ozone <- read.table("../donnees/ozone.txt", header = T, sep = ";")
plot(ozone[,"T12"], ozone[,"O3"],pch=as.numeric(ozone[,"vent"]),
col = as.numeric(ozone[,"vent"]))
a1 <- lm(O3 ~ T12, data = ozone[ozone[,"vent"]=="EST",])
a2 <- lm(O3 ~ T12, data = ozone[ozone[,"vent"]=="NORD",])
a3 <- lm(O3 ~ T12, data = ozone[ozone[,"vent"]=="OUEST",])
a4 <- lm(O3 ~ T12, data = ozone[ozone[,"vent"]=="SUD",])
abline(a1, col=1)
abline(a2, col=2)
abline(a3, col=3)
abline(a4, col=4)
mod1b <- lm(formula = O3 ~ -1 + vent + T12:vent, data = ozone)
summary(mod1b)
Call:
lm(formula = O3 ~ -1 + vent + T12:vent, data = ozone)
Residuals:
Min 1Q Median 3Q Max
-29.903 -9.163 1.153 10.319 32.638
Coefficients:
Estimate Std. Error t value Pr(>|t|)
ventEST 45.6090 13.9343 3.273 0.002133 **
ventNORD 106.6345 28.0341 3.804 0.000456 ***
ventOUEST 64.6840 24.6208 2.627 0.011967 *
ventSUD -27.0602 26.5389 -1.020 0.313737
ventEST:T12 2.7480 0.6342 4.333 8.96e-05 ***
ventNORD:T12 -1.6491 1.6058 -1.027 0.310327
ventOUEST:T12 0.3407 1.2047 0.283 0.778709
ventSUD:T12 5.3786 1.1497 4.678 3.00e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 14.71 on 42 degrees of freedom
Multiple R-squared: 0.9773, Adjusted R-squared: 0.973
F-statistic: 226.1 on 8 and 42 DF, p-value: < 2.2e-16mod1 <- lm(formula = O3 ~ vent + T12:vent, data = ozone)
summary(mod1)
Call:
lm(formula = O3 ~ vent + T12:vent, data = ozone)
Residuals:
Min 1Q Median 3Q Max
-29.903 -9.163 1.153 10.319 32.638
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 45.6090 13.9343 3.273 0.00213 **
ventNORD 61.0255 31.3061 1.949 0.05796 .
ventOUEST 19.0751 28.2905 0.674 0.50384
ventSUD -72.6691 29.9746 -2.424 0.01972 *
ventEST:T12 2.7480 0.6342 4.333 8.96e-05 ***
ventNORD:T12 -1.6491 1.6058 -1.027 0.31033
ventOUEST:T12 0.3407 1.2047 0.283 0.77871
ventSUD:T12 5.3786 1.1497 4.678 3.00e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 14.71 on 42 degrees of freedom
Multiple R-squared: 0.6753, Adjusted R-squared: 0.6212
F-statistic: 12.48 on 7 and 42 DF, p-value: 1.614e-08mod2 <- lm(formula = O3 ~ vent + T12, data = ozone)
mod2b <- lm(formula = O3 ~ -1 + vent + T12, data = ozone)
mod3 <- lm(formula = O3 ~ vent:T12, data = ozone)anova(mod2,mod1)Analysis of Variance Table
Model 1: O3 ~ vent + T12
Model 2: O3 ~ vent + T12:vent
Res.Df RSS Df Sum of Sq F Pr(>F)
1 45 12612.0
2 42 9087.4 3 3524.5 5.4298 0.003011 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(mod3,mod1)Analysis of Variance Table
Model 1: O3 ~ vent:T12
Model 2: O3 ~ vent + T12:vent
Res.Df RSS Df Sum of Sq F Pr(>F)
1 45 11864.1
2 42 9087.4 3 2776.6 4.2776 0.01008 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1plot(rstudent(mod2) ~ fitted(mod2),xlab="ychap",ylab="residus")
library(lattice)
xyplot(rstudent(mod2)~fitted(mod2)|vent,data = ozone, ylab="residus")
mod <- lm(formula = O3 ~ vent + T12 + T12:vent, data = ozone)mod0 <- lm(formula = O3 ~ vent +T12 + T12:vent, data = ozone)
summary(mod0)
Call:
lm(formula = O3 ~ vent + T12 + T12:vent, data = ozone)
Residuals:
Min 1Q Median 3Q Max
-29.903 -9.163 1.153 10.319 32.638
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 45.6090 13.9343 3.273 0.00213 **
ventNORD 61.0255 31.3061 1.949 0.05796 .
ventOUEST 19.0751 28.2905 0.674 0.50384
ventSUD -72.6691 29.9746 -2.424 0.01972 *
T12 2.7480 0.6342 4.333 8.96e-05 ***
ventNORD:T12 -4.3971 1.7265 -2.547 0.01462 *
ventOUEST:T12 -2.4073 1.3614 -1.768 0.08429 .
ventSUD:T12 2.6306 1.3130 2.004 0.05160 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 14.71 on 42 degrees of freedom
Multiple R-squared: 0.6753, Adjusted R-squared: 0.6212
F-statistic: 12.48 on 7 and 42 DF, p-value: 1.614e-08eucalypt <- read.table("../donnees/eucalyptus.txt", header = T, sep = ";")
eucalypt[,"bloc"] <- as.factor(eucalypt[,"bloc"])
m.complet <- lm(ht ~ bloc - 1 + bloc:circ, data = eucalypt)
m.pente <- lm(ht ~ bloc - 1 + circ, data = eucalypt)
m.ordonne <- lm(ht ~ bloc:circ, data = eucalypt)
anova(m.pente, m.complet)Analysis of Variance Table
Model 1: ht ~ bloc - 1 + circ
Model 2: ht ~ bloc - 1 + bloc:circ
Res.Df RSS Df Sum of Sq F Pr(>F)
1 1425 2005.9
2 1423 2005.0 2 0.84752 0.3007 0.7403anova(m.ordonne, m.complet)Analysis of Variance Table
Model 1: ht ~ bloc:circ
Model 2: ht ~ bloc - 1 + bloc:circ
Res.Df RSS Df Sum of Sq F Pr(>F)
1 1425 2009.2
2 1423 2005.0 2 4.1649 1.4779 0.2285m.simple <- lm(ht ~ circ, data = eucalypt)
anova(m.simple, m.pente)Analysis of Variance Table
Model 1: ht ~ circ
Model 2: ht ~ bloc - 1 + circ
Res.Df RSS Df Sum of Sq F Pr(>F)
1 1427 2052.1
2 1425 2005.9 2 46.188 16.406 9.031e-08 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1mod1 <- lm(O3~vent-1,data=ozone)
summary(mod1)
Call:
lm(formula = O3 ~ vent - 1, data = ozone)
Residuals:
Min 1Q Median 3Q Max
-40.250 -13.950 -2.233 14.972 39.857
Coefficients:
Estimate Std. Error t value Pr(>|t|)
ventEST 103.850 4.963 20.92 < 2e-16 ***
ventNORD 78.289 6.618 11.83 1.49e-15 ***
ventOUEST 71.578 4.680 15.30 < 2e-16 ***
ventSUD 94.343 7.504 12.57 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 19.85 on 46 degrees of freedom
Multiple R-squared: 0.9547, Adjusted R-squared: 0.9508
F-statistic: 242.4 on 4 and 46 DF, p-value: < 2.2e-16anova(mod1)Analysis of Variance Table
Response: O3
Df Sum Sq Mean Sq F value Pr(>F)
vent 4 382244 95561 242.44 < 2.2e-16 ***
Residuals 46 18131 394
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1mod2 <- lm(O3 ~ vent, data = ozone)
anova(mod2)Analysis of Variance Table
Response: O3
Df Sum Sq Mean Sq F value Pr(>F)
vent 3 9859.8 3286.6 8.3383 0.0001556 ***
Residuals 46 18131.4 394.2
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod2)
Call:
lm(formula = O3 ~ vent, data = ozone)
Residuals:
Min 1Q Median 3Q Max
-40.250 -13.950 -2.233 14.972 39.857
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 103.850 4.963 20.923 < 2e-16 ***
ventNORD -25.561 8.272 -3.090 0.00339 **
ventOUEST -32.272 6.821 -4.731 2.16e-05 ***
ventSUD -9.507 8.997 -1.057 0.29616
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 19.85 on 46 degrees of freedom
Multiple R-squared: 0.3522, Adjusted R-squared: 0.31
F-statistic: 8.338 on 3 and 46 DF, p-value: 0.0001556lm(O3 ~ C(vent,treatment), data = ozone)
Call:
lm(formula = O3 ~ C(vent, treatment), data = ozone)
Coefficients:
(Intercept) C(vent, treatment)NORD C(vent, treatment)OUEST
103.850 -25.561 -32.272
C(vent, treatment)SUD
-9.507 lm(O3 ~ C(vent,base=2), data = ozone)
Call:
lm(formula = O3 ~ C(vent, base = 2), data = ozone)
Coefficients:
(Intercept) C(vent, base = 2)EST C(vent, base = 2)OUEST
78.289 25.561 -6.711
C(vent, base = 2)SUD
16.054 II <- length(levels(as.factor(ozone$vent)))
nI <- table(ozone$vent)
contraste<-matrix(rbind(diag(II-1),-nI[-II]/nI[II]),II,II-1)
mod3 <- lm(O3 ~ C(vent,contraste), data = ozone)
anova(mod3)Analysis of Variance Table
Response: O3
Df Sum Sq Mean Sq F value Pr(>F)
C(vent, contraste) 3 9859.8 3286.6 8.3383 0.0001556 ***
Residuals 46 18131.4 394.2
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod3)
Call:
lm(formula = O3 ~ C(vent, contraste), data = ozone)
Residuals:
Min 1Q Median 3Q Max
-40.250 -13.950 -2.233 14.972 39.857
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 86.300 2.808 30.737 < 2e-16 ***
C(vent, contraste)1 17.550 4.093 4.288 9.15e-05 ***
C(vent, contraste)2 -8.011 5.993 -1.337 0.187858
C(vent, contraste)3 -14.722 3.744 -3.933 0.000281 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 19.85 on 46 degrees of freedom
Multiple R-squared: 0.3522, Adjusted R-squared: 0.31
F-statistic: 8.338 on 3 and 46 DF, p-value: 0.0001556mod4 <- lm(O3 ~ C(vent,sum), data = ozone)
anova(mod4)Analysis of Variance Table
Response: O3
Df Sum Sq Mean Sq F value Pr(>F)
C(vent, sum) 3 9859.8 3286.6 8.3383 0.0001556 ***
Residuals 46 18131.4 394.2
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod4)
Call:
lm(formula = O3 ~ C(vent, sum), data = ozone)
Residuals:
Min 1Q Median 3Q Max
-40.250 -13.950 -2.233 14.972 39.857
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 87.015 3.027 28.743 < 2e-16 ***
C(vent, sum)1 16.835 4.635 3.632 0.000705 ***
C(vent, sum)2 -8.726 5.573 -1.566 0.124284
C(vent, sum)3 -15.437 4.485 -3.442 0.001240 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 19.85 on 46 degrees of freedom
Multiple R-squared: 0.3522, Adjusted R-squared: 0.31
F-statistic: 8.338 on 3 and 46 DF, p-value: 0.0001556resid2 <- resid(mod2)
ozone$vent <- as.factor(ozone$vent)
plot(resid2~vent,data=ozone, ylab="residus")
plot(resid2 ~ jitter(fitted(mod2)),xlab="ychap",ylab="residus")
xyplot(resid2 ~ I(1:50)|vent, data=ozone,
xlab="index", ylab="residus")
par(mfrow=c(1,2))
with(ozone, interaction.plot(vent, nebulosite, O3, col=1:2))
with(ozone, interaction.plot(nebulosite, vent, O3, col=1:4))
mod1 <- lm(O3 ~ vent + nebulosite + vent:nebulosite, data = ozone)
mod2 <- lm(O3 ~ vent + nebulosite, data = ozone)
anova(mod2, mod1)Analysis of Variance Table
Model 1: O3 ~ vent + nebulosite
Model 2: O3 ~ vent + nebulosite + vent:nebulosite
Res.Df RSS Df Sum of Sq F Pr(>F)
1 45 11730
2 42 11246 3 483.62 0.602 0.6173mod3 <- lm(O3 ~ vent, data = ozone)
anova(mod3, mod2)Analysis of Variance Table
Model 1: O3 ~ vent
Model 2: O3 ~ vent + nebulosite
Res.Df RSS Df Sum of Sq F Pr(>F)
1 46 18131
2 45 11730 1 6401.5 24.558 1.066e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(mod3, mod2, mod1)Analysis of Variance Table
Model 1: O3 ~ vent
Model 2: O3 ~ vent + nebulosite
Model 3: O3 ~ vent + nebulosite + vent:nebulosite
Res.Df RSS Df Sum of Sq F Pr(>F)
1 46 18131
2 45 11730 1 6401.5 23.907 1.523e-05 ***
3 42 11246 3 483.6 0.602 0.6173
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(mod1)Analysis of Variance Table
Response: O3
Df Sum Sq Mean Sq F value Pr(>F)
vent 3 9859.8 3286.6 12.274 6.689e-06 ***
nebulosite 1 6401.5 6401.5 23.907 1.523e-05 ***
vent:nebulosite 3 483.6 161.2 0.602 0.6173
Residuals 42 11246.2 267.8
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1