相關(guān)性系數(shù)確定的舉例

解題過程：首先利用stata軟件生成1000個X~N(1,1)隨機數(shù)列，隨機誤差服從N(0,1)，畫出x、y之間的散點圖，大體確定x與y之間的關(guān)系，模型假設(shè)，模型求解、最后模型檢驗與分析。生成的隨機數(shù)列以附件的形式出現(xiàn)。數(shù)據(jù)生成在stata中利用命令Setobs1000Genx=rnormal(1,1) 隨機生成服從均勻分布xGena=rnormal(0,1) 隨機生成服從均勻分布ageny=5+exp(2-x/3)+a 生成y程序代碼為：setobs1000numberofobservations(_N)was0,now1,000.genx=rnormal(1,1).gena=rnormal(0,1).geny=5+exp(2-x/3)+a.twoway(scyx)(lfityx)生成的圖形1如下：圖1

twoway(scyx)(qfityx)生成的圖形2為：05-2024xyFittedvalues05-2024xyFittedvalues圖2仔細分析對比圖1和圖2，圖1可近似的看成一條直線為線性函數(shù)，則假設(shè)線性模型y=a+bx命令：regyx,beta線性回歸結(jié)果如下：SourceSSdfMSNumberofobs=1,000F(1,998)= 3391.41Model3631.2406213631.24062Prob>F=0.0000Residual1068.576359981.07071778R-squared= 0.7726AdjR-squared= 0.7724Total4699.816979994.70452149RootMSE= 1.0348yCoef?Std?Err.tP>|t|Betax-1.923055.0330219-58.240.000-.8789963cons12.53779.0454848275.650.000—其中R2=0.7726，此時模型為y=12.53779-1.923055x，同時顯著性較高。而圖2明顯為一條曲線，因此我們可以構(gòu)建非線性模型，假設(shè)模型為：命令：nl(y=+exp({c}-x/{d=1})),r回歸結(jié)果為：Iteration0: residual SS = 8574.635Iteration1: residual SS = 961.9622Iteration2: residual SS = 927.7956Iteration3: residual SS = 922.1981Iteration4: residual SS = 922.1225Iteration5: residual SS = 922.1225Iteration6: residual SS = 922.1225NonlinearregressionNumberofobs=1,000R-squared=0.8038AdjR-squared=RootMSE =0.8034.96171572756.8Res.dev. =yCoef?RobustStd?Err.tP>lt|[95%Conf.Interval]/b4.309573.51614428.350.0003.296725.322427/c2.095857.066238831.640.0001.9658732.22584/d3.353167.249961713.410.0002.8626553.843678Parameterbtakenasconstantterminmodel其中R2=0?8034,大于0.7726，明顯