Ex6.1
（1）
> x <- c(5.1, 3.5, 7.1, 6.2, 8.8, 7.8, 4.5, 5.6, 8.0, 6.4)
> y <- c(1907, 1287, 2700, 2373, 3260, 3000, 1947, 2273, 3113,2493)
> plot(x,y)

由此判断，Y和X有线性关系。
（2）
> lm.sol<-lm(y~1+x)
> summary(lm.sol)

Call:
lm(formula = y ~ 1 + x)

Residuals:
     Min       1Q   Median       3Q      Max
-128.591  -70.978   -3.727   49.263  167.228

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept)   140.95     125.11   1.127    0.293   
x             364.18      19.26  18.908 6.33e-08 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 96.42 on 8 degrees of freedom
Multiple R-squared: 0.9781,     Adjusted R-squared: 0.9754
F-statistic: 357.5 on 1 and 8 DF,  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
1 2690.227 2454.971 2925.484
故Y(7)= 2690.227, [2454.971,2925.484]

Ex6.2
(1)
>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.sol<-lm(y~x1+x2+x3,data=pho)
> summary(lm.sol)

Call:
lm(formula = y ~ x1 + x2 + x3, data = pho)

Residuals:
    Min      1Q  Median      3Q     Max
-27.575 -11.160  -2.799  11.574  48.808

Coefficients:
            Estimate Std. Error t value Pr(>|t|)  
(Intercept)  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  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 19.93 on 14 degrees of freedom
Multiple R-squared: 0.551,      Adjusted R-squared: 0.4547
F-statistic: 5.726 on 3 and 14 DF,  p-value: 0.009004
回归方程为 y=44.9290+1.8033x1-0.1337x2+0.1668x3
（2）
回归方程显著，但有些回归系数不显著。
（3）
> lm.step<-step(lm.sol)
Start:  AIC=111.2
y ~ x1 + x2 + x3

       Df Sum of Sq     RSS     AIC
- x2    1      36.0  5599.4   109.3
<none>               5563.4   111.2
- x3    1     849.8  6413.1   111.8
- x1    1    4617.8 10181.2   120.1

Step:  AIC=109.32
y ~ x1 + x3

       Df Sum of Sq     RSS     AIC
<none>               5599.4   109.3
- x3    1     833.2  6432.6   109.8
- x1    1    5169.5 10768.9   119.1

> summary(lm.step)

Call:
lm(formula = y ~ x1 + x3, data = pho)

Residuals:
    Min      1Q  Median      3Q     Max
-29.713 -11.324  -2.953  11.286  48.679

Coefficients:
            Estimate Std. Error t value Pr(>|t|)  
(Intercept)  41.4794    13.8834   2.988  0.00920 **
x1            1.7374     0.4669   3.721  0.00205 **
x3            0.1548     0.1036   1.494  0.15592  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 19.32 on 15 degrees of freedom
Multiple R-squared: 0.5481,     Adjusted R-squared: 0.4878
F-statistic: 9.095 on 2 and 15 DF,  p-value: 0.002589
x3仍不够显著。
再用drop1函数做逐步回归。
> drop1(lm.step)
Single term deletions

Model:
y ~ x1 + x3
       Df Sum of Sq     RSS     AIC
<none>               5599.4   109.3
x1      1    5169.5 10768.9   119.1
x3      1     833.2  6432.6   109.8
可以考虑再去掉x3.
> lm.opt<-lm(y~x1,data=pho);summary(lm.opt)

Call:
lm(formula = y ~ x1, data = pho)

Residuals:
    Min      1Q  Median      3Q     Max
-31.486  -8.282  -1.674   5.623  59.337

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept)  59.2590     7.4200   7.986 5.67e-07 ***
x1            1.8434     0.4789   3.849  0.00142 **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 20.05 on 16 degrees of freedom
Multiple R-squared: 0.4808,     Adjusted R-squared: 0.4484
F-statistic: 14.82 on 1 and 16 DF,  p-value: 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)
> plot(x,y)
> lm.sol<-lm(y~1+x)
> summary(lm.sol)

Call:
lm(formula = y ~ 1 + x)

Residuals:
    Min      1Q  Median      3Q     Max
-9.8413 -2.3369 -0.0214  1.0592 17.8320

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept)  -1.4519     1.8353  -0.791    0.436   
x             1.5578     0.2807   5.549 7.93e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 5.168 on 26 degrees of freedom
Multiple R-squared: 0.5422,     Adjusted R-squared: 0.5246
F-statistic:  30.8 on 1 and 26 DF,  p-value: 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)

Call:
lm(formula = sqrt(y) ~ x)

Residuals:
     Min       1Q   Median       3Q      Max
-1.54255 -0.45280 -0.01177  0.34925  2.12486

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept)  0.76650    0.25592   2.995  0.00596 **
x            0.29136    0.03914   7.444 6.64e-08 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.7206 on 26 degrees of freedom
Multiple R-squared: 0.6806,     Adjusted R-squared: 0.6684
F-statistic: 55.41 on 1 and 26 DF,  p-value: 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.sol<-lm(Y~X1+X2,data=toothpaste); summary(lm.sol)

Call:
lm(formula = Y ~ X1 + X2, data = toothpaste)

Residuals:
     Min       1Q   Median       3Q      Max
-0.37130 -0.10114  0.03066  0.10016  0.30162

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept)   4.0759     0.6267   6.504 1.00e-06 ***
X1            1.5276     0.2354   6.489 1.04e-06 ***
X2            0.6138     0.1027   5.974 3.63e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.1767 on 24 degrees of freedom
Multiple R-squared: 0.9378,     Adjusted R-squared: 0.9327
F-statistic:   181 on 2 and 24 DF,  p-value: 3.33e-15
回归诊断：
> influence.measures(lm.sol)
Influence measures of
         lm(formula = Y ~ X1 + X2, data = toothpaste) :

     dfb.1_   dfb.X1   dfb.X2   dffit cov.r   cook.d    hat inf
1   0.00908  0.00260 -0.00847  0.0121 1.366 5.11e-05 0.1681   
2   0.06277  0.04467 -0.06785 -0.1244 1.159 5.32e-03 0.0537   
3  -0.02809  0.07724  0.02540  0.1858 1.283 1.19e-02 0.1386   
4   0.11688  0.05055 -0.11078  0.1404 1.377 6.83e-03 0.1843   *
5   0.01167  0.01887 -0.01766 -0.1037 1.141 3.69e-03 0.0384   
6  -0.43010 -0.42881  0.45774  0.6061 0.814 1.11e-01 0.0936   
7   0.07840  0.01534 -0.07284  0.1082 1.481 4.07e-03 0.2364   *
8   0.01577  0.00913 -0.01485  0.0208 1.237 1.50e-04 0.0823   
9   0.01127 -0.02714 -0.00364  0.1071 1.156 3.95e-03 0.0466   
10 -0.07830  0.00171  0.08052  0.1890 1.155 1.22e-02 0.0726   
11  0.00301 -0.09652 -0.00365 -0.2281 1.127 1.76e-02 0.0735   
12 -0.03114  0.01848  0.03459  0.1542 1.132 8.12e-03 0.0514   
13 -0.09236 -0.03801  0.09940  0.2201 1.071 1.62e-02 0.0522   
14 -0.02650  0.03434  0.02606  0.1179 1.235 4.81e-03 0.0956   
15  0.00968 -0.11445 -0.00857 -0.2545 1.150 2.19e-02 0.0910   
16 -0.00285 -0.06185  0.00098 -0.1608 1.146 8.83e-03 0.0594   
17  0.07201  0.09744 -0.07796 -0.1099 1.364 4.19e-03 0.1731   
18  0.15132  0.30204 -0.17755 -0.3907 1.087 5.04e-02 0.1085   
19  0.07489  0.47472 -0.12980 -0.7579 0.731 1.66e-01 0.1092   
20  0.05249  0.08484 -0.07940 -0.4660 0.625 6.11e-02 0.0384   *
21  0.07557  0.07284 -0.07861 -0.0880 1.471 2.69e-03 0.2304   *
22 -0.17959 -0.39016  0.18241 -0.5494 0.912 9.41e-02 0.1022   
23  0.06026  0.10607 -0.06207  0.1251 1.374 5.42e-03 0.1804   
24 -0.54830 -0.74197  0.59358  0.8371 0.914 2.13e-01 0.1731   
25  0.08541  0.01624 -0.07775  0.1314 1.249 5.97e-03 0.1069   
26  0.32556  0.11734 -0.30200  0.4480 1.018 6.49e-02 0.1033   
27  0.17243  0.32754 -0.17676  0.4127 1.148 5.66e-02 0.1369   
> source("Reg_Diag.R");Reg_Diag(lm.sol) #薛毅老师自己写的程序
      residual s1    standard s2     student s3 hat_matrix s4      DFFITS s5
1   0.00443843     0.02753865     0.02695925    0.16811819     0.01211949  
2  -0.09114255    -0.53021138    -0.52211469    0.05369239    -0.12436727  
3   0.07726887     0.47112863     0.46335666    0.13857353     0.18584310  
4   0.04805665     0.30111062     0.29532912    0.18427663     0.14036860  
5  -0.09130271    -0.52689847    -0.51881406    0.03838430    -0.10365442  
6   0.30162101     1.79287913     1.88596579    0.09362223     0.60613406  
7   0.03066005     0.19855842     0.19453763    0.23641540  *  0.10824626  
8   0.01199519     0.07085860     0.06937393    0.08226537     0.02077047  
9   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     0.94041623     0.93806144    0.05219432     0.22013204  
14  0.06210727     0.36957277     0.36282531    0.09557411     0.11794546  
15 -0.13650951    -0.81026658    -0.80428349    0.09101221    -0.25449541  
16 -0.11097950    -0.64757782    -0.63955524    0.05943308    -0.16076716  
17 -0.03939381    -0.24515626    -0.24029557    0.17309048    -0.10993940  
18 -0.18593575    -1.11438446    -1.12029013    0.10845395    -0.39073410  
19 -0.33609591    -2.01522068  * -2.16439284  * 0.10922236    -0.75789180  *
20 -0.37130271  * -2.14274943  * -2.33258738  * 0.03838430    -0.46603012  
21 -0.02545527    -0.16420856    -0.16084153    0.23042354  * -0.08801075  
22 -0.26374306    -1.57517595    -1.62848498    0.10217431    -0.54936198  
23  0.04349338     0.27187605     0.26656251    0.18041800     0.12506702  
24  0.28060619     1.74627363     1.82969510    0.17309048     0.83711731  *
25  0.06459859     0.38683016     0.37987153    0.10691352     0.13143357  
26  0.21752520     1.29995371     1.31989945    0.10329116     0.44796770  
27  0.16987516     1.03474390     1.03633781    0.13685835     0.41266341  
   cooks_distance s6  COVRATIO s7
1    5.108777e-05    1.3656752  
2    5.316885e-03    1.1589547  
3    1.190200e-02    1.2827036  
4    6.827446e-03    1.3771332  
5    3.693897e-03    1.1410104  
6    1.106753e-01    0.8143179  
7    4.068871e-03    1.4806452  *
8    1.500251e-04    1.2372586  
9    3.950358e-03    1.1560508  
10   1.218047e-02    1.1550557  
11   1.759216e-02    1.1271148  
12   8.116460e-03    1.1316638  
13   1.623390e-02    1.0710597  
14   4.811117e-03    1.2349272  
15   2.191171e-02    1.1501502  
16   8.832858e-03    1.1457602  
17   4.193532e-03    1.3637206  
18   5.035591e-02    1.0866343  
19   1.659840e-01    0.7313914  
20   6.109050e-02    0.6248838  
21   2.691197e-03    1.4714103  
22   9.412101e-02    0.9121786  
23   5.423856e-03    1.3735324  
24   2.127740e-01  * 0.9139942  
25   5.971157e-03    1.2485557  
26   6.488529e-02    1.0178195  
27   5.658922e-02    1.1479080  
为什么两种方法检测结果不一样呢...不继续了

Ex6.5
> cement<-data.frame(X1=c( 7,  1, 11, 11,  7, 11,  3,  1,  2, 21,  1, 11, 10),X2=c(26, 29, 56, 31, 52, 55, 71, 31, 54, 47, 40, 66, 68),X3=c( 6, 15,  8,  8,  6,  9, 17, 22, 18,  4, 23,  9,  8),X4=c(60, 52, 20, 47, 33, 22,  6, 44, 22, 26, 34, 12, 12),Y =c(78.5, 74.3, 104.3,  87.6,  95.9, 109.2, 102.7, 72.5, 93.1,115.9,  83.8, 113.3, 109.4))
> xx<-cor(cement[1:4])
> kappa(xx,exact=T)
[1] 1376.881
大于1000，认为有严重的多重共线性。
> eigen(xx)
$values
[1] 2.235704035 1.576066070 0.186606149 0.001623746

$vectors
           [,1]       [,2]       [,3]      [,4]
[1,] -0.4759552  0.5089794  0.6755002 0.2410522
[2,] -0.5638702 -0.4139315 -0.3144204 0.6417561
[3,]  0.3940665 -0.6049691  0.6376911 0.2684661
[4,]  0.5479312  0.4512351 -0.1954210 0.6767340
即2.235704035X1+1.576066070X2+0.186606149X3+0.001623746X4=0
可以忽略X4项，可以看出X1，X2，X3存在共线性。
删去X3和X4后：
> xx<-cor(cement[1:2])
> kappa(xx,exact=T)
[1] 1.59262
共线性消失了。
如果去掉X3呢？
> cement1<-cbind(cement$X1,cement$X2,cement$X4)
> xx<-cor(cement1)
> kappa(xx,exact=T)
[1] 77.25113
如果去掉X4呢？
> xx<-cor(cement[1:3])
> kappa(xx,exact=T)
[1] 11.12112
看起来去掉X3和X4是合理的。

Ex6.6
>infection<-data.frame(x1<-c(0,1,0,0,0,1,1,1),x2<-c(0,0,1,0,1,0,1,1),x3<-c(0,0,0,1,1,1,0,1),success<-c(0,0,23,8,28,0,11,1),fail<-c(9,0,3,32,30,2,87,17))
> infection$Ymat<-cbind(infection$success,infection$fail)
> glm.sol<-glm(Ymat~x1+x2+x3,family=binomial,data=infection)
> summary(glm.sol)

Call:
glm(formula = Ymat ~ x1 + x2 + x3, family = binomial, data = infection)

Deviance Residuals:
       1         2         3         4         5         6         7         8 
-2.56229   0.00000   1.49623   1.21563  -0.78520  -0.15231  -0.07162   0.26470 

Coefficients:
            Estimate Std. Error z value Pr(>|z|)   
(Intercept)  -0.8207     0.4947  -1.659   0.0971 . 
x1           -3.2544     0.4813  -6.761 1.37e-11 ***
x2            2.0299     0.4553   4.459 8.25e-06 ***
x3           -1.0720     0.4254  -2.520   0.0117 * 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 83.491  on 6  degrees of freedom
Residual deviance: 10.997  on 3  degrees of freedom
AIC: 36.178

Number of Fisher Scoring iterations: 5
回归模型为
P=exp(-0.8207-3.2544x1+2.0299x2-1.0720x3)/(1+exp(-0.8207-3.2544x1+2.0299x2-1.0720x3))

Ex6.7
（1）
> x<-c(rep(0:6,rep(2,7)))
> y<-c(508.1,498.4,568.2,577.3,651.7,657.0,713.4,697.5,755.3,758.9,787.6,792.1,841.4,831.8)
> lm.sol<-lm(y~1+x)
> summary(lm.sol)

Call:
lm(formula = y ~ 1 + x)

Residuals:
    Min      1Q  Median      3Q     Max
-25.400 -11.484  -3.779  14.629  24.921

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept)  523.800      8.474   61.81  < 2e-16 ***
x             54.893      2.350   23.36 2.26e-11 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 17.59 on 12 degrees of freedom
Multiple R-squared: 0.9785,     Adjusted R-squared: 0.9767
F-statistic: 545.5 on 1 and 12 DF,  p-value: 2.265e-11
线性回归模型为y=523.800+54.893x,通过t检验和F检验。
（2）
> lm.sol<-lm(y~1+x+I(x^2));summary(lm.sol)

Call:
lm(formula = y ~ 1 + x + I(x^2))

Residuals:
     Min       1Q   Median       3Q      Max
-10.6643  -5.6622  -0.4655   5.5000  10.6679

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept) 502.5560     4.8500 103.619  < 2e-16 ***
x            80.3857     3.7861  21.232 2.81e-10 ***
I(x^2)       -4.2488     0.6063  -7.008 2.25e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 7.858 on 11 degrees of freedom
Multiple R-squared: 0.9961,     Adjusted R-squared: 0.9953
F-statistic:  1391 on 2 and 11 DF,  p-value: 5.948e-14
多项式回归模型为：
y=502.5560+80.3857x-4.2488x^2,通过t检验和F检验。
(3)作散点图和拟合曲线：
> plot(x,y)
> xfit<-seq(0,6,0.01)
> yfit<-predict(lm.sol,data.frame(x=xfit))
> lines(xfit,yfit)


Ex6.8
读入数据：
> cancer<-read.table("data",header=T)
> cancer
   x1 x2 x3 x4 x5 y
1  70 64  5  1  1 1
2  60 63  9  1  1 0
3  70 65 11  1  1 0
4  40 69 10  1  1 0
5  40 63 58  1  1 0
6  70 48  9  1  1 0
7  70 48 11  1  1 0
8  80 63  4  2  1 0
9  60 63 14  2  1 0
10 30 53  4  2  1 0
11 80 43 12  2  1 0
12 40 55  2  2  1 0
13 60 66 25  2  1 1
14 40 67 23  2  1 0
15 20 61 19  3  1 0
16 50 63  4  3  1 0
17 50 66 16  0  1 0
18 40 68 12  0  1 0
19 80 41 12  0  1 1
20 70 53  8  0  1 1
21 60 37 13  1  1 0
22 90 54 12  1  0 1
23 50 52  8  1  0 1
24 70 50  7  1  0 1
25 20 65 21  1  0 0
26 80 52 28  1  0 1
27 60 70 13  1  0 0
28 50 40 13  1  0 0
29 70 36 22  2  0 0
30 40 44 36  2  0 0
31 30 54  9  2  0 0
32 30 59 87  2  0 0
33 40 69  5  3  0 0
34 60 50 22  3  0 0
35 80 62  4  3  0 0
36 70 68 15  0  0 0
37 30 39  4  0  0 0
38 60 49 11  0  0 0
39 80 64 10  0  0 1
40 70 67 18  0  0 1
> glm.sol<-glm(y~x1+x2+x3+x4+x5,family=binomial,data=cancer);summary(glm.sol)

Call:
glm(formula = y ~ x1 + x2 + x3 + x4 + x5, family = binomial,
    data = cancer)

Deviance Residuals:
     Min        1Q    Median        3Q       Max 
-1.71500  -0.66725  -0.22254   0.09936   2.23936 

Coefficients:
            Estimate Std. Error z value Pr(>|z|) 
(Intercept) -7.01140    4.47534  -1.567   0.1172 
x1           0.09994    0.04304   2.322   0.0202 *
x2           0.01415    0.04697   0.301   0.7631 
x3           0.01749    0.05458   0.320   0.7486 
x4          -1.08297    0.58721  -1.844   0.0651 .
x5          -0.61309    0.96066  -0.638   0.5233 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 44.987  on 39  degrees of freedom
Residual deviance: 28.392  on 34  degrees of freedom
AIC: 40.392

Number of Fisher Scoring iterations: 6
有的系数并不显著。
下面做逐步回归：
> glm.new<-step(glm.sol)
Start:  AIC=40.39
y ~ x1 + x2 + x3 + x4 + x5

       Df Deviance    AIC
- x3    1   28.484 38.484
- x2    1   28.484 38.484
- x5    1   28.799 38.799
<none>      28.392 40.392
- x4    1   32.642 42.642
- x1    1   38.306 48.306

Step:  AIC=38.48
y ~ x1 + x2 + x4 + x5

       Df Deviance    AIC
- x2    1   28.564 36.564
- x5    1   28.993 36.993
<none>      28.484 38.484
- x4    1   32.705 40.705
- x1    1   38.478 46.478

Step:  AIC=36.56
y ~ x1 + x4 + x5

       Df Deviance    AIC
- x5    1   29.073 35.073
<none>      28.564 36.564
- x4    1   32.892 38.892
- x1    1   38.478 44.478

Step:  AIC=35.07
y ~ x1 + x4

       Df Deviance    AIC
<none>      29.073 35.073
- x4    1   33.535 37.535
- x1    1   39.131 43.131
只留下x1和x4两个变量。
> summary(glm.new)

Call:
glm(formula = y ~ x1 + x4, family = binomial, data = cancer)

Deviance Residuals:
    Min       1Q   Median       3Q      Max 
-1.4825  -0.6617  -0.1877   0.1227   2.2844 

Coefficients:
            Estimate Std. Error z value Pr(>|z|) 
(Intercept) -6.13755    2.73844  -2.241   0.0250 *
x1           0.09759    0.04079   2.393   0.0167 *
x4          -1.12524    0.60239  -1.868   0.0618 .
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 44.987  on 39  degrees of freedom
Residual deviance: 29.073  on 37  degrees of freedom
AIC: 35.073

Number of Fisher Scoring iterations: 6
回归方程为
P=exp(-6.13755+0.09759x1-1.12524x4)/(1+exp(-6.13755+0.09759x1-1.12524x4))
概率估计略。

Ex6.9
我表示不想做了...
我没弄明白nls()函数里所说的start即初始值怎么设置。好像可以随便设置，只要保证函数收敛即可？？