I. Economic background
To promote the sound and rapid development of China's economy and society, one of the fundamental ways out is to increase the gross national income, improve the consumption capacity of residents, comprehensively expand domestic consumption demand, and vigorously enhance the pulling effect of consumption on the economy. At the same time, because China is a populous country, although it has a vast territory and abundant resources, its per capita is very small, so the industrial structure of China plays a vital role in improving people's living standards and increasing people's total income.
Second, the experimental project data
Note: The difference between gross national income (formerly called gross national product) and GDP after 1. 1.980 is the net income of foreign factors.
2. The data from 2005 to 2008 were revised after the second economic census. 3. The data comes from China Statistical Network.
Third, the experimental process
Using EViews software, Yt, X 1, X2, X3, X4 and other data are generated and used in OLS regression of the model. The result is shown in the figure.
OLS regression result
Dependent variable: Y method: least square method Date: 07/03/1Time: 09:42 Sample:1978 Observed value in 2009: 32.
The variable C X 1 X2 X3 X4.
R square
Adjustment of Logarithmic Likelihood of Regression Square Sum Residual R Square Standard Deviation Durbin-Watson Statistics
Coefficient is 845.40851.1089741.4196401.194270-3.8016/kloc.
Std。 Error: 226.3306 0.327668 0.184656 0.158157 2.50086.000000000005
T statistic 3.7352813.384467.68801.551.655438+0.61.553589.
Prob。 0.0009 0.0022 0.0000 0.0000 0. 13 19
0.999983 mean dependent variable 80630.86 0.999980 standard deviation dependent variable 4 19.3736 Akeke information criterion47486686 Schwartz standard -235.9280 F- statistic 0.593024 probability (F- statistic)
94720.64 15.05800 15.28702 395349.6 0.000000
(A) multivariate * * * linear analysis
2=0.999980 can determine that the coefficient is very high. As can be seen from the above figure, the model R2=0.999983, and the RF and RF test values are 395349.6, which is obviously significant. But when α=0.05, tα 2 n? k =t0.025 32？ 5 = 2.05, the coefficient t test of X4 is not significant, and the sign of x4 coefficient is contrary to the expectation, indicating that there may be serious multiple * * * linearity.
Calculate the correlation coefficient of explanatory variables, and select the data of X 1, X2, X3 and X4.
Correlation coefficient matrix
The variable X 1 X2 X3 X4
X 1
1
0.[ 1**********]7
X2 X3 X4
0.[ 1**********]
0.[ 1**********]7 0.[ 1**********] 1
1
0.[ 1**********]3 0.[ 1**********]2
1
0.[ 1**********] 1
1
0.[ 1**********] 1 0.[ 1**********]3 0.[ 1**********]
0.[ 1**********]2 0.[ 1**********] 1
From the correlation coefficient matrix, we can see that the correlation coefficient between explanatory variables is high, which is to determine that there is serious multilinear. Improved multiple * * * linearity
Stepwise regression method is used to test and solve multiple linear problems. Univariate regression was conducted from Yt to X 1, X2, X3 and X4 respectively, and the results are shown in the table.
Unary regression estimation results
Variable parameter estimation test statistics
X 1
9.430853 27. 17066 0.960950
X2
2. 13629 1 263.6278 0.999569
X3
2.354594 124.7 173 0.998075
X4
13.40040 207.0753 0.99930 1
R2
2 R
0.959648 0.999554 0.9980 1 1 0.999278
Among them, R2 of the equation added with X2 is the largest, and based on X2, other variables are added in turn for stepwise regression. The results are shown in the table.
Regression results of new variables (1)
2=0.999867, the biggest improvement, and the t test of each parameter is significant. After comparison, the newly added X3 equation R.
Select to keep X3, and then add other variables for stepwise regression. The results are shown in the table.
2 has increased. When X4 is increased, the significance of parameter t-test of RX3 decreases, while that of parameter t-test of X2 increases. As can be seen from the correlation coefficient, it is highly correlated with other variables, indicating that multiple * * * linearities mainly caused by X4 have been eliminated.
Finally, after correcting the serious multiple linear effects, the regression results are as follows.
y = 59 1.00299 19+ 1. 139730888 * X2+0.955463758 * X3+0.605 1508553 * x 1①(3.690685)(27.48452)(24.89492)(65433)
2 = 0.999979f = 50 1 797.7r2 = 0.999981r (2) heteroscedasticity analysis1,heteroscedasticity test.
Under the premise that there is no multiple * * * linearity in the model, the common method to test whether there is heteroscedasticity in the model is white test. Rubiao
White heteroscedasticity test:
F statistical Obs*R square
Test equation:
6.064554 probability 18.96799 probability
0.000505 0.0042 18
Dependent variable: RESID^2 Method: Least Square Method Date: 07/03/1Time: 12:57 Sample:1978 Observed value in 2009: 32.
Variable cx2x2 2x3 x3 2x1
Coefficient-76332.51-64.358148.32e-05 57.56226 9.59e-05122.9346.
Std。 Error 82000.52 32.48058 0.00016426.802180.00015745.59709.
T statistic-0.930878-1.981435 0.5081802.1476710.61282.
Prob。 0.3608 0.0586 0.6 158 0.04 16 0.5465 0.0 124
X 1^2
R square
Adjustment of Logarithmic Likelihood of Regression Square Sum Residual R Square Standard Deviation Durbin-Watson Statistics
-0.004940 0.00 1798 -2.747488 0.0 1 10
0.592750 mean dependent variable161659.4 0.495010 standard deviation dependent variable14719.5 Akek information criterion 5.41e+.
207027.9 26.82652 27. 147 15 6.064554 0.000505
The white statistic is 18.97, and the p value is 0.0042.
Use the weighted least square method to correct heteroscedasticity, and make regression estimation again, as follows:
Dependent variable: Y method: least square method Date: 07/03/1Time: 13:27 Sample:1978 Observed value included in 2009: 32 weighted series: W.
Variable C X2 X3 X 1
Coefficient: 563.73031.130448 0.90552 0.50552.50555555556
Std。 Error 23.12909 0.027184 0.05609 0.50609.50609888886
Statistics t- 24.37321.41.5854333337.500353366
Prob。 0.0000 0.0000 0.0000 0.0000
Weighted statistical r square
Adjusted R-squared standard deviation of regression and mean square residual log likelihood
Adjusted R-squared standard deviation of Durbin-Watson statistical regression
1.000000 The mean dependent variable is 44275.181.00000005 The standard deviation dependent variable is 65.07 13 1 Akek information criterion11.
10 1268.5 1 1.3053 1 1 1.48853 26627690 0.000000
0.9998 1 mean dependent variable 80630.86 0.999979 standard deviation dependent variable 434.0380 square sum residual 0.574698
94720.64 5274892.
White heteroscedasticity test: f statistical Obs*R square
0.8579 17 probability 5.46805 probability
0.538692 0.485842
The regression expression of the weighted estimation result of eliminating heteroscedasticity is as follows:
y = 563.7302685+ 1. 130448032 * X2+0.9605520007 * X3+0.6279040845 * x 1②(24.3732 1)(4 1.58543)(37.50824)(26.892565445)
autocorrelation analysis
The method to test whether there is autocorrelation in the model is graphic method or D-W test method. 1, autocorrelation test
As can be seen from the figure below, the random interference term presents positive sequence correlation.
2. autocorrelation DW test
At the significance level of 5%, n=32, k=3, dl= 1.244, du = 1.650, because DW=0.79.
The generalized difference method and Cochrane-Orcott iteration method are used for autocorrelation processing. The estimated results of generalized difference of order 1 are as follows:
Dependent variable: y
Methods: Least square method Date: 07/03/1Time: 14:04 Sample (after adjustment): 1979 2009.
Included observations: 3 1 After adjusting the endpoint, convergence is achieved after 25 iterations.
Variable C X2 X3 X 1 AR( 1)
R square
Adjustment of Logarithmic Likelihood of Regression Square Sum Residual R Square Standard Deviation Durbin-Watson stat Inversion of AR Root
Coefficient: 4.8123301.0450641.027800 0.38000.00000000001
Std。 Error 694.1465 0.031463 0.07804 0.074683 0.105436
T statistic 0.006933 33.21578 36.9653210.2408.341099.
Prob。 0.9945 0.0000 0.0000 0.0000 0.0000
0.999992 mean dependent variable var 83114.26 0.999991standard deviation dependent variable var 280.7507 Akek information criterion 2049344. Schwartz standard -2 16 .0223 F statistics 1.846 127 probability (f statistics) .88
9522 1.50 14.25950 14.49079 862752.9 0.000000
DW= 1.85, indicating that there is no autocorrelation. There is no autocorrelation in the modified model, and the equation of the model is:
y = 4.8 12330 108+ 1.04506438 * X2+ 1.0278002 18 * X3+0.765038867 * x 1③(0.006933)(33.2 1578)(36.96532)(632)
2 = 0.99999 1 F = 862752.9 R2 = 0.999992 R
Fourth, the economic significance analysis of the model
2=0.99999 1, which shows that the fitting degree of the equation is very good. It can be seen from Equation ③ that R2 = 0.999992r
F=862752.9 This equation is significant. The value of t test is also significant, indicating that the explanatory variables are significant for y respectively.
According to the equation, when other explanatory variables remain unchanged, every unit of X2 changes, the corresponding GNI y will also change by 1.045438 units on average; Every time X3 changes by one unit, the corresponding GNI Y will also change by 1.438+08 units on average; Every time X 1 changes by one unit, the corresponding GNI Y changes by 0.7867 units on average. It can be seen that from 1978 to 2009, with the increase of output value of various industries, the gross national income is also rising, among which the secondary industry has the greatest influence on gross national income, followed by the tertiary industry and the primary industry. The secondary industry such as industry still dominates, the tertiary industry has surpassed the primary industry, and the tertiary industry is also rising. The country is also slowly improving the industrial structure of China and supporting the rise of the tertiary industry.
Verb (abbreviation of verb) policy suggestion
(1) From the perspective of industrial structure, accelerate scientific and technological progress. Science and technology is the primary productive force, and its contribution to national economic growth is increasingly prominent. It is necessary to increase investment in science and technology, increase efforts to tackle key problems in production technology and technology, and actively support the rise of the tertiary industry. According to the requirements of Scientific Outlook on Development, we should pay more attention to the optimization of economic structure and the improvement of economic benefits.
(2) From the point of view of environmental pollution, the government of China should attach importance to promoting the development of conservation-oriented and environment-friendly economy, building a conservation-oriented and environment-friendly society, and give up the rapid growth at the expense of high input, high consumption and high pollution.