线性回归分析案例

一问题的提出研究学校中的教师的人均工资和对学生的人均经费投入是否存在统计关系（所谓的统计关系是指变园存音不完全的线性关系人如果有能否用来此模型米做统计推断0二问题的处理如卜'表爰1985年美国50个州和哥伦比业特区公立学校中数师的人均工资y（美兀）和刈学生的人均经赞投入買（美元九（数抑;来自应用回归分析第二版何晓甫刘文卿著P61习題2,16）序号VIXv|X119583334627227953366220263311128215702920320325355429220802980426800454230222503731029170■166931209102S5362661018883221800©25337306785710332293427298271705536341844323059258534168353953826421024500354720-IG0312411242743159372111927521227170362138251603129133016837823922482泊17142552542474020969250915273G03982112722454101621690356812258921042172197131554322644340218208163059112⑹0282919180952967452231122972020939328546256102932212264439114726015370522246244517482578811232S271864319192913236082133990502050414808319252338235915125845376G26206272821处理过程1）作散点图并添加趋势线（用线性九UploadUyYdkyQQ2S38J(MIIiKipiVw^-.yclky.nxr(UploadByYrlkyQQ2«383(MII

hc(p:WwH-u'.yclky.acc曲散点图可知数据大致落在回归直线两侧,有异常值,但回归拟合优度如何有待进一步讨论.研究。2）作回归（在excle中点工八下数据分析中的回归选项）SUMMARYOUTPUT回归统计MultipleR0.839428209KScjuare0.704639717.AdjustedRSquare0.698486378标准误差2287.182981观测值50山模型综述可知.相关系数尺三0・839428209,和关系数的平方护=0,704639717,回归的拟合优度较好。回归标准差a=2287.182981,此处只

选取了50个样本別除了其中一个〔共51个样本几由散点图可知存在一个异常值•此处便是別涂了这一异常值再做I川归分帕方香分析dfSSMSFSiilH回归分析总计14819599043117.5251097887.485014100L9599043117.55231205.987114.51338742.62999E-14由方差分析表可知.回归平方和=599043IL7.5,自由度是I•残差平方和=251097857.4,自由度是48.F值=114.5133874,在给定显著性水平0=0.05下,显著性P值二2.6999e-14^0.05r表明回归方税髙度显茗。即变最x対变就y有显著的线性诒响jCoeff标准溟差tSintP-valueLow€i'95%lipper95%Intercept12271.06993.290616031183.324380.307502810.369996710.70109287.6066E-142.63E-149891.836792.6723402214650.3033.90889185II］系数表可知，筱距项=1271.0699.回归系数二£29061603.|川归方程为y=1271.0699+3.29061603,在显著性水平a=0.05下,回归系数的：®信度为95%的咼信区间为［2.67234022.3.90889185］WVl系数逋过检验.说明凹归系数显苦不为0.60000240000®200000(3346LineFitPlot1二亡一■•Illi*19583•预测19583)200040006000800010(3346)00上图为回归拟合直线图•人致呈线性关系。

RESIDUA.OUTPUT彼测y观射＜5预測Y1225*8.0452-2255.0482-0.996367423347.283』-552.28345-0.2439712223965.9193-3640.9193-1.60837582721879.6G87-309.6687-0.1367961327217.0479*417.04790.184230922077.10572.89434162U.U0127858427634.9&611835.04386O.B106305424548.3583-229«.3583-1.0152997528355.601-1745.601-0.77111923021659.1974-719.197420.317705163060.1874-3S2.18743-0.16396383120606.2(1031193.799710.5273609630487.9202-3317.9202-1.46569113221251.16L1682.838970.74339403^2辭・3$75-133,3崭筑-O.Q5991Q?::::19955-9393-1112.939$-0.6211661923942.8849557.115051U.24610555…2096L8774-14M.8774-0.63032310^2666.12591607.874070.710(27829:门22550.9514-2090.9544-0.9236791124186.39052983.609461.31800334:;fi21326.815292.1547971U.01(1709^11224716.1797545i怡20262.40834135--23554.59231605.407740.709186791326246.3162278.683828U.12310857:出25259.1314-2777.1314-1.22679T61425374.3&291985.69708U.87718159jy20527.225544L.774493U.195153861524011.98792521.9879-1.0257384030172.0211-2948.02311.30228821622652.9635-678.963460.29993214125571.7399320.260115u.141474M1722337.0643-1521.0643-0.6719301•1223465.7456-821.74562-0.3630061IS22034.3276-3938.3276-1.7101378•1321580.22263059.777361.35165C5iy23080.7435-21-11.7435-0.94611511119829.614925L1.385091.10910424；：」25150.541-2506.511-1.1072644-21919.15613690.843911.630130122127134.7825-2510.7825-1.109138-If；21462.&I231552.19772U.68568327•26581.959604.D10993U.266835084725838.2798-50.279781-0.0222L1128789.9&245200.037632.297116374824144.6125-iy^S.387472.2036199221097.5439-715.5139-0.31609154939744.42311735.576860.766690992521353.8977-926.89771-0.409457jU21663.529911X1.17011U.52191m3346ResidualPlot腑00•徊0她0W000腑00•徊0她0W000撤5000

塑0-50003346111残箸图可知-数挖大致分布在0尼右.满足G7条件中的均值为0的条件,38Q95.7■:&12427424$(X*]y融216211刃24^0y泗莎:iieo:12UIHOEI2otl0应HH152flac6S：o.?-o17閱列9i:725853：92A94K)旳2^2212C9BS2bUlb*1?斯河■>-.j-,-0752«6102EJ800柑219DQ旳217170AI■1'團'1HI汀1"31呦同S3小希汩05纬現1372科41叭275W39加驭89:UIJ?4122644912J170佗坪44列1嗣is2若LG兀6阳■Il也：1卿皑1：ILJKonnajProbabiIii:yI门匚6000040000200000201060別100120Samp[eIVrcejiLik?ll]j|-MI：»率检验河知,数捋大致服从匸态分布,反过未说明竝汇需足G-M盖件中的」F思性假说一\结论一粽上所述,19