{x}_{i}}}\] and y¯n=(1/n)∑i=1nyi${{\bar{y}}_{n}}=\left( {1}/{n}\; \right)\sum\limits_{i=1}^{n}{{{y}_{i}}}$. pairs β₀ and β₁ are obtained by solving the regular equations in (4) as follows: (5) β^1=∑i=1nxiyi−nx¯ny¯n∑i=1nxi2−nx¯n2β^0=y¯n−β^1x¯n \[\begin{matrix} {{{\hat{\beta }}}_{1}}=\frac{\sum\limits_{i=1}^{n}{{{x}_{i}}}{{y}_{i}}-n{{{\bar{x}}}_{n}}{{{\bar{y}}}_{n}}}{\sum\limits_{i=1}^{n}{x_{i}^{2}}-n\bar{x}_{n}^{2}} \\ {{{\hat{\beta }}}_{0}}={{{\bar{y}}}_{n}}-{{{\hat{\beta }}}_{1}}{{{\bar{x}}}_{n}} \\ \end{matrix}\]

Here is another look at the algorithmic principles of multiple linear regression. Multiple linear regression adds the number of variables affecting the change in y to univariate linear regression in order to be able to fit a multivariate linear function below: (6) y=β0+β1x1+Λ+βkxk \[y={{\beta }_{0}}+{{\beta }_{1}}{{x}_{1}}+\Lambda +{{\beta }_{k}}{{x}_{k}}\]

In this case, it is still possible to obtain the value of β₀,⋯⋯,β_k by least squares calculation, and the principle of the algorithm is the same as that of univariate linear regression. In fact, all computerized statistical software nowadays can quickly compute a least squares regression line.

For the general form of linear regression yi=β0+∑i=1nβixi+εi${{y}_{i}}={{\beta }_{0}}+\sum\limits_{i=1}^{n}{{{\beta }_{i}}}{{x}_{i}}+{{\varepsilon }_{i}}$, there are several assumption theories, and the regression model that satisfies these assumption theories is called the classical linear regression model:

1) Normality assumption:

The random error term ε_i follows a normal distribution.

Structural equation analysis, also often referred to as structural equation modeling (SEM), is a statistical method for analyzing the relationships between variables based on their covariance matrices is an important tool for multivariate data analysis. Its advantages include the ability to handle multiple dependent variables simultaneously, allow both independent and dependent variables to contain measurement error, estimate the factor structure and factor relationships simultaneously, allow for greater flexibility in the measurement model, and estimate the degree of fit of the entire model, which is an advantage not found in other statistical methods.

This paper utilizes correlation analysis to study the correlation between satisfaction with Civic and Political Education and eight secondary indicators, respectively. The paper uses Pearson correlation coefficient to indicate the strength of the correlation. The results of the correlation analysis between the influencing factors and the satisfaction of civic and political education can be seen in Figure 1. The correlation coefficients all exceed 0.95, suggesting that enhancing the influencing factors can directly increase the satisfaction level of Civic Education in colleges and universities. The correlation analysis can lay the foundation for the subsequent investigation of the influencing factors and mechanisms that influence satisfaction with Civic and Political Education.

Figure 1.

The correlation analysis results of the influence factors and the satisfaction

Before conducting structural equation modeling analysis, this paper first conducts regression analysis on the factors that influence the satisfaction of college civic education, and screens out the main influencing factors from the rest of the factors. The results of regression analysis are shown in Table 1, and the regression model R² is 0.953, 0.946 and 0.928 respectively, and the corresponding F-values are significantly different, indicating that satisfaction with the quality of the course, satisfaction with the teaching situation and satisfaction with the learning gains will have an impact on satisfaction with Civic and Political Education in colleges and universities. Meanwhile, the regression coefficients of the four influencing factors, namely, teaching resources effectiveness X2 (0.938**), new media utilization X5 (0.684**), heuristic teaching X6 (0.745**) and knowledge mastery X7 (0.652**), are high and significantly different, which indicates that the four factors mentioned above are the main factors affecting satisfaction with civic and political education in colleges and universities. Accordingly, this paper constructs a model of the influencing factors of satisfaction with civic and political education in colleges and universities for structural equation modeling test and analysis.

Combined with the results of regression analysis, this paper proposes the following hypotheses:

Hypothesis H1: The effectiveness of teaching resources X2 is positively related to the satisfaction of college civic education.

Regarding the results of the goodness-of-fit test, this paper utilized AMOS 24.0 software to test the model of the influencing factors, and the results of the analysis of the structural equation model are shown in Table 2. In this paper, five indicators, GFI (0.942), CFI (0.917), NFI (0.953), NNFI (0.976) and RMR (0.033), were selected to indicate the fitting results of the model. Among them, GFI, CFI, NFI and NNFI over 0.9 represent acceptable model fit, and RMR less than 0.05 indicates good fit results. It can be seen that all the fit indicators are within the standard range, indicating that the fit between the hypotheses proposed in this paper and the actual data is good, and the influence factor model constructed in this paper is able to elucidate the mechanism of influencing the satisfaction of the Civic Education in colleges and universities.

According to the results of structural equation modeling analysis, the P value of the path of the four indicators, namely, teaching resources effectiveness X2, new media use X5, heuristic teaching X6 and knowledge mastery X7, affecting college students’ satisfaction with the learning of Civics courses is less than 0.05, which indicates that the above four influencing factors are positively correlated with satisfaction with Civics education in colleges and universities. The effect sizes of the four influence paths are 0.191, 0.265, 0.309 and 0.152, respectively, in which the influence effect of heuristic teaching is the largest, followed by the use of new media, and the knowledge mastery is the smallest. In conclusion, the research hypotheses proposed in this paper have been confirmed.