數(shù)學建模,教師的薪金

數(shù)學建模,教師的薪金數(shù)學建模,教師的薪金數(shù)學建模,教師的薪金數(shù)學建模,教師的薪金編制僅供參考審核批準生效日期地址：電話：傳真:郵編:昆明理工大學第六屆大學生數(shù)學建模競賽承諾書我們仔細閱讀了昆明理工大學大學生數(shù)學建模競賽的競賽規(guī)則。我們完全明白，在競賽開始后參賽隊員不能以任何方式（包括電話、電子郵件、網(wǎng)上咨詢等）與隊外的任何人研究、討論與賽題有關的問題。我們知道，抄襲別人的成果是違反競賽規(guī)則的。如果引用別人的成果或其他公開的資料（包括網(wǎng)上查到的資料），必須按照規(guī)定的參考文獻的表述方式在正文引用處和參考文獻中明確列出。我們鄭重承諾，嚴格遵守競賽規(guī)則，以保證競賽的公正、公平性。如有違反競賽規(guī)則的行為，我們將受到嚴肅處理。評閱編號（由組委會評閱前進行編號）：

昆明理工大學第六屆大學生數(shù)學建模競賽評閱專用頁評閱編號（由組委會評閱前進行編號）：評閱記錄（供評閱時使用）：評閱人評分備注總分大學教師薪金模型一、摘要：模型一：利用Matlab建立X1--X7與Z（薪金）的線性關系，得到散點圖與一般的線性回歸模型（模型一），模型如下：模型二：由模型一整體效果與StepwiseTable圖推斷部分變量對Z（薪金）的影響并不顯著，由殘差分析法篩選出影響明顯的變量X1、X4，將他們的平方項與交互項加入建立新的回歸模型（模型二），模型如下：得到R2，F(xiàn),P，與模型一相比較。模型一調(diào)用原始參數(shù)較全，但回歸性差，模型二只啟用影響明顯的變量，回歸模型更為顯著，可靠度更高。于是得出：教師的薪金與工作時間、學歷關系明顯，與性別、是否受雇于重點大學、是否接受過培訓的關系較小，即女教師沒有受到不公正的待遇，婚姻狀況也不會影響收入。關鍵詞：回歸分析，互交作用，圖形結(jié)合，殘值分析法。

二、問題重述：某地人事部門為研究中學教師的薪金與他們的資歷、性別、教育程度及培訓情況等因素之間的關系，要建立一個數(shù)學模型，分析人事策略的合理性，特別是考察女教師是否受到不公平的待遇，以及她們的婚姻狀況是否會影響收入。要求從當?shù)亟處熤须S機選了3414位進行觀察后，從中所保留的90個觀察對象的數(shù)據(jù)進行分析。（1）進行變量，建立變量與的回歸模型的關系，說明教師薪金與哪些變量的關系密切，是否存在性別和婚姻狀況上的差異。（2）除了變量本身之外，嘗試將它們的平方項或交叉項加到模型中，建立更好的模型。三、模型假設：1、該地區(qū)的人事部門對中學教師的薪金調(diào)查是可信的；2、各參數(shù)對薪金的影響呈線性關系；3、工作時間、性別、教育程度及培訓情況之間相互獨立，沒有交互作用；四、符號說明：Z：月薪（元）；X1：工作時間（月）；X2：1男性，女性；X3：1男性或單身女性，0已婚女性；X4：學歷（取值0-6，值越大表示學歷越高）；X5：1受雇于重點大學，0其它；X6：1受過培訓的畢業(yè)生，0未受過培訓的畢業(yè)生或受過培訓的肄業(yè)生；X7：1已兩年以上未從事教學工作，0其它。五、分析與建立模型：首先,調(diào)用所有相關變量,運用Matlab分別得到，Z與X1--X7之間的關系及散點圖,由此知Z與各變化量呈線性關系，于是可以建立線性回歸模型：Z（薪金）為因變量,X1--X7分別表示對Z的值產(chǎn)生影響的各個變量,表示回歸系數(shù),表示隨機變量.用Matlab求解模型（見附錄），得到的值與置信區(qū)間如下：參數(shù)參數(shù)估計值置信區(qū)間1.1311[1.02681.2353]0.0027[0.00230.0031]-0.0229[-0.14320.0974]0.0094[-0.10050.1193]0.1089[0.02960.1882]0.0385[-0.06700.1440]0.1817[-0.05070.4142]0[00]=0.7889F=51.6934P=0表一由上表中=0.7889可以知道薪金（）的78.89%可由模型確定,由P=0遠小于0.05,模型從整體上看是成立的,但是還可以看到一個問題，即些部分的置信區(qū)間包含0點,因此我們可以知道這些變量對因變量的影響是不顯著的.在Matlab中運行stepwise命令得到下圖：由圖可知，在模型中對因變量的影響是不顯著的.于是只保留，并將它們的交互項和平方項加入，建立逐步線性回歸方程如下：然后使用Matlab求解模型（程序見附錄），得到值與置信區(qū)間如下：參數(shù)參數(shù)估計值置信區(qū)間6.9026[6.85576.9496]0.0043[0.00370.0049]0.1746[0.10730.2419]-0.0001[-0.00030.0001]-0.0000[-0.0000-0.0000]-0.0228[-0.0371-0.0085]=0.9008F=152.6081P=0通過新建模型中得到的數(shù)據(jù),可以看到明顯提高,薪金的90.08%可由模型確定.遠小于0.05,F遠超過臨界值，回歸模型更為顯著，可靠度增高.然后進行殘差分析，在Matlab中運行命令rcoplot得到殘差圖如下：由圖可知,除個別數(shù)據(jù)外,其他數(shù)據(jù)的殘差離零點均較近,且殘差的置信區(qū)間都包含零點.這說明回歸模型能較好地符合原始數(shù)據(jù)，而個別異常點可以忽略.六、模型的評價優(yōu)點:該方案實用簡單，可行性強，模型簡單，易于理解。模型一首先用簡單的線性規(guī)劃進行分析.結(jié)構(gòu)簡單，計算方便，有利于對相似問題進行求解和對模型進行擴充。模型二的建立是從一般問題到特殊問題的發(fā)展過程.根據(jù)已知的數(shù)據(jù)，從常識和經(jīng)驗進行初步分析，并運用了逐步線性回歸方法以及輔作散點圖，決定取那幾個回歸變量及它們的函數(shù)形式.把對影響不顯著的變量（）予以排除，又運用殘值分析法建立新的回歸模型.使得精確值增高，模型更合理.缺點：1該模型在處理此問題時有假設與理想化的思想，與實際問題的求解還有所差距.比如所求模型結(jié)果只達到了模型設想的80%左右.七、參考文獻【01】趙靜，數(shù)學建模與數(shù)學實驗，北京，高等教育出版社，2003【02】蘇彥華，MATLAB7.0從入門到精通，北京，人民郵電出版社，2010

八、附錄：薪金模型數(shù)據(jù)表：編號ZX1X2X3X4X5X6X7199870000002101514110000310281811010041250191100005102819010100610281900000071018270000018107230000000912903011000010120430010000111352310120101212043100010013110438000000141118411100001511274200000016125942110100171127421100001811274200010019109547000001201113520000012114625201201022118254110000231404540001002411825400000025159455112110261459660001002712376711010028123767010100291496750100003014247811010031142479010000321347911101003313429200000134131094000100351814103002110361534103000000371430103110000381439111110100391946114113110402216114114110411834114114111421416117000001432052139110100442087140002111452264154002111462201158114011472992159115111481695162010000491792167110100501690173000001511827174000001522604175112110531720199010000541720209000000552159209014100561852210010000572104213110100581852220000001591852222000000602210222110000612266223010000622027223110000631852227000100641852232000001651995235000001662616245113110672324253110100681852257010001692054260000000702617284113110711948287110000721720290010001732604308112110741852309110101751942319000100762027325110000771942326110100781720329110100792048337000000802334346112111811720355000001821942357110000832117380110001842742387112111852740403112111861942406110100872266437010000882436453010000892067458010000902000464112110與Z的關系及散點圖：>>x1=[7141819191927303030313138414242424247525254545455666767757879919294103103103111114114114117139140154158159162167173174175199209209210213220222222223223227232235245253257260284287290308309319325326329337346355357380387403406437453458464]';|>>X1=[ones(90,1)x1];>>Z=[99810151028125010281028101810721290120413521204110411181127125911271127109511131462118214041182159414591237123714961424142413471342131018141534143014391946221618341416205220872264220129921695179216901827260417201720215918522104185218522210226620271852185219952616232418522054261719481720260418521942202719421720204823341720194221172742274019422266243620672000]';>>x2=[011100001000010110000100101001010000111110100110100100001001010001100110110111010111110001]';>>X2=[ones(90,1)x2];>>Z=[99810151028125010281028101810721290120413521204110411181127125911271127109511131462118214041182159414591237123714961424142413471342131018141534143014391946221618341416205220872264220129921695179216901827260417201720215918522104185218522210226620271852185219952616232418522054261719481720260418521942202719421720204823341720194221172742274019422266243620672000]';x3=[011110001110010110001100101111110000111110100111100110111001110001110111110111010111111111x3=[011110001110010110001100101111110000111110100111100110111001110001110111110111010111111111]';>>X3=[ones(90,1)x3];>>Z=[99810151028125010281028101810721290120413521204110411181127125911271127109511131462118214041182159414591237123714961424142413471342131018141534143014391946221618341416205220872264220129921695179216901827260417201720215918522104185218522210226620271852185219952616232418522054261719481720260418521942202719421720204823341720194221172742274019422266243620672000]';>>x4=[000000000020000000002000200000000020003440022450000200400000000003000300200000020002200002]';>>X4=[ones(90,1)x4];>>Z=[99810151028125010281028101810721290120413521204110411181127125911271127109511131462118214041182159414591237123714961424142413471342131018141534143014391946221618341416205220872264220129921695179216901827260417201720215918522104185218522210226620271852185219952616232418522054261719481720260418521942202719421720204823341720194221172742274019422266243620672000]';x5=[001010000001000101000010111101010110011110111010100100101000001001100100111011010001110001]';>>X5=[ones(90,1)x5];>>Z=[99810151028125010281028101810721290120413521204110411181127125911271127109511131462118214041182159414591237123714961424142413471342131018141534143014391946221618341416205220872264220129921695179216901827260417201720215918522104185218522210226620271852185219952616232418522054261719481720260418521942202719421720204823341720194221172742274019422266243620672000]';>>x6=[000000000010000000001000100000000010001110011110000100000000000001000100100000010001100001]';>>X6=[ones(90,1)x6];>>Z=[99810151028125010281028101810721290120413521204110411181127125911271127109511131462118214041182159414591237123714961424142413471342131018141534143014391946221618341416205220872264220129921695179216901827260417201720215918522104185218522210226620271852185219952616232418522054261719481720260418521942202719421720204823341720194221172742274019422266243620672000]';>>x7=[000000100000000000110000000000001000000011011110011000000100000110010001010000011011100000]';>>X7=[ones(90,1)x7];>>Z=[99810151028125010281028101810721290120413521204110411181127125911271127109511131462118214041182159414591237123714961424142413471342131018141534143014391946221618341416205220872264220129921695179216901827260417201720215918522104185218522210226620271852185219952616232418522054261719481720260418521942202719421720204823341720194221172742274019422266243620672000]';模型一程序：>>x1;>>x2;>>x3;>>x4;>>x5;>>x6;>>x7;>>x=[x1,x2,x3,x4,x5,x6,x7]; >>stepwise(x,z)>>[b,bint,r,rint,stats]=regress(z,x)Warning:R-squareandtheFstatisticarenotwell-definedunlessXhasacolumnofones.Type"helpregress"formoreinformation.>Inregressat162b=1.0e+003*1.13110.0027-0.0229-0.02290.10890.03850.1817bint=1.0e+003*1.02681.23530.00230.0031-0.14320.0974-0.10050.11930.02960.1882-0.06700.1440-0.05070.41420.00000.0000r=1.0e+003*1.65450.84440.18550.8335-0.13031.62840.87311.60450.80960.49590.75090.95221.58710.78571.57840.13340.78350.92830.82960.81870.70530.75750.90221.55240.36230.87620.0791-0.23460.39810.05520.38940.02690.73180.81531.05301.44590.6510-0.01650.34330.4525-0.28550.6775-0.07730.23460.20420.2691-0.27410.2091-0.13820.55590.55370.10160.12871.2156-0.10650.1048-0.23810.45381.18740.39250.07660.39030.52640.42770.42120.0587-0.3250-0.73521.1048-0.02600.2513-0.8069-0.1873-1.18460.32650.1687-0.4836-0.49010.9376-1.00780.16050.0992-0.6887-1.0969-1.1316-0.6574-0.3883-0.4231-0.4339-0.5262rint=1.0e+003*0.17483.1341-0.62322.3119-1.28301.6541-0.63502.3020-1.54681.28610.14763.1092-0.59152.33760.12273.0863-0.66092.2801-0.96481.9566-0.63062.1323-0.51462.41900.10473.0695-0.68672.25810.09573.0611-1.33991.6067-0.68902.2561-0.53952.3961-0.63832.2975-0.65002.2874-0.68032.0908-0.71702.2319-0.56652.37100.06903.0358-1.08891.8135-0.59342.3457-1.39841.5565-1.66071.1915-1.06991.8662-1.42381.5342-1.07921.8580-1.45381.5077-0.74192.2056-0.65542.2860-0.36922.4751-0.03852.9304-0.82912.1311-1.49941.4664-1.12311.8097-0.96791.8728-1.69541.1244-0.79842.1535-1.56241.4078-1.19141.6607-1.22271.6311-1.10371.6418-1.59581.0476-1.26601.6842-1.62451.3482-0.92212.0338-0.92432.0317-1.36171.5650-1.34651.6040-0.26102.6923-1.12020.9073-1.37011.5798-1.72441.2482-1.02291.9305-0.28732.6621-1.08921.8742-1.39791.5511-1.09131.8719-0.93641.9892-1.04821.9036-1.05451.8969-1.40651.5240-1.80921.1592-2.16470.6943-0.36302.5727-1.48671.4347-1.22391.7264-2.23590.6221-1.64301.2684-2.61240.2432-1.11771.7708-1.30011.6376-1.95880.9916-1.96480.9846-0.51082.3859-2.44630.4306-1.29721.6182-1.36301.5614-2.12750.7501-2.53050.3368-2.5628