1、spss 多元线性回归分析教程（Tutorial of SPSS multiple linear regression analysis）1 linear regression analysisLinear regression analysisSPSS operation of linear regression analysisOperationThis section describes how to establish and establish a linear regression equation. Includes a unary linear regression and o
2、nly one argumentMultiple linear regression with multiple independent variables. In order to ensure that the established regression equations are in line with linear standards, the regression analysis is carried outBefore, we often need linear tests for dependent variables and independent variables.
3、That is, as discussed in Chapter 1 of the relevant analysisThe scatter plots give a rough linear test of the relation between variables, which is no longer repeated here. In addition, data can be found by scatter plotsThe singular values of the singular values in the scatter plots need to be careful
4、ly checked for the rationality of the data.Linear regression analysis1. dataTaking the data of section third in Chapter 3 as an example, this paper briefly introduces how to make a linear regression analysis using SPSS. Data editingThe window displays the data input format, as shown in Figure 7-8 (f
5、ile 7-6-1.sav):Figure 7-8: regression analysis data input2. regression analysis using SPSS, example operations are as follows:Establishment and test of 2.1. regression equation(1) operationClick the main menu Analyze / Regression / Linear. Go to the settings dialog box, as shown in figure 7-9. Chang
6、e table from leftIn the column, select the dependent variable y into the dependent variable (Dependent) box, and select the argument x into the argument (Independent) box.On the method, that is, Method, note that the default option Enter is maintained, and that the selection indicates that the syste
7、m is in the process of establishing a regressionAll the independent variables selected are preserved in the equation at the time of the procedure. Therefore, the method can be named mandatory entry method (in multiple regression analysis)Describe the application of this option in detail. Specific as
8、 shown in the following picture:TwoFigure 7-9 the main dialog box for linear regression analysisPlease click Statistics. Button, you can select some statistics that need to be output. Such as Regression Coefficients (regression)Estimates in the coefficient, we can output regression coefficients and
9、related statistics, including regression coefficient B, standard error, standardized regressionCoefficient BETA, T value and significance level, etc The Model fit term can output the correlation coefficient R, the coefficient of determination R2Adjustment factor,Standard error analysis and variance
10、analysis. Please note that the above two items are the default options. Settings are shown in figure 7-10. Set upAfter you click Continue, return to the main dialog box.Figure 7-10: linear regression analysis of the Statistics option figure 7-11: linear regression analysis of the Options optionWhen
11、the regression equation is established, it is necessary to check whether the equation is violated except for the significance of the equationFor the regression analysis, a lot of residual analysis is needed. Because this part of content is more complex, and the theory is stronger, so not inThis is a
12、 detailed introduction. If you are interested, please refer to the relevant information.When the user carries on the regression analysis, also may choose whether outputs the equation constant. Click Options. Button, open itDialog box, you can see that there is an option Include constant in equation
13、in the middle. Check this item to test the constant.In the Options dialog box, you can also define methods for dealing with missing values and setting up variable entry and elimination equations in stepwise regressionFor the guidelines, here we adopt the default settings for the system, as shown in
14、figure 7-11. When the settings are complete, click Continue to return to the main dialogueFrame.Click the OK in the main dialog box to get the program running results.(32) results and explanationsThe program as defined above runs the results shown below:1.1. 1.The equationEquation equationList of in
15、dependent variables contained in the equationThe list of arguments contained in the argument list of argumentsContains the argument list and displays the entry method at the same time. In this case, the independent variable in the equation is xEnter.Variables Entered/RemovedModelVariables EnteredVar
16、iables RemovedMethod1X.EnterA, All, requested, variables, entered.B, Dependent, Variable:, Y IIII IIModel fittingModel fittingModel fitting overviewOverviewOutlines the R, R2, R2, and standard error estimates for the model. The greater the R2 value, the two change that is reflectedThe higher the rat
17、io of the variables, the better the fit between the model and the data.Model SummaryModelRR SquareAdjusted R SquareStd.Error of the estimate1.859.738.7236.2814To predictors: (Constant), 本例所用数据拟合结果显示 所考察的自变量和因变量之间的相关系数为 X:拟合线性 0.859,回归的确定性系数为 0.738, 经调整后的确定性系数为 0.723, 标准误的估计为 6.2814.方差分析表方差分析表方差分析表方差
18、分析表 列出了变异源、自由度、均方、f 值及对 f 的显著性检验.ANOVAModelsum of squaresdfmean squarefsig.1regression1995.79111995.79150.583.000Residual710.2091839.456Total2706.00019To predictors: (Constant), XB: 回归平方和为 and 本例中回归方程显著性检验结果表明 dependent variable:1995.791, 残差平方和为 710.209, 总平方和为 2706.000, 对应的 f 统计量的值为 50.583, 显著性水平小于0
19、.05, 可以认为所建立的回归方程有效.回归系数表回归系数表回归系数表回归系数表 列出了常数及非标准化回归系数的值及标准化的回归系数, 同时对其进行显4 著性检验.CoefficientsUnstandardizedCoefficientsStandardizedCoefficientsTSIG.Modelbstd. Errorbeta1 (Constant) - 7.08011.068 640.530 -.X.730.103.8597.112.000Dependent variable: and to 本例中非标准化的回归系数B 的估计值为 0.730, 标准误为 0.103, 标准化的回归
20、系数为 0.859,回归系数显著性检验 t 统计量的值为 7.112, 对应显著性水平 sig. = 0.000 0.05, 可以认为方程显著.因此, 本例回归分析得到的回归方程为: y = -7.08 + 0.73x对方程的方差分析及对回归系数的显著性检验均发现, 所建立的回归方程显著.2.2.回归方程的预测(1) 通过因变量的观测值和回归预测值的比较, 可以了解许多关于模型和各种假定对数据的适合程度, 上面回归方程的检验结果表明, 所得到的回归直线是有效的.在回归方程有效的前提下, 研究者往往希望对于给定的预测变量 x 的一个具体数值 (如 x0),预测因变量 y 的平均值或者预测某一个观
21、测的 y0 的值.如对于上面的例子, 我们可以用回归方程来预测智商 x0 = 120 的被试, 这次的平均成绩; 也可以用来预测假如一名工作人员的智商是 120, 那么他参加这次考试,将会得多少分.上面两种情况下, 点预测值是相同的, 不同的是标准误.Y0 = + = + = 86.52 0.73120 -7.08 bx0在 x0 点, y 的预测均值的估计标准误为公式 (7 / 24); 在 x0 点, y 的个体预测值的估计标准误为公式 (7 - 25).(2) spss 可以提供上述两类预测值, 具体操作如下:在如图 7 - 9 的线性回归模型定义的主对话框中, 单击 save, 出现如
22、下对话框 (图 7 - 12):5图 7 - 12: 预测值的定义选择窗口在上面的窗口, 可以选择输出变量的点预测值和平均值及其个体值预测的区间估计, 如上图,我们在 predicted values 选择区选择复选项 unstandardized, 以输出非标准化的点预测值; 在下面的 prediction intervals 选择区选择复选项 means 和 individual, 下面的置信水平采用系统默认的95% 然后点击 continue 返回主对话框, 在主对话框中点击 ok, 得到的输出结果.(3) 结果及解释除了上面介绍的回归方程建立和检验的结果外, 在数据编辑结果, 因为选择
23、了需要保存的预测变量的信息, 数据编辑窗口数据显示如下:6图 7 - 13: 保存预测之后的数据窗口从上面的结果可以看出, 在以前的数据的基础上, 新生成了五列数据, 第一列命名为 pre _ 1的变量对应的数据表示预测变量对应的因变量非标准化的预测值, for example, 智商为 120 的被试, 用回归方程预测的这次考试的点预测值为 82.01;The upper and lower bounds of interval estimation for mean prediction are variable lmci_1 respectivelyAnd umci_1 indicate
24、 that the upper and lower bounds of the interval estimates of individual forecasts are expressed by variables lici_1 and uici_1, for example, intelligence quotientFor 120 of subjects, the mean 95% forecast range was: (76.42, 84.56); the predicted range of 95% for individual prediction was: (66.68,94
25、.30).Two, multivariate linear regression1. dataTaking fourth example 4 in this chapter as an example, the establishment and test of multivariate linear regression equation are briefly explained. Data input is shown in Figure 7-14 (text)Piece 7-6-2.sav):SevenFigure 7-14: data used in multivariate reg
26、ression analysis2.SPSS operation(1) the command statements used in the multiple linear regression are the same as the unary linear regression. The same can be done by clicking the main menu Analyze /Regression / Linear. Go to the settings dialog box, as shown in figure 7-9. Select the variable y fro
27、m the list of variables in the left column to cause changesIn the volume (Dependent) box, select the argument X1 and X2 into the argument (Independent) box. (2) ClickThe drop-down box behind Method, in the Method box, select a regression analysis method. SPSS provides the following variables to ente
28、rRegression equation method:The Enter option forces entry into the regression model, that is, the selected independent variable, which is the default.Remove option, elimination method, the establishment of regression equations, according to the conditions set aside some of the independent variables.
29、The Forward option, the forward selection method, is based on the criteria set in the Option dialog box, starting from independent variables, and then fittingIn the process, variance analysis of the selected independent variables is made, each time adding a F variable, until all the criteria are sat
30、isfiedVariables are entered into the model. The first variable introduced into the regression model should be the most relevant to the dependent variable.? Backward option, backward tick division, based on the criteria set in the Option dialog box, first establish the full model, and then rootAccord
31、ing to the criterion set, each time an independent variable that makes the F value in the variance analysis be excluded, until the regression equation no longer contains discrepanciesBy the independent variable of the criterion.The Stepwise option, step by step approach, is a combination of forward
32、selection and backward culling. Based on the settings in the Option dialog boxAccording to the result of variance analysis, the independent variable with the criterion is chosen and the regression equation with the greatest contribution to the dependent variable is obtained.According to the forward
33、selection rule, enter the independent variable; then, according to the backward culling method, the minimum F value in the model is changed according to the rejection criterionThe quantity elimination model is repeated until the independent variables in the regression equation are consistent with th
34、e criteria of the entry model, and the independent variables outside the model do not agree with each otherEnter the criteria of the model.Here we use the system default forced access method, and the other options are in the default setting of the system.(83) Click OK to get the output of the model
35、defined above as:3. results and interpretation(1Eleven1) the list of independent variables contained in the equationThe list of independent variables included in the list of independent variables in the equationThe list of arguments contained in the equation shows the entry method at the same time.
36、In this example, the independent variables in the equation are X1 and X2The method of selecting variables into equations is Enter.Variables Entered/RemovedModelVariables EnteredVariables RemovedMethod1X2, X1.EnterA, All, requested, variables, entered.B Dependent Variable: Y(2Twenty-two2)Model overvi
37、ewModel overviewModel overview lists the R, R2, R2, and standard errors of the model. The greater the R2 value is, the independent variables and causes are reflectedThe higher the ratio of variables, the better the fit between the model and the data.Model SummaryModelRR, SquareAdjusted, R, SquareStd
38、., Error, of, the, Estimate1.996.991.988.82The square root of the coefficient determined by the model defined by a Predictors: (Constant), X2, and X1 is0.996, the coefficient of determination is 0.991, and the adjusted coefficient is 0.988The correct error is 0.82.(3Thirty-three3)Variance analysis t
39、ableANOVA table of varianceThe ANOVA table listed the source of variability, freedom, mean square, F value, and the significance test of F.ANOVAModelSum of SquaresdfMean SquareFSig.1Regression518.2192259.109387.469.000Residual4.6817.669Total522.9009预测因子：（常数） ，x2，X1B：本例中回归平方和为因变量 Y518.219、残差平方和为 4.68
40、1，总平方和为 522.900，F 统计量的值为387.467，Sig 05，可以认为所建立的回归方程有效。九（4） ）回归系数表回归系数表回归系数表回归系数表列出了常数及回归系数的值及标准化的值，同时对其进行显著性检验。系数不规范系数标准化系数TSIG。modelbstd。errorbeta1（常数）-31.4993.397-9.272.000x11.077.125.4998.612.000x2.828.086.5559.581.000因变量：Y 本例中因变量Y 对两个自变量 X1 X2 的回归的非标准化回归系数分别为和 1.077和 0.828；对应的显著性检验的 T 值分别为 8.612 和 9.581，两个回归系数 B 的显著性水平 SIG。= 0 均小于 0.05，可以认为自变量 X1 X2 对因变量和均有显著影响本例回归分析得到的回归方程为 Y：Y = 31.499 + 1.077x1 + 0.828x2。
