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Research on Affecting Savings Deposits of Urban and Rural Residents Based on Factor Analysis ZHANG Jilin, CAI Jing Department of Mathematic and Physics, Fujian University of Technology, Fuzhou, P.R.C., 350108 [email protected] Abstract: An effective and simple parameter estimating method—Factor Analysis method, for savings deposits of urban and rural residents model is proposed in this paper. As is known to all of us, there are many factors influencing savings deposits. The essential purpose of factor analysis is to describe, if possible, the covariance relationships among many variables in terms of a few underlying, but unobservable, random quantities called factors. This essay uses the method receiving two unrelated common factors which contain the whole information of five original elements. Therefore, we get the principal component deposit model. Through test, the new model could be proved to be accurate. Moreover the principal component deposit model has fairly good analysis result. In the end, this new model is applied to Chinese resident deposit forecasting based on the statistic data. From the comparison between new forecasting data and the statistic data, we could conclude that the main factor deposit model is a quite effective and simple method for forecasting Resident Deposit. Keywords: Factor analysis, Resident deposit, Principal component deposit model, Relation 1. Introduction Currently, there have been many people doing the research about defining variable factors of savings deposits of urban and rural residents. Deaton (1991) and Carroll (1992, 1997) presented the buffering Savings deposits and so on. Obviously, economic growth,income,interest rate, age structure of population, inflation, wealth, savings from abroad, the social security system, spending habits and other factors all will affect the savings deposits of urban and rural residents. The key of create deposits model is factor selection. However, there exist too many factors to be considered, at the same time, we can not decide which ones play important parts in this model. Suppose m the number of factors is n and the real number this model need is m, we will get C n kinds of combination. In the end, we should find out the best one. Frankly, it needs great computational costs. A principle component analysis is concerned with explaining the variance-covariance structure of a set of variables through a few linear combinations of these variables. Its general objectives are data reduction and interpretation. Although k components are required to reproduce the total system variability, often much of this variability can be accounted for by a small number m of the principle components. If so, there is almost as much as information in the m components as there is in the original k components. The m principle components can then replace the initial k variables, and the original data set, consisting of n measurements on k variables, is reduced to a data set consisting of n measurements on m principal components. An analysis of principal components often reveals relationships that were not previously suspected and thereby allows interpretations that would not ordinarily results. Therefore, in this paper, we uses the principal component analysis method to carry on the factor analysis on possible factors influencing savings deposits of urban and rural residents. 2. Factor Combination After summarizing the related research work, we hold that savings deposits model at least need 3 different kinds of factors: a business activities indicator interest rate and composition of population. In this situation, this essay put GDP, exchange rate of RMB to US dollar, worker average wage, household , 804 consumption and the population as the original 5 components, basing on the relevant statistical data of Statistics Yearbook during 1978-2007 of China, to do the factor analysis. 2.1 Linear correlation of the original components In this paper, we use KMO (Kaiser-Meyer-Olkin) test and Bartlett examination (as shown in the table1). KMO statistic value is 0.704, greater than 0.6. According to standard of statistician Kaiser, the principle components are fit for factor analysis. Bartlett test value is 225.269; asymp.sig is 0.000, less than the remarkable level 0.05, so the principle components are fit for factor analysis. GDP GDP exchange rate average wage household consumption population exchange rate wage consumption population 1.000 0.578 0.996 0.993 0.578 0.996 1.000 0.527 0.527 1.000 0.650 0.983 0.993 0.894 0.650 0.827 0.983 0.827 1.000 0.930 Table 1 KMO and Bartlett's Test Kaiser-Meyer-Olkin Measure of Sampling Adequacy. Bartlett's Test of Sphericity Approx. Chi-Square --------- df Sig. 0.894 0.827 0.827 0.930 1.000 704 225 269 10 000 2.2 Principal components 2.2.1 The number of principal components A useful visual aid to determining an appropriate number of principal components is a scree plot. Figure1 shows a scree plot, for a situation with five principal components. An elbow occurs in the figure1 at about i=3. That is, the eigenvalues after the second factor are all relatively small and about the same size. In this case, it appears, without any other evidence, that two sample principal components effectively summarize the total sample variance. 2.2.2 Summarizing sample variation In table2, the first principal component explains 86.69% of the total sample variance. The first two principal components, collectively, explain 99.102 of the total sample variance. Consequently, sample variation is summarized very well by two principal components and a reduction in the data from 12 observations on 5 observations to 12 observations on 2 principal components is reasonable. 2.2.3 Factor rotation The rationale is very much akin to sharpening the focus of a microscope in order to see the detail more clearly. According to the scree plot, this paper makes two principal components to describe the whole information influencing savings deposits of urban and rural residents. Their eigenvalue are 8.744 1.348 0.729 and 0.126. These four components explain a proportion 99.522 of the total population variance. Especially, the first principal component explains a proportion 79.49% of the total population variance. After factor rotation, the eigenvalue are 3.246 and 1.709, explaining a proportion 64.914 and 34.188 of the total population variance, making a total of 99.102 information of five original components. Therefore, that two sample principal components effectively summarize the total sample variance. % 、 、 % % % 805 % Compo nent Initial Eigenvalues Total 1 2 3 4 5 Figure 1 Table 2 Extraction Sums Loadings 4 621 039 005 001 % of Variance 8 12.412 7.78 102 0.18 of Squared Rotation Sums of Squared Loadings Cumulat Total % of Cumul Total % of Cumul 86 99.102 99.880 99.982 100.000 4 621 8 12.412 86 99.102 3 1.709 6 34.188 6 99.102 2.3 Renamed the principal components through Component Matrix(a) and Rotated Component Matrix(a) It can be seen from Table 4 that, before factor rotation, except for exchange rate, GDP, average wage, household consumption and the population these 4 original components, which represent a country’s economic situation, contribute lots to the first principal component. Their values are all above 0.95. On the other hand, GDP, average wage and household consumption have reverse correlation with the second principal component. And, exchange rate and the population are correlated positively with the second principal component. This includes the value of exchange rate is as far as 0.654, others are all less than 0.3. Obviously, two original principal components contain some same information, which is no good for us to find out the different meanings of different principal factor. Therefore, the factors must be rotated. Base on variance maximization, we rotate the Component Matrix. After rotation, each principal component has a relatively clear economic implications, according to table 4 and figure 2. The first 806 rotated principal component mainly reflects GDP, average wage, household consumption and the population, which represent a country’s economic situation. The second rotated principal component mainly reflects variation about exchange rate. Basically, each original indicator variables has been attributed to one rotated principal component. Can be said that the effect of rotation is still good. It can be seen that savings deposits of urban and rural residents is not only mainly related to the level of country's overall economy, but also relevant to exchange rate of RMB to US dollar. Statistical analysis indicated that two rotated principal components are N (0, 1) random variables and completely irrelevant. So, they are very suitable as factors in savings deposits model. Table 3 Component Matrix (a) Component 1 970 752 954 988 971 GDP exchange rate average wage household consumption population 2 -237 654 -296 -145 168 C omponent Plot in Rotated Space 汇率 1.0 人口总数 C omponent 2 0.5 消费水平 GDP 职工平均工资 0.0 -0.5 -1.0 -1.0 -0.5 0.0 0.5 Component 1 Figure 2 GDP Table 4 Rotated Component Matrix(a) Component 1 2 944 326 807 1.0 exchange rate average wage household consumption population 278 962 909 726 957 268 413 667 3. Construction and Inspection of Savings Deposits Model 3.1Construction of savings deposits model By the analysis, we define country's overall economy situation and exchange rate as two new principal components. And through factor scores, we achieve the values of two common factors, using the original 5 components statistical data of Statistics Yearbook during 1978-2007 of China. Given the two principal components as y1 and y2, and zxi as standardized observation. The factor scores is : f1 = 0.944 zx1 + 0.278 zx2 + 0.962 zx3 + 0.909 zx4 + 0.726 zx5 () f 2 = 0.326 zx1 + 0.957 zx2 + 0.268 zx3 + 0.413zx4 + 0.667 zx5 1 Then, do stepwise linear regression analysis between the two principal components and the dependent variable savings deposits of urban and rural residents. The composite factor score is : y = 0.958 f1 + 0.275 f 2 : Based on the above foundation, construct the principal component deposit mode y =0.958f1 +0.275f2 (2) =0.958(0.944zx1 +0.278zx2 +0.962zx3 +0.909zx4 +0.726zx5)+0.275(0.326zx1 +0.957zx2 +0.268zx3 +0.413zx4 +0.667zx5) =0.994zx1 +0.534zx2 +0.995zx3 +0.984zx4 +0.879zx5 () 3 In (3), we can find that in one hand, the sensitivity of savings deposits of urban and rural residents y to the five factors, GDP, exchange rate, average wage, household consumption and the population, are positive. On the other hand, the weighting of different factors is different. Comparing other four factors, the exchange rate smallest relatives to the weight of the principal component deposit mode, that is, the adjustment of the exchange rate change will not largely impact on the savings deposits of urban and rural residents 3.2 Inspection of savings deposits model Model 1 Model 1 R .996(a) Regression Residual Total Table 5 R Square .993 Model Summary (b) Adjusted R Square .992 Std. Error of the Estimate 4903.88294 Table 6 ANOVA (b) Sum of Squares df Mean Square 51444447616.331 2 25722223808.166 384769086.471 16 24048067.904 51829216702 18 808 Durbin-Watson 1.423 F 1069.617 Sig. .000(a) From Table 5 and Table 6 we can see that the regression equation fit better, and there is a significant linear relationship. The last one DW = 1.423 in table 5 shows residual has no correlation properties Unstandardized Coefficients Table 7 Coefficients (a) Standardized Coefficients Collinearity Statistics Modle Sig t 1(Constant) REGRfactorscoe1 for analysis 1 REGRfactorsce 2 for analysis B Std. Error 64068.868 1125.028 51381.063 1155.856 14765.204 1155.856 Beta Tolerance VIF 56.949 0 .958 44.453 0 1.000 1.000 .958 12.774 0 1.000 1.000 From table 7, we get the fitting regression equation: y = 0.958 f1 + 0.275 f 2 y represents savings deposits and f1 , f 2 , represent two principal components. Each independent variable and dependent variable has a significant linear relationship. The last two columns we can see from the table show variables without collinearity. According foregoing analysis, we can believe the principal component deposit model gained by factor analysis is accurate. 4. Conclusion In this paper, we introduce the factor analysis to integrate and simplify five components GDP, exchange rate of RMB to US dollar, worker average wage, household consumption and the population, and extract 2 common factors with a clear significance of economy, respectively, reflecting the role of the country's overall economic level and exchange rate. Relevant statistical analysis shows that these 2 common factors are very effective. This essay constructs and inspects the principal component deposit model using two rotated principal components. Inspection shows that this essay constructs the principal component deposit model through screening for factor based on factor analysis has a good analysis of results. References [1]. wangwei. Dynamic Correlation Study of Savings, investment and economic growth - based on analysis data of years 1952-2006 [J].Nankai Economic Studies,2008,(2):105—125(in Chinese) 809 [2]. chenliping. 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