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1、多元数据分析,刘国庆,Question?,How to determine a fair market value for the property?In building the model,the goal is to predict the market value of the Leslie Salt property,using the information available.,Data,LeslieSaltData.txt,Regression Analysis,It is used to explore the relationship between a set of in
2、dependent variables(Xs)and a single dependent variable(Y).A regression model is a linear combination of independent variables that corresponds as possible to the dependent variable.,Regression for answering questions,How can we describe the relationship between the dependent variable and the indepen
3、dent variables?Is the relationship described by the model statistically significant?Which independent variables are most important?How well does the model generalize to observations outside the sample?,资料预处理,大多数的销售价格低于$10,000,但是有一些价格甚至高于$20,000 or$30,000每亩；一般地，这种价值的差别会带来问题。为此，采用log函数。一些特殊的点需要排除,Vari
4、ables,DescriptionVariables.txt,Correlation Matrix,CorrMatData.txt,分析,从表3中可以看出与log(Price)高度关联的变量是Elevation,Sewer,Date,Flood.从表格中我们也可以看到在独立的变量之间也存在着相关性。比如，Elevation,County.,回归模型,Results of Regression,ResultsRegress.txt,How good is the Fit?,How good is the Fit(continue I),One of the drawbacks of R2 is
5、that whenever an independent variable is added to the model it always increases,no matter how small the contribution in fit.In general,when building models,one wants to make a trade-off between parsimony and improvement in fit.,How good is the Fit(continue II),Is it Significant?,Test the error terms
6、 are normally distributed;that is Testing the model,F-Test,FTest.txtThe critical value for the F-distribution at the 0.01 level is F(4,26)=4.14,which suggests that our model is highly significant.,Detecting problems with the model,One measure of multicollinearity is called the condition index(CI),He
7、teroscedasticity(异方差性),We have assumed that the error terms all have the same variance.This assumption is sometimes called homoscedasticity.When the assumption is violated(i.e.,the variances are not all the same),we have what is called heteroscedasticity.,Weighted least squares(WLS),Influential Obse
8、rvations,Sometimes regression model results can be inordinately influenced by one or a few observations in the data.This type of observation as an outlier.,DFBETAs,We can look at the impact of the observation I on the parameter estimate.,Return to the Leslie model,The observation 2 seems the most ex
9、treme with respect to its lack of fit.Having identified the second observation as a marginally influential observation and a potential outlier,what should we do about it.One thing to remember is that it is never appropriate to discard an observation simply because it seems atypical.,Comparing Models,Forecasting,Model Validation,
