2016 2 nd International Conference on Social, Education and Management Engineering (SEME 2016) ISBN: 978-1-60595-336-6 Predicting Chinese Mobile Phone Users Based on Combined Exponential Smoothing-Linear Regression Method Meng-yun JIANAG and Lin BAI * Beijing University of Posts and Telecommunications Beijing, China * Corresponding author Keywords: Exponential smoothing, Linear regression,, Mobile phone users, Predict. Abstract. In this paper, we propose a combined exponential smoothing-linear regression method to predict the number of mobile phone users in China. The main idea is to use linear regression (LR) to predict the relative of exponential smoothing (ES) method based on the predicted results of exponential smoothing method, and to use the predicted relative to adjust the predicted results of exponential smoothing method. The experimental results show that the proposed method is more accurate than both the exponential smoothing and linear regression method. Introduction Informatization level in China has been increasing year by year since 2000, and the mobile communication technology is developing continuously as well.[1] As the Ministry of Industry and Information Technology of the People s Republic of China issued the 4G license at the end of year 2013, mobile communication in China has entered a new era. Mobile telecommunication service is not limited to meet the communication needs of people but entertainment, social, consumption needs as well and it is making big influence in all aspects of people's life. [2] The result of user prediction is the basis of the communication network planning, thus the accuracy of the predicted results is key to reasonable and scientific planning of the entire communication network. Exponential smoothing, trend extrapolation, moving average method, autoregressive integrated moving average (ARIMA), regression analysis prediction, grey prediction, support vector machine (SVM), markov prediction and artificial neural networks (ANNs) are commonly used in prediction. These models have their characteristics but they are not perfect. Therefore, it is necessary to combine the advantages and avoid the shortcomings of the models to makes the results more accurate. In this article, we use unary linear regression to predict the relative of the cubic exponential smoothing method and adjust the predicted results of the cubic exponential smoothing method. Results show that the proposed method can make more accurate prediction on mobile phone users. Organization of the Text Combined Exponential Smoothing-Linear Regression Method Exponential Smoothing Method. [3] Single exponential smoothing establish the smooth to predict the index combined with the real. Double exponential smoothing establish the double smooth by re-smoothing and predict the index on the basis of the single exponential smoothing results, and represents the long-term trend of index. Cubic exponential smoothing make cubic smoothing on or on the basis of the double exponential smoothing and establish the smooth to predict index, and represents the cyclical trends of index. In this paper, we use the HoltWinters function in R language to implement the cubic exponential smoothing method, shown as below. The basic equation of the cubic exponential smoothing (refer with: Eq. 1, Eq. 2, Eq. 3):
(1) (2) The prediction equation of the cubic exponential smoothing (refer with: Eq. 4): (3) (4) Linear Regression Prediction. Regression analysis is to find out the estimated value of the parameter under certain statistical rules and get the regression curve. Regression analysis is divided into unary linear regression and multiple regression. [4] The function of unary linear regression is shown as below (refer with: Eq. 5): (5) Combined Exponential Smoothing-Linear Regression Method. We use cubic exponential smoothing method in this paper rather than single and double exponential smoothing method for the former can be applied on nonlinear prediction as well as linear prediction and has more accurate results. But the accuracy reduces when the exponential smoothing method is applied to long-term prediction. Thus, a combined exponential smoothing-linear regression method is proposed in this paper which may get a more accurate result. Firstly, use the exponential smoothing method to predict the number of mobile users according to the historical. Secondly, use the linear regression model to fit the relative of the ES predicted results. Finally, correct the predicted results of exponential smoothing method using the predicted relative. Figure (refer with: Figure 1) shows the process of the proposed method. Part a Initial Part b Use ES to predict correct Use linear regression to predict the relative Corrected result Part a Use ES to predict b on the base of a Part b The predicted result b Calculate the relative Figure 1. Combined exponential smoothing-linear regression method. (1) Use exponential smoothing method to predict existing. Divide the existing into two parts, named as and. Use exponential smoothing method to predict on the basis of and get the predicted results. ( means time here). (2) Calculate the relative of exponential smoothing method, named as. (6) (3) Use linear regression model to match the relative, and get the linear regression equation (refer with: Eq. 7) of and. (7)
And then use the equation (refer with: Eq. 7) to predict the relative. (4) Use exponential smoothing method to predict on the basis of and get the predicted results. (5) Use the predicted relative in (3) to correct the predicted results of exponential smoothing method and get the corrected results. So the corrected results can be calculated in the following equation (refer with: Eq. 9): (8) Implement of Combined Exponential Smoothing-Linear Regression Method in Predicting Chinese Mobile Phone Users Data Sources. The following is number of Chinese mobile phone users from 2007/1 to 2015/9, totally 105 (refer with: Table 1). The are from the Ministry of Industry and Information Technology of the People s Republic of China and National Bureau of Statistics of the People s Republic of China. (Unit : million) Table 1. Number of Chinese mobile phone users. 2007 2008 2009 2010 2011 2012 2013 2014 2015 1 46741 55576.9 64971.5 75660.4 86972.3 99659.8 112211.6 123527 129048.5 2 47392.9 56522.7 65978 76597.2 87882.9 100692.3 113204.3 123977.7 128971.2 3 48065.2 57463.4 67033.1 77687.2 89027 101882.3 114572.1 124842.5 129600 4 48743.4 58351.1 67880.1 78650.1 90038.9 103005.2 115512.5 125186.7 128985.5 5 49459.6 59213 68694.9 79591.5 91014.8 104072.4 116523.7 125636.1 129200 6 50164.8 60075.7 69519.9 80535.4 92054 105198 117585.8 126043.2 129310.3 7 50856.4 60837.8 70265.1 81409.2 92983.7 106202.8 118522.9 126340.6 128866 8 51566.9 61601.7 71050.4 82305.7 94008.5 107224.2 119561.6 126698.5 129439.3 9 52331.5 62404.6 71983.8 83330 95230.5 108474.4 120655.3 127258.3 131304.3 10 53144.7 62726.5 72953.7 84204.4 96399.1 109541.6 121579.2 127666.1 11 53937.9 63384 73857 85028.7 97533.5 110421.5 122329.7 128103.2 12 54728.6 64123 74738.4 85900.3 98625.3 111215.5 122911.3 128609.3 The Process of Predicting the Number of Chinese Mobile Phone Users. The process is shown as follow: (1) Use exponential smoothing method to predict existing. Divide the initial into three parts. The first part is from 2007/1 to 2013/12, totally 84. And predict the of mobile phone users from 2014/1 to 2014/12(second part, totally 12) based on the first part of. The third part is from 2015/1 to 2015/9, this part of is for verifying. In this paper, we use R language to implement the cubic exponential smoothing method, and you can see the predicted results in the following figure (refer with: Figure 2). The deep blue curve is the predicted value, and the light blue area is the confidence interval of the 80% confidence level, and the gray white area is the confidence interval of the 95% confidence level. (2) Calculate relative. = (predicted - initial ) / initial. The results are shown in this table (refer with: Table 2). (3) Use linear regression model to match the relative calculated in step 2. In this paper, we use SPSS 20 to do this step. The results are shown in the following figure (refer with: Figure 3). (9)
The value of R 2 is 0.998, and it is very close to 1. The sig value is smaller than 0.05. This proves that the fitting degree of the model is very good. And the linear regression model of the relative is as the following equation (refer with: Eq. 10): (10) (4) Use cubic exponential smoothing to predict the from January 2015 to September 2015 based on the from January 2007 to December 2014. (5) Correct the predicted results of exponential smoothing method and get the corrected results. Figure 2. The predicted results of exponential smoothing method. Table 2. The relative. initial relative 123527 123905.1 0.003061 123977.7 124991.3 0.008175 124842.5 126068.5 0.00982 125186.7 127111.6 0.015376 125636.1 128155 0.020049 126043.2 129207.1 0.025101 126340.6 129798.2 0.027367 126698.5 130734.4 0.031855 127258.3 131701.4 0.034914 127666.1 132697 0.039407 128103.2 133657.9 0.043361 128609.3 134603.6 0.046609 Figure 3. Model summary of linear regression. Result Analysis. The results of the exponential smoothing method, the linear regression method and the combined method are shown in the following table (refer with: Table 3). Compared with the exponential smoothing method and linear regression method, the relative of corrected results are smaller. So we can get the conclusion that the method proposed in this paper can get higher accuracy and be closer to the initial. As we can see from the result comparison (refer with: Figure 4), the blue line is the initial and the yellow line is the predicted using the combined method which is very close to the initial.
So the combined method proposed in this paper proves to have high accuracy compared with the exponential smoothing method and linear regression method. This method can be used in the prediction of Chinese mobile phone users. From the result comparison we can see that, as time goes, the relative of the exponential smoothing method grow bigger and bigger. So we use the liner regression method to fit the relative and use the predicted relative to correct the results of the exponential smoothing method to get the corrected results. In this process, we reduced the relative of the exponential smoothing method so that we can get a more accurate result. Table 3. The results of three methods. Data Initial Exponential smoothing method Linear regression method The combined method 2015.1 129048.5 129334.3 0.002215 133004.9 0.030658 128878.5-0.00132 2015.2 128971.2 130006.5 0.008028 133932.9 0.038471 129036.6 0.000507 2015.3 129600 130758 0.008935 134860.9 0.040593 129271.8-0.00253 2015.4 128985.5 131442 0.019045 135788.9 0.052745 129438.7 0.003514 2015.5 129200 132145.9 0.022801 136716.9 0.05818 129623.8 0.00328 2015.6 129310.3 132859.9 0.027451 137644.9 0.064454 129817.4 0.003922 2015.7 128866 133147.6 0.033225 138572.9 0.075326 129594.5 0.005653 2015.8 129439.3 133714 0.033025 139500.9 0.077732 129643.6 0.001578 2015.9 131304.3 134350.3 0.023198 140428.9 0.069492 129759.8-0.01176 Summary Figure 4. The result comparison. In this paper, we first proposed a combined exponential smoothing-linear regression method in predicting Chinese mobile phone users. Use linear regression to fit the relative of the exponential smoothing method, and then use the predicted relative to correct the results of exponential smoothing method. The results show that the proposed method have smaller relative and can get higher accuracy. We can use the proposed method to predict the number of Chinese mobile phone users. References [1] 2014.04: China Informatization Development Index (II) Research Report in 2003. [2] Feng Yi, Cao Heng, Tian Yuanbing. Modeling and analysis of Business volume prediction[j]. Designing Techniques of Posts and Telecommunications, 2008(9):25-30. [3] Li Ming. R language and website analysis [M]. Machinery Industry Press, 2014. [4] Baidu Encyclopedia: Linear regression prediction.