It is estimated that mainland Chinese tourists travelling to Taiwan can bring annual revenues of 400 billion NTD to the Taiwan economy. Thus, how the Taiwanese Government formulates relevant measures to satisfy both sides is the focus of most concern. Taiwan must improve the facilities and service quality of its tourism industry so as to attract more mainland tourists. This paper conducted a questionnaire survey of mainland tourists and used grey relational analysis in grey mathematics to analyze the satisfaction performance of all satisfaction question items. The first eight satisfaction items were used as independent variables, and the overall satisfaction performance was used as a dependent variable for quantile regression model analysis to discuss the relationship between the dependent variable under different quantiles and independent variables. Finally, this study further discussed the predictive accuracy of the least mean regression model and each quantile regression model, as a reference for research personnel. The analysis results showed that other variables could also affect the overall satisfaction performance of mainland tourists, in addition to occupation and age. The overall predictive accuracy of quantile regression model
The opening up of Taiwan to visitors from mainland China can boost Taiwan's tourism industry and periphery industries. Based on the estimate by the Taiwan Visitors Association, if Taiwan opens up to 3,000 mainland visitors per day, there will be 1 million visitors per year. If each mainland visitor stays in Taiwan for seven to ten days and spends 50,000 NTD, this could contribute about 50 billion NTD to Taiwan's tourism industry. Due to the multiplier effect of consumption, the output value of the Taiwan service industry could reach over 100 billion NTD, in industries such as the airline industry, travel industry, tourist hotels, transportation, food, recreation areas, department stores, and native products. This represents good news, and it can increase the number of employment opportunities in Taiwan. However, the business opportunity resulted from opening up to mainland visitors is too large for Taiwan. The aim of this paper was to discuss whether Taiwan has engaged in appropriate planning and relevant industry software and hardware facilities and services.
A great deal of the literature on consumer behavior already exists [
This paper is organized as follows. Section
The grey mathematic theory, proposed by Long [
From the original decision matrix
Normalize the data of original decision matrix
Calculate grey relational distance
Calculate grey relational coefficient
Calculate grey relational grade
Grey relational analysis has been applied in many industries, such as business [
The quantile regression method [
STATA was used to perform quantile regression analysis; its graphics is similar to Figure
Quantile regression diagram.
There were a total of 144 mainland visitors traveling to Taiwan who participated in the questionnaire survey. The question items in the questionnaires were written using simplified Chinese characters and included basic information items such as gender (
Descriptive statistic value of the nine satisfaction variables.
Satisfaction 










Max  100  100  100  100  100  100  95  90  100 
Min  40  50  40  50  40  40  30  10  30 
Avg  80.76  83.26  81.17  81.88  79.84  76.24  70.38  67.19  78.10 
Std  14.15  12.74  12.10  11.80  13.90  11.57  13.30  16.80  13.86 

144  144  144  144  144  144  144  144  144 
This paper used the grey relational grade analysis proposed by Deng and the grey relational analysis MATLAB procedure developed by Wen et al. [
Output chart of grey relational grade of eight satisfaction items.
In this paper, the first eight satisfaction items were used as independent variables (
Analysis results of least square regression model and quantile regression model for overall satisfaction performance.
Regression 
OLS 





Coefficient 

Significant  Coefficient 

Significant  Coefficient 

Significant  Coefficient 

Significant  
Sex  −0.004  −1.074  −0.0001  −1.77  *  −0.0001  −2.93  ***  −0.0001  −1.13  
Occupation  0.001  1.004  0.0013  0.43  −0.0025  −0.63  −0.0057  −0.90  
Age  −0.002  −0.949  −0.0001  −0.24  −0.0001  −0.08  0.0002  0.19  
Tourist attraction  0.001  3.837  ***  0.0006  2.64  ***  0.0007  2.45  **  0.0008  2.02  ** 
Food  0.001  6.103  ***  0.0015  5.56  ***  0.0015  4.18  ***  0.0017  4.05  *** 
Hotel facilities  0.001  2.989  ***  0.0012  4.60  ***  0.0013  3.46  ***  0.0003  0.52  
Hotel service attitude  0.002  6.016  ***  0.0013  4.86  ***  0.0010  2.84  ***  0.0019  3.89  *** 
Night fair culture  0.001  4.552  ***  0.0012  5.64  ***  0.0009  3.40  ***  0.0007  1.91  * 
Architectural style  0.001  5.568  ***  0.0015  5.44  ***  0.0015  4.43  ***  0.0016  3.16  *** 
Weather conditions  0.002  7.091  ***  0.0015  5.33  ***  0.0019  4.43  ***  0.0021  5.39  *** 
Street cleanliness  0.000  2.167  **  0.0007  2.61  ***  0.0007  2.20  **  0.0004  1.11  
Pseudo 
0.9670  0.8744  0.8349  0.7985 
Note: *is significant at the 10% significance level; **is significant at the 5% significance level; ***is significant at the 1% significance level.
Output of analysis results of least square regression model and quantile regression model for overall satisfaction performance.
As shown in Tables
Verification result of coefficient difference under high and low quantiles (
Variable  Sex  Occupation  Age  Tourist attraction  Food  Hotel facilities  Hotel service attitude  Night fair culture  Architectural style  Weather conditions  Street cleanliness 


3.02  0.11  0.20  3.16  0.12  5.15  0.36  3.41  0.03  1.59  4.59 
Different significance  *  *  ***  **  *** 
Note: *is significant at the 10% significance level; **is significant at the 5% significance level; ***is significant at the 1% significance level.
From Table
From Table
It was found that hotel facilities (
It was found that night fair culture, architectural styles, and weather conditions (
Tables
In this section, the quantile regression model was used to analyse the reliability of the satisfaction of mainland tourists and determine the accuracy of the quantile regression model. The original sample data were divided into four groups; three groups were used as training data to establish the regression model, and one group was used as the testing data for crossvalidation of the prediction methods, so as to test the reliability and predictive ability of the models. In this paper, five assessment indicators and the overall predictive accuracy were used to compare the predictive ability of the four models, as follows:
the root mean squared error (
the revised Theil inequality coefficient (
the mean absolute error (
the mean absolute percentage error (
the coefficient of efficiency (
For indicators 1 to 4, a result closer to 0 indicated that the model had higher accuracy. For the fifth indicator, a result closer to 1 indicated that the model had higher accuracy. The analysis and test results are shown in Table
Table
Evaluation indicators and result of total predictive accuracy.
Regression  RMSE  RTIC  MAE  MAPE  CE  Accuracy % 

OLS  1.788  0.031  1.526  0.017  0.903  91.25 

1.024  0.019  0.996  0.011  0.967  97.60 

1.332  0.026  1.288  0.015  0.935  94.87 

2.156  0.045  1.961  0.030  0.866  89.16 
The main contribution of this paper is different from the past literature. In this paper, quantile regression and the OLS method were used to discuss the impact of the satisfaction of mainland tourists with service quality on the overall satisfaction performance. The causes for the impact of the variables on the overall satisfaction under different quantiles and improvement solutions were further analyzed. The empirical results showed that gender, tourist attractions, hotel facilities, night fair culture, and street cleanliness affected the overall satisfaction performance of the mainland tourists and had significant differences in the high and low quantiles. Besides work and age, other variables could also affect the overall satisfaction performance of mainland tourists. In addition, quantile regression was used to analyze the reliability of the satisfaction of mainland tourists in this paper. Further, the original data were divided into several groups to establish the prediction models. Five evaluation indicators and the overall predictive accuracy were used to conduct cross verification and analysis of the four models. The findings showed that the overall accuracy of the
The authors declare that there is no conflict of interests regarding the publication of this paper.