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Regress_HettestSpearman    

简述
基于等级相关系数的异方差检验
定义
Regress_HettestSpearman(y;x:Array;alpha:Real;constant:Boolean):Array
参数
名称类型说明
YArray数组,因变量,一维数字数组
XArray数组,自变量,二维数字数组
AlphaReal实数,显著性水平,值域为[0,1]
ConstantBoolean布尔值,是否有常数项
返回Array数组,其中含义如下:
下标 说明
"Statistic" t统计量
"P-Value" p值
"Hypothesis" 是否接受假设
  • 算法

    做y关于x的普通最小二乘回归,求出εi的估计值,即ei的值
    取ei的绝对值,即|ei|,将xi与|ei|按递增或递减的次序排列并分等级
    根据公式 rs=1-6n(n2-1)i=1ndi2 算出等级相关系数,其中n为样本量;di对应于xi与|ei|的等级差数
    做等级相关系数的显著性检验。在n>8的情况下,用t=n-2rs1-rs对相关系数进行t检验,若|t|≤tα/2(n-2),则认为异方差问题不存在;否则说明xi与|ei|之间存在系统关系,异方差问题存在。
    范例

    y:=array(49.00,50.2,50.5,48.5,47.5,44.5,28.00,31.5,34.5,35.00,38.00,38.5,15.00,17.00,20.5,29.5);
      x:=array(
          (1300.00,7.5,0.012,9750.00,15.6,0.09),
          (1300.00,9.00,0.012,11700.00,15.6,0.108),
          (1300.00,11.00,0.0115,14300.00,14.95,0.1265),
          (1300.00,13.5,0.013,17550.00,16.9,0.1755),
          (1300.00,17.00,0.0135,22100.00,17.55,0.2295),
          (1300.00,23.00,0.012,29900.00,15.6,0.276),
          (1200.00,5.3,0.04,6360.00,48.00,0.212),
          (1200.00,7.5,0.038,9000.00,45.6,0.285),
          (1200.00,11.00,0.032,13200.00,38.4,0.352),
          (1200.00,13.5,0.026,16200.00,31.2,0.351),
          (1200.00,17.00,0.034,20400.00,40.8,0.578),
          (1200.00,23.00,0.041,27600.00,49.2,0.943),
          (1100.00,5.3,0.084,5830.00,92.4,0.4452),
          (1100.00,7.5,0.098,8250.00,107.8,0.735),
          (1100.00,11.00,0.092,12100.00,101.2,1.012),
          (1100.00,17.00,0.086,18700.00,94.6,1.462));
      alpha := 0.05;
      constant := 0;
      return Regress_HettestSpearman(y,X,alpha,constant);

    返回结果:
    Statistic 1.227706414781371
    P-Value 0.2398000476741131
    Hypothesis 1
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