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1、研究生考試錄取相關(guān)因素的實驗報告一， 研究目的通過對南開大學(xué)國際經(jīng)濟研究所1999級研究生考試分數(shù)及錄取情況的研究，引入錄取與未錄取這一虛擬變量，比較線性概率模型與Probit模型，Logit模型，預(yù)測正確率。二， 模型設(shè)定表1，南開大學(xué)國際經(jīng)濟研究所1999級研究生考試分數(shù)及錄取情況見數(shù)據(jù)表obsYSCOREobsYSCOREobsYSCORE114013403326702752140135033268027331392360332690273413873703317002725138438033071026761379390328720266713784003287302638137841

2、032874026191376420321750260101371430321760256111362440318770252121362450318780252131361460316790245140359470308800243150358480308810242161356490304820241170356500303830239180355510303840235190354520299850232200354530297860228210353540294870219220350550293880219230349560293890214240349570292900210250

3、348580291910204260347590291920198270347600287930189280344610286940188290339620286950182300338630282960166310338640282970123320336650282330334660278定義變量SCORE ：考生考試分數(shù)；Y ：考生錄取為1，未錄取為0。 上圖為樣本觀測值。1 線性概率模型根據(jù)上面資料建立模型用Eviews得到回歸結(jié)果如圖：Dependent Variable: YMethod: Least SquaresDate: 12/10/10 Time: 20:38Sample:

4、 1 97Included observations: 97VariableCoefficientStd. Errort-StatisticProb.  C-0.8474070.159663-5.3074760.0000SCORE0.0032970.0005216.3259700.0000R-squared0.296390    Mean dependent var0.144330Adjusted R-squared0.288983    S.D. dependent var0.353250S.

5、E. of regression0.297866    Akaike info criterion0.436060Sum squared resid8.428818    Schwarz criterion0.489147Log likelihood-19.14890    F-statistic40.01790Durbin-Watson stat0.359992    Prob(F-statistic)0.000000參數(shù)估計結(jié)果為：

6、-0.847407+0.003297 Se=(0.159663)( 0.000521) t=(-5.307476) (6.325970) p=(0.0000) (0.0000) 預(yù)測正確率：Forecast: YFActual: YForecast sample: 1 97Included observations: 97Root Mean Squared Error0.294780Mean Absolute Error     0.233437Mean Absolute Percentage Error8.689503Theil Inequa

7、lity Coefficient 0.475786     Bias Proportion        0.000000     Variance Proportion 0.294987     Covariance Proportion 0.7050132.Logit模型Dependent Variable: YMethod: ML

8、- Binary Logit (Quadratic hill climbing)Date: 12/10/10 Time: 21:38Sample: 1 97Included observations: 97Convergence achieved after 11 iterationsCovariance matrix computed using second derivativesVariableCoefficientStd. Errorz-StatisticProb.  C-243.7362125.5564-1.9412480.0522SCORE0.6794410.3

9、504921.9385360.0526Mean dependent var0.144330    S.D. dependent var0.353250S.E. of regression0.115440    Akaike info criterion0.123553Sum squared resid1.266017    Schwarz criterion0.176640Log likelihood-3.992330    Hanna

10、n-Quinn criter.0.145019Restr. log likelihood-40.03639    Avg. log likelihood-0.041158LR statistic (1 df)72.08812    McFadden R-squared0.900282Probability(LR stat)0.000000Obs with Dep=083     Total obs97Obs with Dep=114得Logit模型估計結(jié)果如下 pi

11、 = F(yi) = 拐點坐標 (358.7, 0.5)其中Y=-243.7362+0.6794X預(yù)測正確率Forecast: YFActual: YForecast sample: 1 97Included observations: 97Root Mean Squared Error0.114244Mean Absolute Error     0.025502Mean Absolute Percentage Error1.275122Theil Inequality Coefficient 0.153748  

12、;   Bias Proportion        0.000000     Variance Proportion 0.025338     Covariance Proportion 0.9746623.Probit模型Dependent Variable: YMethod: ML - Binary Probit (Quadratic hill climbing

13、)Date: 12/10/10 Time: 21:40Sample: 1 97Included observations: 97Convergence achieved after 11 iterationsCovariance matrix computed using second derivativesVariableCoefficientStd. Errorz-StatisticProb.  C-144.456070.19809-2.0578330.0396SCORE0.4028680.1961862.0535040.0400Mean dependent var0.

14、144330    S.D. dependent var0.353250S.E. of regression0.116277    Akaike info criterion0.122406Sum squared resid1.284441    Schwarz criterion0.175493Log likelihood-3.936702    Hannan-Quinn criter.0.143872Restr. log likel

15、ihood-40.03639    Avg. log likelihood-0.040585LR statistic (1 df)72.19938    McFadden R-squared0.901672Probability(LR stat)0.000000Obs with Dep=083     Total obs97Obs with Dep=114Probit模型最終估計結(jié)果是 pi = F(yi) = F (-144.456 + 0.4029 xi) 拐點

16、坐標 (358.5, 0.5)預(yù)測正確率Forecast: YFActual: YForecast sample: 1 97Included observations: 97Root Mean Squared Error0.115072Mean Absolute Error     0.025387Mean Absolute Percentage Error1.216791Theil Inequality Coefficient 0.154476     Bias Proportion        0.000084     Variance Proportion 0.020837     Covariance Proportion 0.979080預(yù)測正確率結(jié)論：線性概率模型RMSE=0.294780 MAE=0.233437 MAPE=8.689503 Logit模型 RMSE=0.114244

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