《最新医学统计学直线相关与回归实习精品课件》由会员分享，可在线阅读，更多相关《最新医学统计学直线相关与回归实习精品课件（63页珍藏版）》请在金锄头文库上搜索。
1、医学统计学直线相关与回归实医学统计学直线相关与回归实习习2Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC目的和要求：目的和要求：p熟悉相关和回归的熟悉相关和回归的SPSSSPSS操作过程操作过程p掌握结果的分析和解释掌握结果的分析和解释3Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC4Department of Healt
2、h Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC5Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC6Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC7Department of Health Statistics, Departm
3、ent of Health Statistics, SchoolofPublicHealth, LZMC8Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC9Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC第一步第一步: :数据录入数据录入设置两个变量：设置两个变量：px体重体重( )py肾总体积肾总体积(mL)10Depart
4、ment of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC1.1.正态性检验正态性检验AnalyzeDescriptiveStatisticsExploreDependentlist:xyPlots:Normalityplotswithtests正态性检验正态性检验第二步第二步: :统计分析统计分析11Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZM
5、C正态性检验结果正态性检验结果P0.10，服从正态分布，服从正态分布12Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC第二步第二步: :统计分析统计分析2 2.绘制散点图绘制散点图GraphsScatterSimple13Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMCGraphsScatterSimple简单散点图简单散点
6、图14Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMCSimpleScatterplot对话框对话框应变量应变量y自变量自变量x15Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC从图中可见，从图中可见，体重和肾总体重和肾总体积有比较体积有比较明显的明显的直线直线相关趋势相关趋势，也没有发现也没有发现影响过强的影响过强的异常点
7、，可异常点，可以进行相关以进行相关分析。分析。16Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC3.相关性分析：相关性分析：AnalyzeCorrelateBivariate17Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMCBivariate对话框对话框xy同时选入同时选入默认默认18Department of Healt
8、h Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMCx和和y的相关系数的相关系数r=0.875对对r假设检验的假设检验的P0.00119Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC秩相关的适用条件秩相关的适用条件pp不服从双变量正态分布不服从双变量正态分布p用用等级资料等级资料表示的原始资料表示的原始资料p总体分布未知或边界不确定的资料总体分布未知或边界不确定的资
9、料21Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC22Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC1、数据录入：设置、数据录入：设置x和和y两个变量两个变量设置两个变量：设置两个变量：px舒张压舒张压py夜间最低血氧夜间最低血氧含量分级含量分级23Department of Health Statistics, Dep
10、artment of Health Statistics, SchoolofPublicHealth, LZMC2、秩相关操作、秩相关操作xy同时选入同时选入选择选择Spearman24Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC3、秩相关结果、秩相关结果x和和y的相关系数的相关系数rs=0.897对对r假设检验的假设检验的P0.00125Department of Health Statistics, Department of Health Stati
11、stics, SchoolofPublicHealth, LZMC分类变量的关联性分析分类变量的关联性分析教材教材 例例13.713.7DescriptiveStatisticsCrosstabs Chi-square是否有关联是否有关联Contingencycoeficient列联系数列联系数26Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC计算列联系数计算列联系数27Department of Health Statistics, Department
12、of Health Statistics, SchoolofPublicHealth, LZMC列联系数列联系数=0.355,P0.00128Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC直线回归直线回归LinearRegression29Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC直线回归含义p用用直直线线回回归归方方
13、程程描描述述成成对对观观测测数数据据中中两变量两变量间的间的数量依存关系数量依存关系30Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMCv直线回归方程：直线回归方程：px为自变量为自变量(independentvariable),也称为解释变也称为解释变量量(explanatoryvariable)py为因变量为因变量(dependentvariable),也称为应变量也称为应变量(responsevariable)直线回归方程31Department of
14、Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC直线回归方程：直线回归方程：p为当为当 x取某一值时应变量取某一值时应变量y的的平均估计值平均估计值pa为截距为截距(intercept)，即当，即当x =0时时y的的平均估平均估计值计值p b为回归系数为回归系数(regressioncoefficient)，即直线，即直线的斜率，表示的斜率，表示x改变一个单位时改变一个单位时y的的平均改变平均改变量量。32Department of Health Statistics, Departme
15、nt of Health Statistics, SchoolofPublicHealth, LZMC直线回归方程直线回归方程p直线回归分析目的在于找出一条直线回归分析目的在于找出一条最能代表这些数最能代表这些数据关系据关系的直线，用直线方程来描述两变量的回归的直线，用直线方程来描述两变量的回归关系。关系。p最小二乘法原理：实测点到直线的最小二乘法原理：实测点到直线的纵向距离平方纵向距离平方之和之和达到最小。达到最小。33Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth,
16、 LZMC直线回归的统计推断直线回归的统计推断p对对的两种假设检验方法包括：的两种假设检验方法包括：t检验检验方差分析方差分析H0：=0，即无直线关系，即无直线关系H1：0，即有直线关系，即有直线关系34Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC方差分析的基本思想方差分析的基本思想将全部数据的离均差平方和将全部数据的离均差平方和SS总总分解成分解成若干部分，其自由度也做相应的分解。若干部分，其自由度也做相应的分解。35Department of Heal
17、th Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC36Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMCp方差分析法的原理：方差分析法的原理：对应变量对应变量y的离均差平方和进行的离均差平方和进行分解分解直线回归的统计推断直线回归的统计推断37Department of Health Statistics, Department of Health Statisti
18、cs, SchoolofPublicHealth, LZMCP(x,y)0残差残差回归回归总变异总变异因变量因变量y的离均差平方和分解示意图的离均差平方和分解示意图Y的均值的均值实测值实测值y估计值估计值38Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC的分解的分解p上述三段的数学表达式为：上述三段的数学表达式为：将等式两端平方后再求和，最后得到：将等式两端平方后再求和，最后得到：即即SS总总(lYY)=SS回回+SS残残39Department of He
19、alth Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC：总离均差平方和：总离均差平方和，即不考虑，即不考虑y与与x回归关系的回归关系的y的总的总变异变异：回归平方和，：回归平方和，即即y的总变异中可以用的总变异中可以用y与与x的回归关的回归关系所解释的部分。值越大，说明回归效果越好系所解释的部分。值越大，说明回归效果越好。：残差平方和，即：残差平方和，即y的总变异中无法用的总变异中无法用y与与x的回归关的回归关系解释的部分，反映系解释的部分，反映随机误差随机误差。在散点图中，各实。在散点图中，各实
20、测点离回归直线越近，测点离回归直线越近，SS残残越小，说明直线回归越小，说明直线回归的估计误差越小。的估计误差越小。40Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC自由度的分解自由度的分解41Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC构造构造F统计量统计量42Department of Health Statisti
21、cs, Department of Health Statistics, SchoolofPublicHealth, LZMC方差分析表方差分析表变异变异来源来源离均差离均差平方和平方和SS自由度自由度 均方均方MS统计量统计量F总总 总总=n-1回归回归 回回=1MS回回=SS回回/1MS回回/MS残残残差残差 残残=n-2MS残残=SS残残/(n-2)43Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC本例本例1.建立检验假设，确定检验水准建立检验假设，确
22、定检验水准44Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC2.计算检验统计量计算检验统计量45Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC3.确定确定P值，作出统计推断值，作出统计推断 P0.01，按照，按照0.05检验水准拒绝检验水准拒绝H0。回归方程有回归方程有统计学意义，可以认为腹腔内脂肪面积与腰围之间有统计学意
23、义，可以认为腹腔内脂肪面积与腰围之间有直线回归关系。直线回归关系。46Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC直线回归的步骤：直线回归的步骤：1.1.考察数据的分布考察数据的分布, ,即分析即分析y y变量的变量的正态性正态性。2.2.作作散点图散点图, ,确定有无线性趋势。确定有无线性趋势。3.3.建立建立直线回归方程直线回归方程。4.4.对方程及其对方程及其参数参数进行进行估计估计与与假设检验假设检验。5.5.绘制回归直线绘制回归直线。47Depa
24、rtment of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC 例例14.1某研究欲探讨男性腰围与腹腔某研究欲探讨男性腰围与腹腔内脂肪面积的关系，对内脂肪面积的关系，对20名男性志愿受名男性志愿受试者测量其腰围试者测量其腰围(cm)，并采用磁共振成，并采用磁共振成像法测量其腹腔内脂肪面积像法测量其腹腔内脂肪面积(cm2)，结，结果如表果如表14.1所示。试建立腹腔内脂肪面所示。试建立腹腔内脂肪面积积(y )和腰围和腰围(x )的直线回归方程。的直线回归方程。48Department
25、 of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC第一步第一步: :数据录入数据录入设置两个变量：设置两个变量：px腰围腰围(cm)py腹腔内脂肪面积腹腔内脂肪面积(cm2) 与直线相关相同与直线相关相同注意区分注意区分x和和y49Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC第二步第二步: :统计分析统计分析1.1.绘制散点图绘制散点图Grap
26、hsScatterSimplenYAxis框框:ynXAxis框框:x50Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC从图中可见，腰从图中可见，腰围和腹腔内脂肪围和腹腔内脂肪面积有比较明显面积有比较明显的线性趋势，也的线性趋势，也没有发现影响过没有发现影响过强的异常点，可强的异常点，可以进行回归分析。以进行回归分析。51Department of Health Statistics, Department of Health Statistics, Sch
27、oolofPublicHealth, LZMC2.直线回归分析：直线回归分析：AnalyzeRegressionLinear52Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC应变量应变量y自变量自变量x点击点击53Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMCStatistics对话框对话框默认，计算相关系默认，计算相关系
28、数、决定系数等数、决定系数等要勾选，计算回归要勾选，计算回归系数的置信区间系数的置信区间默认，计算回归系默认，计算回归系数及假设检验数及假设检验54Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC第三步：结果解释第三步：结果解释 介绍了模型拟合优度的情况：介绍了模型拟合优度的情况： 相关系数相关系数r=0.762r=0.762 决定系数决定系数R R2 2=SS=SS回回/SS/SS总总=0.581=0.581 剩余标准差（残差标准差）剩余标准差（残差标准差）
29、S Syxyx=13.0353=13.0353模型总结模型总结55Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC决定系数决定系数(coefficientofdetermination) 反映了回归贡献的相对程度，即在反映了回归贡献的相对程度，即在因变量因变量y的的总变异中用总变异中用y与与x回归关系所能解释的比例回归关系所能解释的比例。在实。在实际应用中，常用际应用中，常用决定系数来反映回归的实际效果决定系数来反映回归的实际效果。值越大，说明方程拟合的效果越
30、好。值越大，说明方程拟合的效果越好。本例决定系数为本例决定系数为0.581，说明男性的，说明男性的腰围信息可腰围信息可以解释其腹腔内脂肪面积变异的以解释其腹腔内脂肪面积变异的58.1%，还有剩，还有剩余的余的41.9%的信息需要通过腰围以外的其它因素的信息需要通过腰围以外的其它因素来加以解释。来加以解释。56Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC F =24.924 P 0.001 按按0.05的检验水准拒绝的检验水准拒绝H0接受接受H1，回归方回归
31、方程有统计学意义程有统计学意义，可以认为腹腔内脂肪面，可以认为腹腔内脂肪面积与腰围之间积与腰围之间有直线回归关系有直线回归关系。结果解释结果解释回归方程的回归方程的方差分析方差分析57Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC1.截距截距a=-96.392，回归系数，回归系数b=2.1112.tb=4.992，P0.001，结论同前（，结论同前（F检验）。检验）。3.写出直线回归方程：写出直线回归方程：回归系数的假设检验等价于相关系数的结果回归系数的假设
32、检验等价于相关系数的结果结果解释结果解释回归系数的假回归系数的假设检验：设检验：t检验检验58Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC故所求回归方程为：故所求回归方程为：b=2.11053表明腹腔内脂肪面积随腰围增加而增加，表明腹腔内脂肪面积随腰围增加而增加，且腰围每增加且腰围每增加1cm，腹腔内脂肪面积增加，腹腔内脂肪面积增加2.11053cm259Department of Health Statistics, Department of Heal
33、th Statistics, SchoolofPublicHealth, LZMC4.绘制回归直线绘制回归直线pAnalyzeCurveEstimation60Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMCCurveEstimation对话框对话框应变量应变量y自变量自变量x61Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC62Department of Health Statistics, Department of Health Statistics, SchoolofPublicHealth, LZMC结束语结束语谢谢大家聆听！谢谢大家聆听！63
