###############################################
sink('exam1_2012.sink')
postscript('exam1_2012.ps')
mfrow = c(2,2)
data(InsectSprays)
attach(InsectSprays)
print(InsectSprays)
shapiro.test(count)
hist(count)
ncount=sqrt(count)  # transformation de variable
shapiro.test(ncount)
state=factor(spray)
m1=lm(ncount~spray)
summary(m1)

dev.off()
sink()
###############################################
   count spray
1     10     A
2      7     A
3     20     A
4     14     A
5     14     A
6     12     A
7     10     A
8     23     A
9     17     A
10    20     A
11    14     A
12    13     A
13    11     B
14    17     B
15    21     B
16    11     B
17    16     B
18    14     B
19    17     B
20    17     B
21    19     B
22    21     B
23     7     B
24    13     B
25     0     C
26     1     C
27     7     C
28     2     C
29     3     C
30     1     C
31     2     C
32     1     C
33     3     C
34     0     C
35     1     C
36     4     C
37     3     D
38     5     D
39    12     D
40     6     D
41     4     D
42     3     D
43     5     D
44     5     D
45     5     D
46     5     D
47     2     D
48     4     D
49     3     E
50     5     E
51     3     E
52     5     E
53     3     E
54     6     E
55     1     E
56     1     E
57     3     E
58     2     E
59     6     E
60     4     E
61    11     F
62     9     F
63    15     F
64    22     F
65    15     F
66    16     F
67    13     F
68    10     F
69    26     F
70    26     F
71    24     F
72    13     F

	Shapiro-Wilk normality test

data:  count 
W = 0.9216, p-value = 0.0002525


	Shapiro-Wilk normality test

data:  ncount 
W = 0.9673, p-value = 0.05765


Call:
lm(formula = ncount ~ spray)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.24486 -0.39970 -0.01902  0.42661  1.40089 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   3.7607     0.1814  20.733  < 2e-16 ***
sprayB        0.1160     0.2565   0.452    0.653    
sprayC       -2.5158     0.2565  -9.807 1.64e-14 ***
sprayD       -1.5963     0.2565  -6.223 3.80e-08 ***
sprayE       -1.9512     0.2565  -7.606 1.34e-10 ***
sprayF        0.2579     0.2565   1.006    0.318    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.6283 on 66 degrees of freedom
Multiple R-squared: 0.7724,	Adjusted R-squared: 0.7552 
F-statistic:  44.8 on 5 and 66 DF,  p-value: < 2.2e-16