1、基于glm （廣義線性模型）的數據分析sas里的glm應用在實際中比較廣泛，對數據的分析具有比較強的普適 性。趨勢面回歸分析（trend analysis）是以多元回歸分析為理論基礎的一 種預測 與統計技術。它用空間坐標法進行多項式回歸，從中估計出最佳的 回歸模型，因 此也被稱為趨勢面分析，當不知道手中的數據呈線性還是非 線性相關時，可以采用趨勢面數據分析方法，以便找出擬合數據的最佳統計 預測模型。本文運用glm對一定的數據進行glm分析。一、數據與要求此處選取15名吧不同程度的煙民的每日飲酒（啤酒）量與心電圖指標（zb）的對應數據。然后設法建立zb與日抽煙量（x） /支和日飲酒量（y） /升

2、之間的關系。序號組另ij日抽煙量（x） /支日飲酒量（y） /升心電圖指標/ 、113010280212511260313513330414014400514514410622012270721811210822512280922513300102231329011340144101234515420133481642514350184501535519470二、運用glm過程進行趨勢面分析1 .趨勢分析的glm程序data beer;input obsn x y zb; cards;01 30 10 28002 25 11 26003 35 13 33004 40 14 40005 45 1

3、441006 20 12 27007 18 11 21008 25 12 28009 25 13 30010 23 13 29011 40 1441012 45 15 42013 48 16 42514 50 18 45015 55 19 470 proc glm; model zb=x y/p;proc glm;model zb=x y x*x x*y y*y/p;proc glm;model zb=x y x*x*x x*x*y x*y*y y*y*y/p;proc glm;model zb=x y x*x*x x*x*y x*y*y y*y*y x*x*x*x x*x*x*y x*x*y

4、*y x*y*y*y y*y*y*y/p; run;2.四種分析模型結果（1）一階趨勢模型dependent variable: zb源變量自由度平方和均值3sum ofsourcedfsquaresmean squaref valuepr fmodel90615.2099345307.60497127.19fx189541.5655889541.56558251.36 f114652.2435114652.2435141.13x |t|intercept64.0499938033.065399191.940.07665.383855650.839475676.41 f18666.167161

5、07.75 fx189541.5655889541.56558516.86 fx1965.2913631965.29136315.570.0426y1127.4395437127.43954370.740.4133x*x143.662297243.66229720.250.6277x*y1242.0343234242.03432341.400.2675y*y149.843031649.84303160.290.6047standardparameterestimateerrort valuepr|t|intercept-262.7664793109.1074817-2.410.0394x16.

6、06997796.80786202.360.0426y23.539132727.44498670.860.4133x*x0.06387730.12723830.500.6277x*y-1.16510160.9857119-1.180.2675y*y1.16733622.17629820.540.60476270.0000000255.125602414.8743976observation12345observed280.0000000260.0000000330.0000000400.0000000410.0000000predicted279.4168700258.6814596351.0

7、997183388.1251282414.0657505residual0.58313001.3185404-21.099718311.8748718-4.06575057210.0000000216.6773768-6.677376868280.0000000300.00000009290.000000010410.000000011420.000000012425.000000013450.00000001415470.0000000279.9417834303.5367795295.5572467388.1251282419.0280585436.4318573453.755470646

8、5.43176990.0582166-3.5367795-5.557246721.87487180.9719415-11.4318573-3.75547064.5682301-0.0000001559.164195-0.000000-0.3542052.694808dependent variable: zb 源變量自由度平方和均值f值概率值sourcedfsum ofsquaresmean squaref value pr fmodel93393.4641415565.5773683.21 fx189541.5655889541.56558478.66 fx11643.3470811643.

9、3470818.780.0180197.474017197.4740171.060.3343y10.56x*x*x1105.516422105.5164220.4741x*x*y1113.710330113.7103300.610.4580x*y*y1146.610010146.6100100.780.4018y*y*y1173.116161173.1161610.930.3642standardparameterestimateerror t valuepr|t|intercept-166.007458982.37772231-2.020.0786x11.13825983.757952332

10、.960.0180y15.778434015.357039051.030.3343x*x*x-0.01541320.02052250-0.750.4741x*x*y0.12031870.154323330.780.4580x*y*y-0.34167860.38595313-0.890.4018y*y*y0.31348940.325876140.960.364215470.0000000463.53108336.4689167observationobservedpredictedresidual1280.0000000281.0906363-1.09063632260.0000000256.0

11、4837833.95162173330.0000000351.8935219-21.89352194400.0000000390.57078969.42921045410.0000000409.23096520.76903486270.0000000257.998349012.00165107210.0000000220.0483966-10.04839668280.0000000275.01603684.98396329300.0000000299.47099730.529002710290.0000000295.8228899-5.822889911410.0000000390.57078

12、9619.429210412420.0000000420.5758580-0.575858013425.0000000437.4437284-12.443728414450.0000000455.6875798-5.6875798-0.0000001496.535862-0.000000-0.3575452.686333sum of residualssum of squared residualssum of squared residuals - error ssfirst order autocorrelationdurbin-watson d4）四階趨勢模型dependent vari

13、able: zb 源變量自由度平方和均值f值概率值sum ofsourcedfsquaresmean squaref valuepr fmodel1194480.319198589.1199362.900.0029error3409.68081136.56027corrected total1494890.00000r-squarecoeff varroot msezb mean0.9956833.367695 11.68590347.0000sourcedftype i ssmean squaref valuepr fx189541.5655889541.56558655.690.0001y

14、11073.644351073.644357.860.0676x*x*x12078.776642078.7766415.220.0299x*x*y1508.85526508.855263.730.1491x*y*y117.5061417.506140.130.7440y*y*y1173.11616173.116161.270.3421x*x*x*x152.9156652.915660.390.5777x*x*x*y1193.81980193.819801.420.3192x*x*y*y1452.42798452.427983.310.1663x*y*y*y140.3287940.328790.

15、300.6246y*y*y*y1347.36281347.362812.540.2090sourcedftype iii ssmean squaref valuepr fx153.834735453.83473540.390.5746y118.442245818.44224580.140.7376x*x*x1707.3985134707.39851345.180.1073x*x*y1688.7276032688.72760325.040.1104x*y*y1669.2155979669.21559794.900.1137y*y*y1614.9897506614.98975064.500.123

16、9x*x*x*x173.525495773.52549570.540.5162x*x*x*y121.572098721.57209870.160.7176x*x*y*y1150.8940383150.89403831.100.37040.2581x*y*y*y1264.7516451264.75164511.94y*y*y*y1347.3628138347.36281382.540.2090standardparameterestimateerrort valuepr |t|intercept-748.5352475602.9093096-1.240.3026x21.526850134.285

17、57060.630.5746y63.4532525172.66693160.370.7376x*x*x1.11290830.48897822.280.1073x*x*y-7.84664423.4939960-2.250.1104x*y*y17.69195997.99199322.210.1137y*y*y-12.81731806.0398396-2.120.1239x*x*x*x-0.00528950.0072088-0.730.5162x*x*x*y-0.03396280.0854515-0.400.7176x*x*y*y0.42181270.40127851.050.3704x*y*y*y

18、-1.09527330.7866207-1.390.2581y*y*y*y0.84110790.52737831.590.2090observation1234567891011121314observed280.0000000260.0000000330.0000000400.0000000410.0000000270.0000000210.0000000280.0000000300.0000000290.0000000410.0000000420.0000000425.0000000450.0000000predicted280.6428697254.9148649336.2353148399.8451524409.0029100265.5623644212.0079405287.4716063292.6701245295.8090433399.8451524428.1747562422.5228478450.5733972residual-0.64286975.0851351-6.23531480.15484760.99709004.4376356-2.0079405-7.47160637.3298755-5.80