计量经济学检验

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 analysis. 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 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 the 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)The 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 to 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 students (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 Explain Here, using the same area (ie, China) time-series data were fitted2. Data collectionTime series data from 1986 to 2005, the specific circumstances are shown in Table 1Table 1：YX1X2X3X41986110371963107507264.4105419871201911112109300276.6106319881127761366111026296.2107519891013391519112704377.910751990930181644114333383.210751991881281893115823352.210751992941642311117171363.9105319931067712998118517420.1106519941279354044119850476.4108019951454435046121121519.6105419961633225846122389552.8103219971763536420123626576.81020199819888567961247615711022199923351371591257865751071200030123978581267435951041200139325686221276276811225200250098093981284537701396200365126010542129227800155220048198961233612998882717312005978610140401307568391792四、Model parameter estimation, inspection and correction1. Model parameter estimation and its economic significance, statistical inference testtwoway(scatter Y X2)twoway(scatter Y X3)twoway(scatter Y X4)graph twoway lfit y X1graph twoway lfit y X2graph twoway lfit y X3graph twoway lfit y X4Y = 59.22454816*X1- 7.158602346*X2- 366.8774279*X3+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 total 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, 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, with 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 correlated. X2, X3 coefficient sign contrary to expectations, which may indicate the existence of severe multicollinearity. 2.计量经济学检验The above table can be seen to explain the positive 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：Y = 60.21976901*X1 - 61096.25048（6.311944） （42959.23） t = (9.540606) (-1.422191)Adjusted R-squared=0.825725 F=91.02316Y = 27.05878289*X2 - 2993786.354 ( 5.622791) (680596.9)t = (4.812340) (-4.398766)R-squared=0.562668 F=23.15862Y = 1231.659997*X3 - 371863.6509 (161.9045) (90051.37)t = (7.607324) (-4.129461)Adjusted R-squared=0.749576 F=57.87138Y = 1053.519847*X4 - 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) (79072.71)t = (15.99648) (-12.20016)Adjusted R-squared=0.930628 F=255.887Y = 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=700.7988Y = 886.3583756*X4 + 8.974091045*X2 - 1852246.686（55.52670） （1.837722） （189180.7）t = （15.96274） （4.883269） （-9.790886）Adjusted R-squared=0.969430 F=302.2581Y = 791.519267*X4 + 436.7502136*X3 - 885870.134（69.64253） （90.10899） （55171.66）t = （11.36546） （4.846910） （-16.05662）Adjusted R-squared=0.969163 F=299.5666By the data analysis, comparison, per capita GDP of the new entrants to the X1 equation of the Adjusted R-squared = .986606, The largest improvement, and each parameter, T-test significant, so I chose to retain the X1Then add the other new variables to the stepwise regression:Y = 570.3757921*X4 + 53.53863254*X1 - 12.18901747*X2 + 777507.8381（46.57535） （6.618152） （2.747500） （336370.1）t = （12.24630） （8.089665） （-4.436403） （2.311466）Adjusted R-squared=0.994626 F=987.1753Through analysis, we can find: add a new variable X2, X2 coefficient - 12.18901747, indicating a negative correlation between X2 and Y, but in the real economic significance, X2 total population, and Y number of graduate studentsa positive correlation between the more general economic significance of the total population, the absolute amount of the number of graduate student will be more. So, X2, should be removed.Y = 700.5113451*X4 + 53.63805156*X1 - 597.614061*X3 - 534866.1749 （33.11564） （6.480707） （131.3478） （49101.16）t = （12.24630） （ 8.089665） （-4.436403） （2.311466）Adjusted R-squared=0.994626 F=987.1753Similarly, adding a new variable X3, its parameter estimate is still negative, X3, represented by the number of unemployment in urban areas, the economic significance, the more unemployment in urban areas, will encourage more and more people go to PubMed in order to achieveimprove their own quality, employability and opportunities. So, in reality, the two should be positively correlated, it should be removed X33.White testFinal results of a series of inspection and correction：Y = -51055.44688 + 66.53070046*X1 + 382.1680346*X4（9052.520）（9.443438）（78.77833）t = （-5.639916） （7.045178） （4.851182）Adjusted R-squared=0.921287 F=106.33951.627477五、Analysis and conclusions of the modelIt can be seen from the model:(1) model: significantly correlated only with colleges and universities total and per capita GDP in the total number of graduate students.(2) X1, X4 is in line with economic significance of the test. Economic sense, the total number of graduate students with the increase in per capita GDP increases, the increase with the increase in the total number of universities. And universities is the total impact of the total number of the most important factor in the graduate students.(3) the amendment of the model coefficient of determination and F values are very high goodness of fit of the model is good