y=do+d,+d2x 2+dx3 其中d=y-d1x1-d2x2-d2x 1、计算必要数据,列出正规方程组 级数据: ∑x1=38,∑x2=x2=270,∑x3=∑x=2144,2y=34,∑x2=2x=18066,2y2=176,∑x3=x2=1430610, ∑x1X=∑x=2144,∑xx=Ex2=18066,∑xX∑x3=158408,∑xy=189,∑x2y=∑x2y=129,∑xy=∑ xy=9675 二级数据: x1=475,x2=x2=33.75,x3=x3=286,j=425 l1=Σx2-(Σx)2/n=270-382/8=895 12=∑xx2-∑x∑x2/m=2144-38×270/8=861.5 l13=∑x1x3-∑x12x3/n=18066-38×2144/8=7882 l2=∑x2-(∑x2)2/n=18066-2702/8=89535 l23=∑x2x3-∑x2∑x3/n=158408-270×2144/8=86048 l3=∑x3-(Σx3)2/n=143060-21448=85608 ly=Σxy-∑xy/n=189-38×34/8=275 l2y=Σx2y-2x2y/n=1293-270×34/8=1455 ly,=Σx3y-2x32y/n=9675-2144×34/8=563 ln=∑y2-(2y)2/mn=176-34/8-315 于是正规方程组为: .5d1+861.5d2+7882d3=275 8615d1+8953.5d2+86048d3=1455 7892d1+86048d2+856018d3=563 2、计算偏回归系数,列出回归方程,仍可用(1-16)式对下列增广矩阵作消元变换,求得系数矩阵的逆 及各偏回归系数 895861.5788227.5 A0=861.58953586048145.5 (78886048856018563 00177739625698880670390.307263 ()=-9625698660960915101782459-119206704 8806739101782459161873.5986-1858.84357 0.151354 0.014563-60.1606 2.04329 A2)=-0014563000151315.399165-0.180354 60.160677-15.3991655137.11465-23.16028 0.855 0.1949010.0117111.772064 A(3=-01949010047673-0002998-0.1108 0.011711-0.0029980.0001950.004508 d1=1.7721,d2=-0.1109,d3=-0.0045 d=4.25-1.7721×4.75+0.1109×33.75+0.0045×256=0.781432 0 1 1 2 2 3 3 y ˆ = d + d x + d x + d x 其中 0 1 1 2 2 3 3 d = y − d x − d x − d x ⚫ 1、计算必要数据，列出正规方程组 一级数据： ∑x1=38，∑x2=∑x 2=270，∑x3=∑x 3=2144，∑y=34，∑ 2 2 x =∑x 4=18066，∑y 2=176，∑ 2 3 x =∑x 6=1430610， ∑x1x2=∑x3=2144，∑x1x2=∑x 4=18066，∑x2x3∑x 5=158408，∑x1y=189，∑x2y=∑x 2y=1293，∑x3y=∑ x 3y=9675 二级数据： 4.75, x1 = 33.75, 2 x2 = x = 286, 3 x3 = x = y = 4.25 l x x n 2 1 2 11 =  1 −（ ） =270－382／8=89.5 l 12 = x1 x2 − x1 x2 n =2144－38×270／8=861.5 l 13 =  x1 x3 −  x1  x3 n =18066－38×2144／8=7882 l x x n 2 2 2 22 =  2 −（ ） =18066－2702／8=8953.5 l 23 =  x2 x3 −  x2  x3 n =158408－270×2144／8=86048 l x x n 2 3 2 33 =  3 −（ ） =1430610－21442／8=856018 l 1y =  x1 y −  x1  y n =189－38×34／8=27.5 l 2 y =  x2 y −  x2  y n =1293－270×34／8=145.5 l 3y =  x3 y −  x3  y n =9675－2144×34／8=563 l yy y y n 2 2 =  − ( ) =176－342／8=31.5 于是正规方程组为：      + + = + + = + + = 7882 86048 856018 563 861.5 8953.5 86048 145.5 89.5 861.5 7882 27.5 1 2 3 1 2 3 1 2 3 d d d d d d d d d 2、计算偏回归系数，列出回归方程，仍可用（1—16）式对下列增广矩阵作消元变换，求得系数矩阵的逆 及各偏回归系数。           = 7882 86048 856018 563 861.5 8953.5 86048 145.5 89.5 861.5 7882 27.5 (0) A           − − = − − 88.067.39 10178.2459 161873.5986 1858.84357 9.625698 660.960915 10178.2459 119.206704 0.017773 9.625698 88.067039 0.307263 (1) A           − − − − − − = 60.160677 15.399165 5137.11465 23.16028 0.014563 0.001513 15.399165 0.180354 0.151354 0.014563 60.160677 2.043292 (2) A           − − − − − − = 0.011711 0.002998 0.000195 0.004508 0.194901 0.047673 0.002998 0.110928 0.855590 0.194901 0.011711 1.772064 (3) A d1=1.7721，d2=－0.1109，d3=－0.0045 d0=4.25－1.7721×4.75+0.1109×33.75+0.0045×256=0.7814