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    188宝金博页面版: AMS-256 Linear Models

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    内容提示： Checking normalityNormality is a key assumption in order to obtain the rightproperties of the estimates and justify the tests of hypotheses basedon t and F distributions.The most commonly used procedures to check for normality of theresiduals are based on graphic exploration of the distribution ofthese.For normal residuals the function boxplot should produce asymmetric box centered around zero and contained between -3 and3 if the standardized residuals are used.The function hist should produce a bell shape...

    文档格式：PDF | 页数：5 | 浏览次数：16 | 上传日期：2015-12-31 23:21:32 | 文档星级：
    Checking normalityNormality is a key assumption in order to obtain the rightproperties of the estimates and justify the tests of hypotheses basedon t and F distributions.The most commonly used procedures to check for normality of theresiduals are based on graphic exploration of the distribution ofthese.For normal residuals the function boxplot should produce asymmetric box centered around zero and contained between -3 and3 if the standardized residuals are used.The function hist should produce a bell shaped figure, symmetric,centred around zero and with a support between -3 and 3. We canuse the function density to superimpose the estimated density ofthe residuals to the histogram.For the Oxygen example we have the following set of commandsAMS-256: Linear Models159> ex2=read. table(’example2. dat’,header=T)> ex2. mod=lm(IgC~Oxygen+I(Oxygen^2),data=ex2)> par(mfrow=c(1,2))> boxplot(rstandard(ex2. mod))> hist(rstandard(ex2. mod),prob=T)> lines(density(rstandard(ex2. mod)),col=2)producing the plotsAMS-256: Linear Models160−1012Histogram of rstandard(ex2.mod)rstandard(ex2.mod)Density−2−101230.000.050.1 00.1 50.200.250.30AMS-256: Linear Models161Q-Q PlotsA very useful tool to assess the normality of the residuals is givenby the q-q plot that consists in plotting the quantiles estimatedfrom the sample versus the theoretical quantiles that correspond tothe assumption of normality.The idea of the plot is that all points should be distributed along astraight line of slope one and intercept zero.The R commands to obtain a q-q plot are> qqnorm(rstandard(ex2. mod))> qqline(rstandard(ex2. mod),col=2)> #adds the reference line to the plotAMS-256: Linear Models162

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