1、Graduates to apply for the quantitative analysis of changes in number of graduate students一 Topics raisedIn this paper, the total number of students from graduate students (variable) multivariate analysis (see below) specific analysis, and collect relevant data, model building, this quantitative ana
2、lysis. The number of relations between the school the total number of graduate students with the major factors, according to the size of the various factors in the coefficient in the model equations, analyze the importance of various factors, exactly what factors in changes in the number of graduate
3、 students aspects play a key role in and changes in the trend for future graduate students to our proposal.The main factors affect changes in the total number of graduate students for students are as follows：Per capita GDP - which is affecting an important factor to the total number of students in t
4、he graduate students (graduate school is not a small cost, and only have a certain economic base have more opportunities for post-graduate)The total population - it will affect the total number of students in graduate students is an important factor (it can be said to affect it is based on source)Th
5、e number of unemployed persons - this is the impact of a direct factor of the total number of students in the graduate students (it is precisely because of the high unemployment rate, will more people choose Kaoyan will be their own employment weights)Number of colleges and universities - which is t
6、o influence precisely because of the emergence of more institutions of higher learning in the school the total number of graduate students is not a small factor (to allow more people to participate in Kaoyan)二 Establish Model Y=+1X1+2X2+3X3+4X4 +uAmong them, theY-in the total number of graduate stud
7、ents (variable)X1 - per capita GDP (explanatory variables)X2 - the total population (explanatory variables)X3 - the number of unemployed persons (explanatory variables)X4 - the number of colleges and universities (explanatory variables)三、Data collection1. date ExplainHere, using the same area (ie, C
8、hina) time-series data were fitted2. Data collectionTime series data from 1986 to 2005, the specific circumstances are shown in Table 1Table 1：Y X1 X2 X3 X41986 110371 963 107507 264.4 10541987 120191 1112 109300 276.6 10631988 112776 1366 111026 296.2 10751989 101339 1519 112704 377.9 10751990 9301
9、8 1644 114333 383.2 10751991 88128 1893 115823 352.2 10751992 94164 2311 117171 363.9 10531993 106771 2998 118517 420.1 10651994 127935 4044 119850 476.4 10801995 145443 5046 121121 519.6 10541996 163322 5846 122389 552.8 10321997 176353 6420 123626 576.8 10201998 198885 6796 124761 571 10221999 233
10、513 7159 125786 575 10712000 301239 7858 126743 595 10412001 393256 8622 127627 681 12252002 500980 9398 128453 770 13962003 651260 10542 129227 800 15522004 819896 12336 129988 827 17312005 978610 14040 130756 839 1792四、Model parameter estimation, inspection and correction1. Model parameter estimat
11、ion and its economic significance, statistical inference test. twoway(scatter Y X1)020004000600080001.0e+06Y0 500 100 1500X1twoway(scatter Y X2)020004000600080001.0e+06Y10500 100 1500 1200 12500 1300X2twoway(scatter Y X3)020004000600080001.0e+06Y20 40 60 80X3twoway(scatter Y X4)020004000600080001.0e
12、+06Y100 120 140 160 180X4graph twoway lfit y X102000400060008000Fited values0 500 100 1500X1graph twoway lfit y X2-20000200040006000Fited values10500 100 1500 1200 12500 1300X2graph twoway lfit y X302000400060008000Fited values20 40 60 80X3graph twoway lfit y X4020004000600080001000Fited values100 1
13、20 140 160 180X4_cons 270775.2 369252.9 0.73 0.475 -516268.7 1057819X4 621.3348 46.72257 13.30 0.000 521.748 720.9216X3 -366.8774 157.9402 -2.32 0.035 -703.5189 -30.23585X2 -7.158603 3.257541 -2.20 0.044 -14.10189 -.2153182X1 59.22455 6.352288 9.32 0.000 45.68496 72.76413Y Coef. Std. Err. t P|t| 95%
14、 Conf. IntervalTotal 1.3040e+12 19 6.8631e+10 Root MSE = 18535Adj R-squared = 0.9950Residual 5.1533e+09 15 343556320 R-squared = 0.9960Model 1.2988e+12 4 3.2471e+11 Prob F = 0.0000F( 4, 15) = 945.14Source SS df MS Number of obs = 20. reg Y X1 X2 X3 X4Y = 59.22454816*X1- 7.158602346*X2- 366.8774279*X
15、3+621.3347694*X4 （6.352288） （3.257541） （157.9402） （46.72256） t= （9.323341 ） （-2.197548） （-2.322889 ） （13.29839） + 270775.151（369252.8）（0.733306）R2=0.996048 Adjusted R-squared =0.994994 F=945.1415 DW=1.596173Visible, X1, X2, X3, X4 t values are significant, indicating that the per capita GDP, the tot
16、al population of registered urban unemployed population, the number of colleges and universities are the main factors affecting the total number of graduate students in school. Model coefficient of determination for 0.996048 amendments coefficient of determination of 0.994994, was relatively large,
17、indicating high degree of model fit, while the F value of 945.1415, indicating that the model overall is significant。In addition, the coefficient of X1, X4, in line with economic significance, but the coefficient of X2, X3, does not meet the economic significance, because from an economic sense, wit
18、h the increase in the total population (X2), the total number of graduate students should be increased, and due to the increase in the number of unemployed, there will be more and more people choose graduate school, so that the total number of unemployed and graduate students should be positively co
19、rrelated. X2, X3 coefficient sign contrary to expectations, which may indicate the existence of severe multicollinearity. 2.计量经济学检验X4 0.8021 0.6165 0.7762 1.0000X3 0.9808 0.9593 1.0000X2 0.9422 1.0000X1 1.0000X1 X2 X3 X4(obs=20). corr X1 X2 X3 X4. X4 0.7762 1.0000 X3 1.0000X3 X4(obs=20). corr X3 X4X
20、4 0.6165 1.0000 X2 1.0000X2 X4(obs=20). corr X2 X4X3 0.9593 1.0000 X2 1.0000X2 X3(obs=20). corr X2 X3X4 0.8021 1.0000 X1 1.0000X1 X4(obs=20). corr X1 X4X3 0.9808 1.0000 X1 1.0000X1 X3(obs=20). corr X1 X3X2 0.9422 1.0000 X1 1.0000X1 X2(obs=20). corr X1 X2The above table can be seen to explain the pos
21、itive correlation between the height of the variable X1 and X2, X3, X4, X2, X1, X3, between the highly positively correlated, showing that there is serious multicollinearity. Following amendment stepwise regression：_cons -61096.25 42959.23 -1.42 0.172 -151350.3 29157.75X1 60.21977 6.311944 9.54 0.00
22、0 46.95887 73.48067 Y Coef. Std. Err. t P|t| 95% Conf. Interval Total 1.3040e+12 19 6.8631e+10 Root MSE = 1.1e+05 Adj R-squared = 0.8257Residual 2.1529e+11 18 1.1961e+10 R-squared = 0.8349 Model 1.0887e+12 1 1.0887e+12 Prob F = 0.0000F( 1, 18) = 91.02 Source SS df MS Number of obs = 20. reg Y X1Y =
23、60.21976901*X1 - 61096.25048（6.311944） （42959.23）t = (9.540606) (-1.422191)Adjusted R-squared=0.825725 F=91.02316_cons -2993786 680596.9 -4.40 0.000 -4423667 -1563905X2 27.05878 5.622791 4.81 0.000 15.24574 38.87183 Y Coef. Std. Err. t P|t| 95% Conf. Interval Total 1.3040e+12 19 6.8631e+10 Root MSE
24、= 1.8e+05 Adj R-squared = 0.5384Residual 5.7028e+11 18 3.1682e+10 R-squared = 0.5627 Model 7.3371e+11 1 7.3371e+11 Prob F = 0.0001F( 1, 18) = 23.16 Source SS df MS Number of obs = 20. reg Y X2Y = 27.05878289*X2 - 2993786.354( 5.622791) (680596.9)t = (4.812340) (-4.398766)R-squared=0.562668 F=23.1586
25、2_cons -371863.7 90051.37 -4.13 0.001 -561054.6 -182672.8X3 1231.66 161.9045 7.61 0.000 891.5113 1571.809 Y Coef. Std. Err. t P|t| 95% Conf. Interval Total 1.3040e+12 19 6.8631e+10 Root MSE = 1.3e+05 Adj R-squared = 0.7496Residual 3.0936e+11 18 1.7187e+10 R-squared = 0.7628 Model 9.9463e+11 1 9.9463
26、e+11 Prob F = 0.0000F( 1, 18) = 57.87 Source SS df MS Number of obs = 20. reg Y X3Y = 1231.659997*X3 - 371863.6509(161.9045) (90051.37)t = (7.607324) (-4.129461)Adjusted R-squared=0.749576 F=57.87138_cons -964699.8 79072.71 -12.20 0.000 -1130825 -798574.2X4 1053.52 65.85948 16.00 0.000 915.1542 1191
27、.885 Y Coef. Std. Err. t P|t| 95% Conf. Interval Total 1.3040e+12 19 6.8631e+10 Root MSE = 69000 Adj R-squared = 0.9306Residual 8.5699e+10 18 4.7610e+09 R-squared = 0.9343 Model 1.2183e+12 1 1.2183e+12 Prob F = 0.0000F( 1, 18) = 255.89 Source SS df MS Number of obs = 20. reg Y X4Y = 1053.519847*X4 -
28、 964699.7964(65.85948) (79072.71)t = (15.99648) (-12.20016)Adjusted R-squared=0.930628 F=255.8874The analysis shows that the four simple regression model, the total number of graduate students for the linear relationship between Y college x4, goodness of fit：Y = 1053.519847*X4 - 964699.7964(65.85948
29、) (79072.71)t = (15.99648) (-12.20016)Adjusted R-squared=0.930628 F=255.887_cons -708247.7 45496.23 -15.57 0.000 -804236.4 -612259.1X1 25.58238 2.930053 8.73 0.000 19.40051 31.76425 X4 714.1694 48.45708 14.74 0.000 611.9339 816.4049Y Coef. Std. Err. t P|t| 95% Conf. IntervalTotal 1.3040e+12 19 6.863
30、1e+10 Root MSE = 30318 Adj R-squared = 0.9866Residual 1.5627e+10 17 919210968 R-squared = 0.9880 Model 1.2884e+12 2 6.4418e+11 Prob F = 0.0000F( 2, 17) = 700.80 Source SS df MS Number of obs = 20. reg Y X4 X1Y = 714.1694264*X4 + 25.58237739*X1 - 708247.7381（48.45708） （2.930053） （45496.23）t = （14.73818 ） （8.731029 ） （-15.56718）Adjusted R-squared=0.986606 F=700.7988
