统计建模与R软件第六章课后习题答案Word格式.docx
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统计建模与R软件第六章课后习题答案Word格式.docx
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0.001'
**'
0.01'
*'
0.05'
.'
0.1'
'
1
Residualstandarderror:
96.42on8degreesoffreedom
MultipleR-squared:
0.9781,
AdjustedR-squared:
0.9754
F-statistic:
357.5on1and8DF,
p-value:
6.33e-08
回归方程为Y=140.95+364.18X
(3)
β1项很显著,但常数项β0不显著。
回归方程很显著。
(4)
new<
-data.frame(x=7)
lm.pred<
-predict(lm.sol,new,interval="
prediction"
)
lm.pred
fit
lwr
upr
12690.2272454.9712925.484
故Y(7)=2690.227,[2454.971,2925.484]
Ex6.2
pho<
-data.frame(x1<
-c(0.4,0.4,3.1,0.6,4.7,1.7,9.4,10.1,11.6,12.6,10.9,23.1,23.1,21.6,23.1,1.9,26.8,29.9),x2<
-c(52,34,19,34,24,65,44,31,29,58,37,46,50,44,56,36,58,51),x3<
-c(158,163,37,157,59,123,46,117,173,112,111,114,134,73,168,143,202,124),y<
-c(64,60,71,61,54,77,81,93,93,51,76,96,77,93,95,54,168,99))
-lm(y~x1+x2+x3,data=pho)
lm(formula=y~x1+x2+x3,data=pho)
-27.575-11.160
-2.799
11.574
48.808
44.9290
18.3408
2.450
0.02806*
x1
1.8033
0.5290
3.409
0.00424**
x2
-0.1337
0.4440
-0.301
0.76771
x3
0.1668
0.1141
1.462
0.16573
19.93on14degreesoffreedom
0.551,
0.4547
5.726on3and14DF,
0.009004
回归方程为y=44.9290+1.8033x1-0.1337x2+0.1668x3
回归方程显著,但有些回归系数不显著。
lm.step<
-step(lm.sol)
Start:
AIC=111.2
y~x1+x2+x3
DfSumofSq
RSS
AIC
-x2
1
36.0
5599.4
109.3
<
none>
5563.4
111.2
-x3
849.8
6413.1
111.8
-x1
4617.810181.2
120.1
Step:
AIC=109.32
y~x1+x3
833.2
6432.6
109.8
5169.510768.9
119.1
summary(lm.step)
lm(formula=y~x1+x3,data=pho)
-29.713-11.324
-2.953
11.286
48.679
41.4794
13.8834
2.988
0.00920**
1.7374
0.4669
3.721
0.00205**
0.1548
0.1036
1.494
0.15592
19.32on15degreesoffreedom
0.5481,
0.4878
9.095on2and15DF,
0.002589
x3仍不够显著。
再用drop1函数做逐步回归。
drop1(lm.step)
Singletermdeletions
Model:
可以考虑再去掉x3.
lm.opt<
-lm(y~x1,data=pho);
summary(lm.opt)
lm(formula=y~x1,data=pho)
-31.486
-8.282
-1.674
5.623
59.337
59.2590
7.4200
7.9865.67e-07***
1.8434
0.4789
3.849
0.00142**
20.05on16degreesoffreedom
0.4808,
0.4484
14.82on1and16DF,
0.001417
皆显著。
Ex6.3
x<
-c(1,1,1,1,2,2,2,3,3,3,4,4,4,5,6,6,6,7,7,7,8,8,8,9,11,12,12,12)
y<
-c(0.6,1.6,0.5,1.2,2.0,1.3,2.5,2.2,2.4,1.2,3.5,4.1,5.1,5.7,3.4,9.7,8.6,4.0,5.5,10.5,17.5,13.4,4.5,30.4,12.4,13.4,26.2,7.4)
-9.8413-2.3369-0.0214
1.059217.8320
-1.4519
1.8353
-0.791
0.436
1.5578
0.2807
5.5497.93e-06***
5.168on26degreesoffreedom
0.5422,
0.5246
30.8on1and26DF,
7.931e-06
线性回归方程为y=-1.4519+1.5578x,通过F检验。
常数项参数未通过t检验。
abline(lm.sol)
y.yes<
-resid(lm.sol)
y.fit<
-predict(lm.sol)
y.rst<
-rstandard(lm.sol)
plot(y.yes~y.fit)
plot(y.rst~y.fit)
残差并非是等方差的。
修正模型,对相应变量Y做开方。
lm.new<
-update(lm.sol,sqrt(.)~.)
summary(lm.new)
lm(formula=sqrt(y)~x)
-1.54255-0.45280-0.01177
0.34925
2.12486
0.76650
0.25592
2.995
0.00596**
0.29136
0.03914
7.4446.64e-08***
0.7206on26degreesoffreedom
0.6806,
0.6684
55.41on1and26DF,
6.645e-08
此时所有参数和方程均通过检验。
对新模型做标准化残差图,情况有所改善,不过还是存在一个离群值。
第24和第28个值存在问题。
Ex6.4
toothpaste<
-data.frame(X1=c(-0.05,0.25,0.60,0,0.20,0.15,-0.15,0.15,0.10,0.40,0.45,0.35,0.30,0.50,0.50,0.40,-0.05,-0.05,-0.10,0.20,0.10,0.50,0.60,-0.05,0,0.05,0.55),X2=c(5.50,6.75,7.25,5.50,6.50,6.75,5.25,6.00,6.25,7.00,6.90,6.80,6.80,7.10,7.00,6.80,6.50,6.25,6.00,6.50,7.00,6.80,6.80,6.50,5.75,5.80,6.80),Y=c(7.38,8.51,9.52,7.50,8.28,8.75,7.10,8.00,8.15,9.10,8.86,8.90,8.87,9.26,9.00,8.75,7.95,7.65,7.27,8.00,8.50,8.75,9.21,8.27,7.67,7.93,9.26))
-lm(Y~X1+X2,data=toothpaste);
lm(formula=Y~X1+X2,data=toothpaste)
-0.37130-0.10114
0.03066
0.10016
0.30162
4.0759
0.6267
6.5041.00e-06***
X1
1.5276
0.2354
6.4891.04e-06***
X2
0.6138
0.1027
5.9743.63e-06***
0.1767on24degreesoffreedom
0.9378,
0.9327
181on2and24DF,
3.33e-15
回归诊断:
influence.measures(lm.sol)
Influencemeasuresof
lm(formula=Y~X1+X2,data=toothpaste):
dfb.1_
dfb.X1
dfb.X2
dffitcov.r
cook.d
hatinf
1
0.00908
0.00260-0.00847
0.01211.3665.11e-050.1681
2
0.06277
0.04467-0.06785-0.12441.1595.32e-030.0537
3
-0.02809
0.07724
0.02540
0.18581.2831.19e-020.1386
4
0.11688
0.05055-0.11078
0.14041.3776.83e-030.1843
*
5
0.01167
0.01887-0.01766-0.10371.1413.69e-030.0384
6
-0.43010-0.42881
0.45774
0.60610.8141.11e-010.0936
7
0.07840
0.01534-0.07284
0.10821.4814.07e-030.2364
8
0.01577
0.00913-0.01485
0.02081.2371.50e-040.0823
9
0.01127-0.02714-0.00364
0.10711.1563.95e-030.0466
10-0.07830
0.00171
0.08052
0.18901.1551.22e-020.0726
11
0.00301-0.09652-0.00365-0.22811.1271.76e-020.0735
12-0.03114
0.01848
0.03459
0.15421.1328.12e-030.0514
13-0.09236-0.03801
0.09940
0.22011.0711.62e-020.0522
14-0.02650
0.03434
0.02606
0.11791.2354.81e-030.0956
15
0.00968-0.11445-0.00857-0.25451.1502.19e-020.0910
16-0.00285-0.06185
0.00098-0.16081.1468.83e-030.0594
17
0.07201
0.09744-0.07796-0.10991.3644.19e-030.1731
18
0.15132
0.30204-0.17755-0.39071.0875.04e-020.1085
19
0.07489
0.47472-0.12980-0.75790.7311.66e-010.1092
20
0.05249
0.08484-0.07940-0.46600.6256.11e-020.0384
21
0.07557
0.07284-0.07861-0.08801.4712.69e-030.2304
22-0.17959-0.39016
0.18241-0.54940.9129.41e-020.1022
23
0.06026
0.10607-0.06207
0.12511.3745.42e-030.1804
24-0.54830-0.74197
0.59358
0.83710.9142.13e-010.1731
25
0.08541
0.01624-0.07775
0.13141.2495.97e-030.1069
26
0.32556
0.11734-0.30200
0.44801.0186.49e-020.1033
27
0.17243
0.32754-0.17676
0.41271.1485.66e-020.1369
source("
Reg_Diag.R"
);
Reg_Diag(lm.sol)#薛毅老师自己写的程序
residuals1
standards2
students3hat_matrixs4
DFFITSs5
0.00443843
0.02753865
0.02695925
0.16811819
0.01211949
-0.09114255
-0.53021138
-0.52211469
0.05369239
-0.12436727
0.07726887
0.47112863
0.46335666
0.13857353
0.18584310
0.04805665
0.30111062
0.29532912
0.18427663
0.14036860
-0.09130271
-0.52689847
-0.51881406
0.03838430
-0.10365442
0.30162101
1.79287913
1.88596579
0.09362223
0.60613406
0.03066005
0.19855842
0.19453763
0.23641540
*
0.10824626
0.01199519
0.07085860
0.06937393
0.08226537
0.02077047
0.08491891
0.49217591
0.48426323
0.04664158
0.10711246
10
0.11625405
0.68315814
0.67537315
0.07261134
0.18897969
11-0.13874451
-0.81570765
-0.80983786
0.07348894
-0.22807820
12
0.11540228
0.67051940
0.66263761
0.05137589
0.15420864
13
0.16178406
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