应用回归分析例8.2SAS程序

例8.2 1,建立数据集 data a;

input year y x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13@@; cards;

1997 11355.53 13.88 16074.14 227.03 11511.41 559.83

2036.9 574.40 725.76 2820.96 51173.8 16630.7 10894.2 9978.93 1998 11670 13.32 16100 232.79 11863.67 542 2171 539.37 744 3010 53600 17194.03 11559 10737.8

1999 12393 13.64 16000 251.98 12539.24 567 2356 580.14 766 3251 57300 17419.79 12426 12109.78

2000 13556 13.84 16300 272 13101.48 657 2427 667.88 834 3186 59700 18352.2 12850 13146

2001 14808.02 14.72 16395.87 303.29 15554.25 760.68 2696.3 787.96 914.37 3383.01 66103.99 20964.12 15163.4 16067.61

2002 16540 15.5 16700 326.61 17084.6 850 3050.4 877.97 1033.15 3791 72500 23445.56 18236.6 19251.59

2003 19105.75 18.35 16959.98 350.15 21366.68 983.58 3371.2 945.27 1133.56 3881.31 86208.11 27702.6 22233.6 24108.01 2004 22033.09 21.23 17587.33 414.6 26830.99 1291.34 3928.9 1041.12 1334.7 4804.82 96681.99 37026.17 28291.1 31975.72 2005 25002.6 23.50 18135.29 493.2 34375.19 1450.54 4544.70 1239.98 1421.08 5177.86 106884.79 40210.24 35324 37771.14 2006 28657.26 25.29 18476.57 585.53 41245.19 1742.96 5033.20 1511.78 1560.03 5345.05 123676.48 46574.70 41914.90 46893.36 2007 32815.53 26.92 18631.82 692.40 47651.63 2068.17 5412.60 1759.29 1765.00 5824.98 136117.25 53918.07 48928.80 56560.87 2008 34957.61 28.02 19043.06 802.99 47824.42 2170.92 5098.00 1926.01 1854.60 6028.05 142355.73 59890.39 50305.80 60460.29 2009 37146.51 29.73 18948.96 852.69 55283.46 2393.46 5960.90 1832.37 1944.77 6385.01 164397.78 58574.07 57218.20 69405.40 ; run;

proc print data=a; run;

2进行相关分析

proc corr data=a noprob; var y x1-x13; run; Pearson 相关系数, N = 13 y y 1.00000 x0.91 9231 x0.92 8743 x0.93 9086 x0.94 9564 x0.95 9866 x0.96 8657 x0.97 9299 x0.98 9744 x0.99 8993 x0.919670 7 x0.9x1 0.99231 1.00000 0.99348 0.97331 0.99256 0.99156 0.98974 0.97896 0.99268 0.99187 0.99064 0.9x2 0.98743 0.99348 1.00000 0.96525 0.98323 0.98426 0.98514 0.98183 0.99062 0.99039 0.97985 0.9x3 0.99086 0.97331 0.96525 1.00000 0.98742 0.99210 0.96094 0.98724 0.98138 0.97039 0.98713 0.9x4 0.99564 0.99256 0.98323 0.98742 1.00000 0.99708 0.98827 0.98557 0.98984 0.98596 0.99473 0.9x5 0.99866 0.99156 0.98426 0.99210 0.99708 1.00000 0.98456 0.99070 0.99518 0.98798 0.99600 0.9x6 0.98657 0.98974 0.98514 0.96094 0.98827 0.98456 1.00000 0.97097 0.98924 0.99148 0.98891 0.9x7 0.99299 0.97896 0.98183 0.98724 0.98557 0.99070 0.97097 1.00000 0.98886 0.97544 0.98225 0.9x8 0.99744 0.99268 0.99062 0.98138 0.98984 0.99518 0.98924 0.98886 1.00000 0.99424 0.99408 0.9x9 0.98993 0.99187 0.99039 0.97039 0.98596 0.98798 0.99148 0.97544 0.99424 1.00000 0.98769 0.9x10 x11 x12 x13 0.99677 0.99064 0.97985 0.98713 0.99473 0.99600 0.98891 0.98225 0.99408 0.98769 1.00000 0.90.99565 0.99301 0.99141 0.98508 0.99056 0.99511 0.97873 0.99140 0.99474 0.98971 0.98784 1.00.99771 0.99384 0.98562 0.98893 0.99944 0.99831 0.98909 0.98758 0.99335 0.98938 0.99642 0.90.99783 0.98934 0.97916 0.99431 0.99725 0.99905 0.98254 0.98771 0.99256 0.98565 0.99723 0.9Pearson 相关系数, N = 13 y 19561 5 x0.919772 1 x0.919783 3 x1 9301 0.99384 0.98934 x2 9141 0.98562 0.97916 x3 8508 0.98893 0.99431 x4 9056 0.99944 0.99725 x5 9511 0.99831 0.99905 x6 7873 0.98909 0.98254 x7 9140 0.98758 0.98771 x8 9474 0.99335 0.99256 x9 8971 0.98938 0.98565 x10 x11 x12 x13 8784 0.99642 0.99723 0000 0.99313 0.99228 9313 1.00000 0.99839 9228 0.99839 1.00000 可见数据存在多重共线性 3,逐步回归法进行回归 proc reg data=a;

model y=x1-x13/selection=stepwise ; run;

方差分析 源 模型 误差 自由度 5 7 平方 和 均方 F 值 Pr > F 1038185283 207637057 6234.78 <.0001 233121 33303 校正合计 12

1038418404 变量 参数 估计值 标准 误差 II 型 SS F 值 Pr > F 1.32 0.2889 5.06 0.0592 6.28 0.0406 7.69 0.0276 20.20 0.0028 3.95 0.0873 Intercept -511.85733 446.06170 43852 x3 x4 x7 x8 x10

4.99186 0.09315 3.11448 7.65064 0.04718 2.21844 0.03717 1.12293 1.70232 0.02374 168621 209206 256184 672662 131472 4,偏最小二乘法建立回归方程

proc standard data=a out=out1 mean=0 std=1; var y x1-x13; run;

proc pls data=out1 nfac=3 details ; model y=x1-x13/solution; run; Model Effect Weights Numx1 ber of Extracted Factors 1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 Inner Regression Coefficients 0.20.20.20.20.20.20.20.20.20.20.20.20.20.277697557657787867537717837627817787847848642 25 62 19 54 95 22 15 56 59 69 57 32 66 -0.-0.0.5-0.0.1-0.0.40.1-0.0.10.0-0.0.10.113423683120971443745090963426770430387845999 665 354 93 015 99 648 89 43 339 86 06 847 95 -0.0.0-0.-0.-0.0.30.30.60.00.3-0.-0.-0.0.141254073064811730951540096305491322811818790 413 78 449 455 700 57 22 26 22 35 335 008 789 2 3 如上表,我们得到结果 tk与y*的回归方程

Parameter Estimates 聽 y Intercept -.0000000000 x1 x2 x3 0.0026784396 0.0228334843 0.1182505437 Parameter Estimates 聽 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13

回归方程:

y -.0099499098 0.0705926287 0.0617308722 0.1978398150 0.1849619153 0.0305830683 0.1577970756 0.0585309087 0.0295283056 0.0797684735 y*?0.0027x1?0.0228x2?0.1183x3?0.001x4?0.0706x5?0.0617x6?0.1978x7?0.1850x8?0.0306x9?0.1578x10?0.0585x11?0.0295x12?0.0798x13

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