商务统计学Ch12

Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,Chap 12-,*,第,12,章,一元线性回归,商务统计学,(,第,5,版,),Chap 12-,1,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,学习目标,在本章中你将学到,:,如何利用一元线性回归分析理论，由自变量来预测因变量,回归系数,b,0,和,b,1,的含义,如何评价一元线性回归分析的假设条件，并且了解假设违背时的处理方法,斜率和相关系数的推断,均值估计和个值预测,2,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,相关与回归,一个,散点图,可以用来表示两个变量之间的关系,相关性,分析是用来测量两个变量之间的关联（线性关系）强度,相关性仅仅是关心关联的强度,没有因果关系是隐含相关性,散点图首次出现在第,2,章,相关性首次出现在第,3,章,3,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,回归分析简介,回归分析,被应用于,:,基于至少一个自变量的值，预测因变量的值,解释一个自变量的变化对因变量的影响,因变量,:,我们要预测或解释的变量,自变量,:,用来预测或解释因变量的变量,4,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,一元线性回归模型,只有,一个自变量,X,X,与,Y,的关系可以通过线性函数表示,假定,Y,的变化与,X,的变化有关,5,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,相关类型,Y,X,Y,X,Y,Y,X,X,线性相关,曲线相关,6,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,关系类型,Y,X,Y,X,Y,Y,X,X,强相关,弱相关,(,续,),7,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,相关类型,Y,X,Y,X,不相关,(,续,),8,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,线性组成部分,一元线性回归模型,总体的,Y,轴截距,总体的斜率,随机误差项,因变量,自变量,随机误差部分,9,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,(,续,),取值,X,i,时，因变量的随机误差,Y,X,与,X,i,对应的,Y,的,观测值,与,X,i,对应的,Y,的预测值,X,i,斜率,=,1,截距,0,i,一元线性回归模型,10,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,一元线性回归方程可以,估计,总体回归直线,一元线性回归方程,(,预测线,),回归截距的估计值,回归斜率的估计值,第,i,个观测值的,Y,的估计（预测）值,第,i,个观测值,X,的值,11,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,最小二乘法,我们可以求出使得,Y,和 的,离差平方和最小,的,b,0,和,b,1,的值,12,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,求出最小二乘方程的解,系数,b,0,和,b,1,以及本章的其它回归结果，通过,Excel,或者,Minitab,求出,文章中为感兴趣的读者列出了公式,13,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,b,0,是当,X,为零时，,Y,的期望值,b,1,是当,X,发生一个单元的变化时，,Y,的期望值发生的变化,对斜率和截距的解释,14,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,一个房地产经纪人希望得出房屋售价与房屋大小（以平方英尺为单位）的关系,随意抽取,10,间房子作为一个样本,因变量,(Y) =,房价（,1000,美元,）,自变量,(X) =,平方英尺,一元线性回归的例子,15,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,一元线性回归例子：数据,房价,(1000,美元）,(Y),平方英尺,(X),245,1400,312,1600,279,1700,308,1875,199,1100,219,1550,405,2350,324,2450,319,1425,255,1700,16,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,一元线性回归例子,:,散点图,房价模型,:,散点图,17,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,一元线性回归的例子,:,利用,Excel,18,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,一元线性回归的例子,: Excel,输出,Regression Statistics,Multiple R,0.76211,R Square,0.58082,Adjusted R Square,0.52842,Standard Error,41.33032,Observations,10,ANOVA,df,SS,MS,F,Significance F,Regression,1,18934.9348,18934.9348,11.0848,0.01039,Residual,8,13665.5652,1708.1957,Total,9,32600.5000,Coefficients,Standard Error,t Stat,P-value,Lower 95%,Upper 95%,Intercept,98.24833,58.03348,1.69296,0.12892,-35.57720,232.07386,Square Feet,0.10977,0.03297,3.32938,0.01039,0.03374,0.18580,回归方程为,:,19,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,一元线性回归的例子,: Minitab,输出,The regression equation is,Price = 98.2 + 0.110 Square Feet,Predictor,Coef,SE,Coef,T P,Constant 98.25 58.03 1.69 0.129,Square Feet 0.10977 0.03297 3.33 0.010,S = 41.3303 R-Sq = 58.1% R-,Sq(adj,) = 52.8%,Analysis of Variance,Source DF SS MS F P,Regression 1 18935,18935,11.08 0.010,Residual Error8 13666 1708,Total 9 32600,回归方程为,:,房价,= 98.24833 +,0.10977 (,平方英尺,),20,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,一元线性回归的例子,:,图表分析法,房价模型,:,散点图和预测线,斜率,= 0.10977,截距,= 98.248,21,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,一元线性回归的例子,:,对,b,o,的解释,b,0,是当,X,的值为零时，,Y,的期望值（如果,0,在被观测到的,X,的取值范围内,),因为一个房子的面积不可能为,0,，所以截距,b,0,没有实际解释意义,22,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,b,1,是,X,增加一个单位，导致,Y,的期望值发生的变化,这里, b,1,= 0.10977,意味着，房子每增加一平方英尺，房价的期望值平均增加,0.10977(1000,美元,) = 109.77,美元,一元线性回归的例子,:,对,b,1,的解释,23,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,预测有,2000,平方英尺的房子的价格,:,一个有,2000,平方英尺的房子的预测价格是,317.85(1,000,美元,) = 317,850,美元,一元线性回归的例子,:,预测,24,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,一元线性回归的例子,:,预测,使用回归模型进行预测时，只能在数据的相关范围内做预测,相关范围内插值,不要试图推断超出观测,X,的相关范围的房价,25,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,离差的度量,总方差有两部分组成,:,总平方和,回归平方和,残差平方和,其中,:,=,因变量的均值,Y,i,=,因变量的观测值,=,与,X,i,对应的,Y,的观测值,26,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,(,续,),离差的度量,SST =,总平方和,(,总变差,),度量 观测值,Y,i,与均值,Y,的差异,SSR =,回归平方和,(,能解释的离差平方和,),由,X,和,Y,之间的关系所决定的偏差,SSE =,残差平方和,(,不能解释的离差平方和,),由,X,和,Y,关系以外的其它因素所造成的偏差,27,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,(,续,),X,i,Y,X,Y,i,SST,=,(Y,i,-,Y,),2,SSE,=,(Y,i,-,Y,i,),2,SSR =,(,Y,i,-,Y,),2,_,_,_,Y,Y,Y,_,Y,离差的度量,28,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,可决系数,是总变差中由回归模型解释的部分所占的比例,可决系数也被称为：,r-,平方,，并以,r,2,表示,可决系数,r,2,注意,:,29,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,r,2,= 1,r,2,值的例子,Y,X,Y,X,r,2,= 1,r,2,= 1,X,和,Y,是强线性关系,:,100%,的,Y,的离差可以由,X,的离差来解释,30,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,r,2,值的例子,Y,X,Y,X,0 r,2, 1,X,和,Y,之间是弱线性关系,:,一部分但并不是所有的,Y,的离差都可以用,X,的离差可以解释,31,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,r,2,值的例子,r,2,= 0,X,和,Y,之间没有线性关系,:,Y,的值不依赖于,X. (Y,的离差不能用,X,的离差解释,),Y,X,r,2,= 0,32,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,一元线性回归的例子,:,在,Excel,输出中的可决系数,r,2,Regression Statistics,Multiple R,0.76211,R Square,0.58082,Adjusted R Square,0.52842,Standard Error,41.33032,Observations,10,ANOVA,df,SS,MS,F,Significance F,Regression,1,18934.9348,18934.9348,11.0848,0.01039,Residual,8,13665.5652,1708.1957,Total,9,32600.5000,Coefficients,Standard Error,t Stat,P-value,Lower 95%,Upper 95%,Intercept,98.24833,58.03348,1.69296,0.12892,-35.57720,232.07386,Square Feet,0.10977,0.03297,3.32938,0.01039,0.03374,0.18580,58.08%,的,房价离差可以由平方英尺的离差来解释,33,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,一元线性回归的例子,:,在,Minitab,输出中的可决系数,r,2,The regression equation is,Price = 98.2 + 0.110 Square Feet,Predictor,Coef,SE,Coef,T P,Constant 98.25 58.03 1.69 0.129,Square Feet 0.10977 0.03297 3.33 0.010,S = 41.3303 R-Sq = 58.1% R-,Sq(adj,) = 52.8%,Analysis of Variance,Source DF SS MS F P,Regression 1 18935,18935,11.08 0.010,Residual Error8 13666 1708,Total 9 32600,58.08%,的,房价离差可以有平方英尺的离差来解释,34,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,估计值的标准误差,观测值偏离回归线的标准差的计算公式为：,其中,SSE =,残差平方和,n =,样本量,35,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,一元线性回归的例子,:,在,Excel,中，估计值的标准差,Regression Statistics,Multiple R,0.76211,R Square,0.58082,Adjusted R Square,0.52842,Standard Error,41.33032,Observations,10,ANOVA,df,SS,MS,F,Significance F,Regression,1,18934.9348,18934.9348,11.0848,0.01039,Residual,8,13665.5652,1708.1957,Total,9,32600.5000,Coefficients,Standard Error,t Stat,P-value,Lower 95%,Upper 95%,Intercept,98.24833,58.03348,1.69296,0.12892,-35.57720,232.07386,Square Feet,0.10977,0.03297,3.32938,0.01039,0.03374,0.18580,36,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,一元线性回归的例子,:,在,Minitab,中，估计值的标准差,The regression equation is,Price = 98.2 + 0.110 Square Feet,Predictor,Coef,SE,Coef,T P,Constant 98.25 58.03 1.69 0.129,Square Feet 0.10977 0.03297 3.33 0.010,S = 41.3303 R-Sq = 58.1% R-,Sq(adj,) = 52.8%,Analysis of Variance,Source DF SS MS F P,Regression 1 18935,18935,11.08 0.010,Residual Error8 13666 1708,Total 9 32600,37,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,标准差的比较,Y,Y,X,X,S,YX,表示,Y,的观测值偏离回归线的程度,S,YX,的 大小应该是相对于样本数据中,Y,值的大小而言的,例如,相对于房价在,200000,美元,-400000,美元的范围,S,YX,= $41.33K,比较小,38,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,回归的假设条件,L.I.N.E,线性（,L,inearity,）,X,和,Y,之间的关系是线性的,误差项相互独立（,I,ndependence of Errors,）,误差值是在统计上是独立的,误差项呈正态分布（,N,ormality of Error,）,给定任意,X,值，误差项是服从正态分布的,同方差（方差齐性）（,E,qual Variance,）,误差项所服从分布的方差为常数,39,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,残差分析,对于第,i,个观测的残差,e,i,是观测值与预测值之间的差,通过残差检验回归的假设条件,检验线性假设,评估独立性假设,评估正态分布假设,对各种层次的,X,检验方差相同（方差齐性）的假设,残差的图形分析,可以画出残差随,X,的变化图,40,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,检验线性的残差分析,非线性,线性,x,残差,x,Y,x,Y,x,残差,41,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,检验独立性的残差分析,不独立,独立,X,X,残差,残差,X,残差,42,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,检验正态性,检查残差的茎叶图,检查残差的盒须图,检查残差的直方图,建立残差的正态概率图,43,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,检验正态性的残差分析,百分率,残差,当使用正态概率图时,正态误差大约将会排列在一条直线上,-3 -2 -1 0 1 2 3,0,100,44,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,检验同方差的残差分析,不同方差,同方差,x,x,Y,x,x,Y,residuals,residuals,45,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,一元线性回归的例子,:,残差在,Excel,中的输出,残差输出,预测的房价,残差,1,251.92316,-6.923162,2,273.87671,38.12329,3,284.85348,-5.853484,4,304.06284,3.937162,5,218.99284,-19.99284,6,268.38832,-49.38832,7,356.20251,48.79749,8,367.17929,-43.17929,9,254.6674,64.33264,10,284.85348,-29.85348,没有违背任何回归假设,46,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,有关斜率的统计推断,回归的斜率,(b,1,),的标准差可以通过下式求出：,其中,:,=,斜率标准差的估计值,=,这个估计值的标准差,47,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,有关斜率的统计推断,: t,检验,总体斜率的,t,检验,X,和,Y,之间存在线性关系吗,?,零假设与备择假设,H,0,:,1,= 0(,不存在线性关系,),H,1,:,1, 0(,线性关系确实存在,),检验统计量,其中,:,b,1,=,回归斜率系数,1,=,斜率假定值,S,b1,=,样本斜率的标准差,48,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,有关斜率的统计推断,: t,检验的例子,房价（,1000,）,(y),平方英尺,(x),245,1400,312,1600,279,1700,308,1875,199,1100,219,1550,405,2350,324,2450,319,1425,255,1700,估计的回归方程,:,这个模型的斜率,0.1098,房价与房子建筑面积（平方英尺）有关系吗？,49,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,H,0,:,1,= 0,H,1,:,1, 0,来自,Excel,的输出,:,Coefficients,Standard Error,t Stat,P-value,Intercept,98.24833,58.03348,1.69296,0.12892,Square Feet,0.10977,0.03297,3.32938,0.01039,b,1,Predictor,Coef,SE,Coef,T P,Constant 98.25 58.03 1.69 0.129,Square Feet 0.10977 0.03297 3.33 0.010,来自,Minitab,的输出,:,b,1,有关斜率的统计推断,: t,检验的例子,50,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,检验统计量,:,t,STAT,= 3.329,有足够的证据表明建筑面积影响房价,决策,:,拒绝,H,0,拒绝,H,0,拒绝,H,0,a,/2=.025,-t,/2,不拒绝,H,0,0,t,/2,a,/2=.025,-2.3060,2.3060,3.329,d.f,. = 10- 2 = 8,H,0,:,1,= 0,H,1,:,1, 0,有关斜率的统计推断,: t,检验的例子,51,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,H,0,:,1,= 0,H,1,:,1, 0,来自,Excel,输出,:,Coefficients,Standard Error,t Stat,P-value,Intercept,98.24833,58.03348,1.69296,0.12892,Square Feet,0.10977,0.03297,3.32938,0.01039,p-,值,有足够的证据表明建筑面积影响房价,.,决策,:,拒绝,H,0,因为,p-,值,Predictor,Coef,SE,Coef,T P,Constant 98.25 58.03 1.69 0.129,Square Feet 0.10977 0.03297 3.33 0.010,来自,Minitab,输出,:,有关斜率的统计推断,: t,检验的例子,52,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,显著性的,F,检验,F,检验统计量,:,其中,其中,F,STAT,服从,自由度,为,1,和,(n 2),的,F,分布,53,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,显著性,F,检验的,Excel,输出,Regression Statistics,Multiple R,0.76211,R Square,0.58082,Adjusted R Square,0.52842,Standard Error,41.33032,Observations,10,ANOVA,df,SS,MS,F,Significance F,Regression,1,18934.9348,18934.9348,11.0848,0.01039,Residual,8,13665.5652,1708.1957,Total,9,32600.5000,自由度为,1,和,8,F,检验的,p-,值,54,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,显著性,F,检验的,Minitab,输出,Analysis of Variance,Source DF SS MS F P,Regression 1 18935,18935,11.08 0.010,Residual Error8 13666 1708,Total 9 32600,自由度为,1,和,8,F,检验的,p-,值,55,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,H,0,:,1,= 0,H,1,:,1, 0,= .05,df,1,= 1 df,2,= 8,检验统计量,:,决策,:,结论,:,拒绝,H,0,，在显著性水平,= 0.05,的 情况下,有足够的证据表明房子的大小影响销售价格,0,= .05,F,.05,= 5.32,拒绝,H,0,不拒绝,H,0,临界值,:,F,= 5.32,显著性的,F,检验,(,续,),F,56,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,斜率的置信区间估计,斜率置信区间的估计,:,房价的,Excel,打印输出,:,在,95%,的置信水平下， 斜率的置信区间为,(0.0337, 0.1858),Coefficients,Standard Error,t Stat,P-value,Lower 95%,Upper 95%,Intercept,98.24833,58.03348,1.69296,0.12892,-35.57720,232.07386,Square Feet,0.10977,0.03297,3.32938,0.01039,0.03374,0.18580,d.f,. = n - 2,57,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,由于变量房价的变化单元为,1000,美元，我们有,95%,的把握保证，每平方英尺的建筑面积对销售价格的影响在,33.74,美元到,185.8,美元之间,Coefficients,Standard Error,t Stat,P-value,Lower 95%,Upper 95%,Intercept,98.24833,58.03348,1.69296,0.12892,-35.57720,232.07386,Square Feet,0.10977,0.03297,3.32938,0.01039,0.03374,0.18580,95%,的置信区间,不包括,0,.,结论,:,在,0.05,的显著性水平下，房价与平方英尺的关系是显著的,(,续,),斜率的置信区间估计,58,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,相关系数的,t,检验,假设,H,0,:,= 0,(X,与,Y,不相关,),H,1,:, 0,(,相关,),检验统计量,(,自由度为,n 2),59,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,在,.05,的,显著性水平下，有证据显示平方英尺与房价是线性关系吗？,H,0,:,= 0 (,不相关,),H,1,:, 0 (,相关,),=.05 ,df,=,10 - 2 = 8,(,续,),相关系数的,t,检验,60,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,结论,:,在,5%,的显著性水平下，有证据表明存在线性关系,决策,:,拒绝,H,0,拒绝,H,0,拒绝,H,0,a,/2=.025,-t,/2,不拒绝,H,0,0,t,/2,a,/2=.025,-2.3060,2.3060,3.329,d.f,. = 10-2 = 8,(,续,),相关系数的,t,检验,61,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,均值的估计和单个数值的预测,Y,X,X,i,Y = b,0,+b,1,X,i,给定,X,i,，,Y,均值,的置信区间,给定,Xi,单个,Y,值的预测区间,目标,:,对于给定的,X,i,，,形成因变量均值的置信区间表示对其值的不确定,Y,62,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,给定,X,Y,均值的置信区间,给定特定的,Xi,，估计,Y,均值,的置信区间,区间的大小取决于与均值,X,的距离,63,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,给定,X,单个因变量,Y,的预测值区间,给定特定的,Xi,，估计,单个因变量,Y,的预测值区间,为了反映单个个别事件的不确定性，将区间宽度增加一项额外项,64,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,均值估计的例子,求面积为,2,000,英尺的房子平均售价的,95%,置信区间,预测价格,Y,i,= 317.85 (1,000,美元,),估计,Y|X=X,置信区间,置信区间的端点是,280.66,和,354.90,或者从,280,660,美元到,354,900,美元,i,65,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,单个因变量估计的例子,一个面积有,2,000,英尺的,95%,预测价格区间,预测价格,Y,i,= 317.85 (1,000,美元,),估计,Y,X=X,的预测值区间,预测区间的端点是,215.50,和,420.07,或者从,215,500,美元到,420,070,美元,i,66,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,用,Excel,得到的对置信区间的估计与预测区间的估计,在,Excel,中,利用,PHStat,| regression | simple linear regression ,选择对话框,“confidence and prediction interval for X=”,，,并且输入,X,的值，以及置信水平,67,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,输入值,(,续,),对,Y|X=Xi,置信区间的估计,对,Y,X=Xi,预测区间的估计,Y,用,Excel,得到的对置信区间的估计与预测区间的估计,68,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,用,minitab,得到的对置信区间的估计与预测区间的估计,Predicted Values for New Observations,New,Obs,Fit SE Fit 95% CI 95% PI,1 317.8 16.1 (280.7, 354.9) (215.5, 420.1),Values of Predictors for New Observations,New Square,Obs,Feet,1 2000,Y,输入值,对,Y|X=Xi,置信区间的估计,对,Y,X=Xi,预测区间的估计,69,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,回归分析的缺陷,对最小二乘法回归的假设条件了解不足,不知如何评估最小二乘法的假设条件是否成立,当违背某个假设条件时，不知道如何选择其他适用的回归方法,在对实际问题了解不足的情况下，应用回归模型,在相关范围之外，外推预测值,70,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,避免回归缺陷的策略,首先画出散点图来观察,X,与,Y,之间可能的关系,使用残差分析法，检验回归的假设是否成立,将残差对自变量作散点图，判断该模型有没有违背同方差的假设,利用残差的直方图、茎叶图、盒须图、正态概率图判断正态性的假设能否满足,71,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,避免回归缺陷的策略,如果显示有违背假设条件，采用其他方法或模型,如果没有显示违背假设条件，那么应着手检验回归系数的显著性，以及估计置信区间与预测值区间,避免在自变量的区域范围之外进行预测外推,(,续,),72,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,小结,介绍了各种回归模型,回顾了回归假设与相关性,讨论了确定一元线性回归方程,描述了离差的度量,讨论了残差分析,73,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,小结,描述了对斜率的统计推断,讨论了相关系数,衡量关联强度,解决了估计均值与预测单个值的问题,讨论了回归可能存在的缺陷，并针对可能的缺陷提出了避免策略,(,续,),74,Business Statistics: A First Course, 5e 2009 Prentice-Hall, Inc.,