SAS 回归分析 作业6

sas线性回归分析案例（Case study of SAS linear regressionanalysis）linear regression20094788 Chen Lei calculates 2Southwest Jiao Tong UniversitySouthWest JiaoTong University-------------------------------------------------------------------Linear regression is divided into single linear regression and multiple linear regression.The model of unary linear regression isY=..0+..1X+ epsilon,HereXIndependent variable,YDependent variable,Epsilon is a random error term.It is usually assumed that the mean of the random error isZeroThe variance is(..2..2>0),..2 andXValue independent. If further assumptionsRandom errorThe difference follows a normal distribution, which is called a normal linear model. In general, withKAn independent variable and a dependent variable, dependent variableThe value can be broken down into two parts: part is due to theinfluence of the independent variable, that is to sayFunction as an argumentAmong them, the function form is alreadyKnow, but contain some unknown parameters; another part is due to other UN considered factors and random effects, that is, random errors.When a function is a linear function of unknown parameters, it is called a linear regression analysis model.If there are multiple dependent variables, the regression model is:Y=..0+..1X1+..2X2+.+..IXi+..Due to the linear dieThe model contains random errors, so the regressionThe straight line reflected by the model is uncertain. The main purpose of regression analysis is to derive from theseIn the uncertain straight line, find a line which can best fit the original data information and describe it as a regression modelRelationship between independent variables,The straight line is called the regression equation.throughOften in regression analysis, yesEpsilon has the most commonly used classical assumptions.1. The expected value of epsilon isZero2, epsilon for allXFor example, it has the same variance.3, epsilon obeys normal distribution and is independent of each otherVariable.Explanation of linear regression,This paperBased on examples.In the following example, there is a one element regression analysis, and another twoMeta regression analysis.Examples(Data analysis method_exercises2.4_page79)A company manager who knows about the monthly sales of a cosmetics in a cityY(unit: box) with the middle of the cityThe number of people who use the cosmetics..1 (unit: thousand persons) and their per capita monthly income..2 (unit: yuan) betweenIn a certain monthFifteenThree cities were surveyed to obtain the above views Measured values, such as tableTwo point one twoAs shown.surfaceTwo point one twoCosmetics sales dataCitySales volume (y)Number of people (x1)Income (x2)CitySales volume (y)Number of people (x1)Income (x2)OneOne hundred and sixty-twoTwo hundred and seventy-fourTwo thousand four hundred and fiftyNineOne hundred and sixteenOne hundred and ninety-fiveTwo thousand one hundred and thirty-seven TwoOne hundred and twentyOne hundred and eightyThree thousand two hundred and fifty-four TenFifty-fiveFifty-threeTwo thousand five hundred and sixtyThreeTwo hundred and twenty-threeThree hundred and seventy-fiveThree thousand eight hundred and two ElevenTwo hundred and fifty-twoFour hundred and thirtyFour thousand and twentyFourOne hundred and thirty-oneTwo hundred and fiveTwo thousand eight hundred and thirty-eight TwelveTwo hundred and thirty-twoThree hundred and seventy-twoFour thousand four hundred and twenty-seven FiveSixty-sevenEighty-sixTwo thousand three hundred and forty-seven ThirteenOne hundred and forty-fourTwo hundred and thirty-sixTwo thousand six hundred and sixtySixOne hundred and sixty-nineTwo hundred and sixty-fiveThree thousand seven hundred and eighty-twoFourteenOne hundred and threeOne hundred and fifty-sevenTwo thousand and eighty-eight SevenEighty-oneNinety-eightThree thousand and eightFifteenTwo hundred and twelveThree hundred and seventyTwo thousand six hundred and five EightOne hundred and ninety-twoThree hundred and thirtyTwo thousand four hundred and fiftyhypothesisYand..1,Linear regression relation is found between..2 ....=..0+..1....1+..2....2+..,..=1,2,... 15.amongIndependent and identically distributed... (0,..2)(One)Coefficient of linear regression..0,..1,Least squares estimation and error variance of..2..2 estimates, writes regression equations, and...Regression coefficientInterpret;(Two)The ANOVA table was used to explain the significance of linear regression test. Square of the coefficient of the complex correlation..2valueAnd explain its meaning;(ThreeSeparately seek..1 andThe confidence of..2 is95%Confidence interval;(Four)YesThe number of people tested by alpha =0.05 ..1 and income..2Sales volumeYIs the effect significant?Regression coefficientTest of general hypothesis test method ..1 andThe interaction of..2 (i.e...1..2) yesYIs the effect significant?;Data importEdit window inputThis questionTheData import code:TitleData analysis method_exercises2.4_page79"; / *Title, omission does not affect analysis results * /DataMylib.ch2_2_4;*First, a new logical library,Logical LibrariesMylibCreate data setCh2_2_4*/Input y X1 x2 @ @ /*@@; Represents a continuous input,YDependent variable,X1,X2Independent variable* /Cards; / *Start input data* /1622742450120180, 32542233753802131205283867862347, 1692653782819830081923302450, 1161952137Fifty-five532560252430402023, 37244271442362660103157, 20882123702605;*Missing data"."Otherwise, the corresponding set of data will be automatically deleted* /Run/*runStatement is used to illustrate all rows before the statement in the current procedure step* /PressF8After run,Open logical libraryMylibYou can see the new data setCh2_2_4.SASA variety of imports are provided According to the manner, for example: One,Read data from file,INFILEF:\Mylib\CH2_2_4.txt";TwoAnd the use of established data sets,Proc reg data=mylib.ch2_2_4;You can also import directly from outsideExcelOther ways. The program above is entered directly in the editbox.procedure callThe procedure to call in this questionyesProc regProcess.Proc regProcess isSASsystemMany regression analysis process of the system in the Except that it can fit the general linear regression model,A variety of optimal model selection methods and model checking methods are also provided.Among themOneTwo)ThreeThe results of multivariate linear regression analysis are mainly used. (Four) will use a linear regression analysisResults.(I)Yand..,Linear regression analysisProcReg*transferRegProcess use* /MOdel y=x1 x2;*Dependent variableYThe independent variable is X1,X2*/Run;ModelStatement: used to define the model's dependent variables, arguments, model options, and output options.Common options areSelection=,Specifies the variable selection method:FORWARD(forward input method),BACKWARDXiang HoushanDivision),STEPWISE(stepwise regression),ADJRSQ(modified multiple correlation coefficient criterion),CP(Cp criterionEtc..NOINTSaid, is often included in the modelNumber item;STBThe regression coefficient, output standard;CLIThe output of single predictive value, confidence interval; RResidual scores are performedAnalysis of results of the analysis and output; IOutput(XTX).1matrix.Format:MODELDependent variable name=Argument rankingTheseoption]Cases:Model y=x1 / x2 selection=stepwise / *; stepwise regression* /After running the program, get the results Parameter estimation table(One)Least squares estimation:= = (0,... 1,... 2) = (3.45261,0.49600,0.00920) Regression equation:Y=3.45261+0.49600..1+0.00920..2ANOVA table(TwoError variance estimate:... 2=MSE=4.74040Multiple correlation coefficientSquares:..2=0.9989(R-Square)Significance: from the value of the complex correlation coefficient, it can be seen that it is highly significantand..1,..2)Multiple correlation coefficient SquaresCan also passBy calculation:..2=SSR/SST=53845/53902=0.9989 (Three)Confidence interval:K+....t1..2 (N.P) s...)...0.975 (12) =2.17881 (via check) T distribution table obtained) You can also pass the functionY=TINV(P,DFObtain...1=0.496+/-2.179*0.00605Draw (Zero point four eight two eight ,Zero point five zero nine two )..2=0.0092+/-2.179*0.00096811,DrawZero point zero zero seven one ,Zero point zero one one three )(Two)YandLinear regression analysisProcRegData=mylib.ch2_2_4; / *Direct reference data set* /Model y=x1;Run;(FourThe coefficient of multiple correlation is: Zero point nine nine one zeroX1YesYSignificant influence(Three)YandLinear regression analysis ProcRegData=mylib.ch2_2_4; / * Direct reference data set * /Model y=x2;Run;(Four)The coefficient of quadratic correlation is square: Zero point four zero eight seven,X2YesYThe effect is not significant(Four)YandLinear regression analysis of... Data mylib.ch2_2_4;Set mylib.ch2_2_4;*Read data set* /Z=x1*x2;*New argumentZ*/Run;Proc reg;Model y=z;*Argument isZ*/Run;(Four)The square of the complex correlation coefficient is: Zero point nine zero three zero,X1X2YesYSignificant impactLinear regression analysis using modules (I)Linear regression analysisstart-upSASSystem, and click "solution" in turn"->"Analysis"->"Analysts"And then click "file""->Open, open the data set"Ch2_2_4.sas7bdat",FigureVariable listindependent variable dependent variableThe value of confidence a Click "Statistics" in turn" ->"Regression"->"Simple" pop-up dialog boxOne)Variable settingsOn the left hand side of the variables listCentral ElectionYClick"DependentThe button is set as dependent variable ;SelectedX2Click"Explanatory"Button, set it as an argument."ModelIn the settings bar, select by default" Linear"" means linear regression.(Two)TestsSet upClick"TestsButton to eject the dialog boxConfidence defaults toZero Point Zero FiveMay change.Click"OK".(Three)PlotsSet upClick"Plots"Button" pops up the plotting Options dialog boxChoice"ResidulTab."Studentized"Represents a student residual," Normal quantile-Quantile plot"Stands for normality."QQGraph check.Settings as shownResidual columnNormal inspectionTest barVariable columnvariance analysisparameter estimationClick"OK"And click on the main settings dialog box "OK",ThereforeAnd get resultsregression equationClick"Analysis (new, project) "Dialog box""Plot of RSTUDENTVsX2"" pops up the residual graph Dialog boxClick again"Plot of RSTUDENTVsNQQ"Pop upQQchartThe normal state of the residual by the studentQQIt can be seen that the model error term is approximately normal distribution.Independent variable selection(two) manyLinear regression analysisstart-upSASSystem, click "solution" in turnResolution"->"Analysis">"Analyst", and then click "file"" ->Open, open the data set"Ch2_2_4.sas7bdat".Click "Statistics" in turn"->"Regression"->"Linear" pop-up dialog boxSelect argumentX1,X2Dependent variableY. Click"ModelButton to eject the dialog boxIn"Selection method"Column" provides independent variable selection, such as: Stepwise selectionExpressStep regression method;Adjusted R-SquareIndicates the modified multiple correlation coefficient criterion. This example selectsStepwise regression method. Click"OK".PlotsThe setting is similar to the one element regression analysis. Last click"OK".Multivariate linear analysis:Residual plotQQIn addition, click"Analysis (New project)"Dialog box"Code"Pop-up program dialog box.The above process is mainly explained by linear regressionSASThe use of the system, and therefore less analysis of the results. For example: byQQAs can be seen from the graphspotApproach a straight line, IndicateError termApproximatejuststateDistribution.。

proc import out= xt49 /*使用import过程导入数据并输出到数据集xt4.9*/datafile="E:\xt49.xls"dbms=excel2000 replace;getnames=yes; /*首行为变量名*/run;proc plot data=xt49;/*对xt49绘图*/plot y*x='*';/*以x为横坐标,y为纵坐标,以*为各点,画散点图*/run;proc corr pearson data=xt49;/*对xt49运行相关分析过程*/var y x;/*计算y和x的Pearson相关系数*/run;proc reg data=xt49;/*对xt4.9运行回归分析过程*/model y=x;/*建立以y为因变量,以x为自变量的线性回归方程*/model y=x/p r dw;/*建立以y为因变量,以x为自变量的线性回归方程，p 是要求输出拟合值，r是要求输出残差值, dw是要求输出DW检验统计量的值*/model y=x1-x4/vif；/*建立以y为因变量,以x1-x4为自变量的线性回归方程，vif是要求输出各自变量的VIF值*/output out=res p=yhat r=residual;/*输出拟合值和残差值至数据集res，以便绘制残差图*/run;-------------------------以下是绘制残差图的程序，data res_new;/*创建新数据集res_new*/set res;/*先把res 数据集复制过来*/lag1residual=lag1(residual);/*lagn （n 自定）函数可把一变量的各观测值移后n 位；residual 即t e ,lag1residual 即1t e -*/t=_n_;/*_n_是data 步内读取观测值的计数器变量，从1开始，每读取一观测值自加1，因此变量t 的观测值即为期数1,2,...,n*/run;proc plot data=res_new;/*绘制残差图*/plot residual*lag1residual='*';/*以residual 即残差值为纵坐标，以residual2即拟合值为横坐标*/plot residual*t='*';/*以residual 即残差值为纵坐标，以t 即拟合值为横坐标*/run;- ------------------以下是进行一阶差分后建立回归模型以及其自相关检验的程序data et49_new;/*创建新数据集ch4_new*/set xt49;/*先把ch4数据集复制过来*/difx=x-lag1(x);/*lagn （n 自定）函数可把一变量的各观测值移后n 位；对x 各观测值作一阶差分*/dify=y-lag1(y);/*lagn （n 自定）函数可把一变量的各观测值移后n 位；对y 各观测值作一阶差分*/run;proc reg;/*对ex4.9_new运行回归分析过程*/model dify=difx/p r dw;/*建立以y为因变量,以difx为自变量的线性回归方程，p是要求输出拟合值，r是要求输出残差值,dw是要求输出DW检验统计量的值*/output out=res p=yhat r=residual;/*输出拟合值和残差值至数据集res，以便绘制残差图*/run;data res_new;/*创建新数据集res_new*/set res;/*先把res数据集复制过来*/lag1residual=lag1(residual);/*lagn（n自定）函数可把一变量的各观测值移后n位；residual即 ,lag1residual即 */t=_n_;/*_n_是data步内读取观测值的计数器变量，从1开始，每读取一观测值自加1，因此变量t的观测值即为期数1,2,...,n*/run;proc plot data=res_new;/*绘制残差图*/plot residual*lag1residual='*';/*以residual即残差值为纵坐标，以residual2即拟合值为横坐标*/plot residual*t='*';/*以residual即残差值为纵坐标，以t即拟合值为横坐标*/run;_ _ _ _ _ _ _ _ _ 异常值的的识别假定有一数据集ch，因变量为y，自变量为x1-x2(或x)。

数学建模培训 徐雅静 08年7月
Ⅲ 用SAS做回归分析
(2) 剔除自变量 在上面的例子中首先考虑剔除变量x3，对此只需在刚 才已打开的拟合窗的任一处选中变量x3，如图4-31所示， 再在主菜单中选择“Edit”→“Delete”所有的结果就会修改 为不含x3的拟合结果。
类似地剔除作用不显著的自变量x2，得到拟合结果如图432所示。
首先制作变量之间的散点图，以便判断变量之间的相 关性。步骤如下：
1) 在INSIGHT模块中，打开数据集Mylib.bldk； 2) 选择菜单“Analyze（分析）”→“Scatter Plot (Y X) （散点图）”； 3) 在打开的“Scatter Plot (Y X)”对话框中选定Y变量： Y；选定X变量：x1、x2、x3、x4； 4) 单击“OK”按钮，得到变量的分析结果。
数学建模培训 徐雅静 08年7月
Ⅲ 用SAS做回归分析
在显示的结果中可以看到，多元回归分析的输出类似于 一元线性回归的输出，同样分为七张表：
第一张表提供关于拟合模型的一般信息； 第二张表给出模型方程(即回归方程)，如图。
可知回归方程为： Yˆ 1.0216 0.0400x1 0.1480x2 0.0145x3 0.0292x4
… 139.4 368.2 95来自7 109.6 196.2 102.2
本年累计应收 贷款(亿元)x3 6.8 19.8 7.7 7.2 16.5
… 7.2 16.8 3.8 10.3 15.8 12.0
贷款项目个数 (个)x4 5 16 17 10 19
… 28 32 10 14 16 10
本年固定资产投资额 (亿元)x5 51.9 90.9 73.7 14.5 63.2
数学建模培训 徐雅静 08年7月

SAS 统计分析与应用 从入门到精通 三、曲线回归
1、可化为线性的曲线回归
由于曲线回归没有固定的模型和方法，因而很难进行处理和分析。但 是对于一些基本的曲线模型，我们可以通过变换将它们转化为线性模型， 继而利用线性回归的方法进行分析。
SAS 统计分析与应用 从入门到精通 三、曲线回归
2、REG 过程
3、逐步回归
在实际问题中，影响因变量的因素可能很多，其中有些因素的影响 显著，而有些因素的作用可以忽略，如何从大量的因素中挑出对因变量 有显著影响的自变量来，这就涉及到变量的选择问题。 逐步回归是在建立模型的过程中对变量进行逐个筛选的回归方法， 其基本思想是：在建立回归模型时，逐个引入自变量，每次引入的变量 都经过检验对因变量的影响是显著的，同时对已有的变量也进行检验， 将不显著的变量剔除。这样最后得到的回归方程中，所有变量都是显著 的。
SAS 统计分析与应用 从入门到精通
回归分析


一元线性回归
多元线性回归


曲线回归
非线性回归 Logistic回归
SAS 统计分析与应用 从入门到精通 一、一元线性回归
1、基本模型
SAS 统计分析与应用 从入门到精通 一、一元线性回归
1、基本模型
SAS 统计分析与应用 从入门到精通 一、一元线性回归
2、模型的检验
SAS 统计分析与应用 从入门到精通 一、一元线性回归
2、模型的检验
SAS 统计分析与应用 从入门到精通 一、一元线性回归
3、利用回归方程进行预测
SAS 统计分析与应用 从入门到精通 一、一元线性回归
4、REG过程
REG过程是SAS系统中提供的用于一般线性回归的过程，通过此 过程可以实现一元回归分析，包括模型的建立和检验等。REG过程中 有很多的语句和选项，其中用于一元回归的基本语句格式为： PROC REG DATA=数据集名 <选项>; MODEL 因变量名=自变量名 </选项>; PLOT 纵轴变量名*横轴变量名 <=符号> </选项>; BY 分组变量名; RUN; 其中，PROC语句和MODEL语句是必须的，其他语句可以根据用 户需要进行选用。