Infestation de pins par des chenilles processionnaires

Infestation de pins par des chenilles processionnaires 1 Présentation du problème: On souhaite connaître l influence de certaines caractéristiques de peuplements forestiers sur le développement de la processionnaire. L unité, qui représente ici l observation, est une parcelle forestière, c est-à-dire une surface de 10 hectares d un seul tenant. Les valeurs obtenues sont les moyennes de mesures faites sur des placettes échantillon de 5 ares. La variable à expliquer (variable nbnids) est le nombre de nids de processionnaires par arbre d une placette. On a mesuré dix variables explicatives: ˆ le nombre de nids de processionnaires par arbre (variable NbNids), ˆ l altitude (en mètre) (variable Altitude), ˆ la pente (en degrés) (variable Pente), ˆ le nombre de pins dans une placette (variable NbPins), ˆ la hauteur de l arbre échantillonné au centre de la placette (variable Hauteur), ˆ le diamètre de cet arbre (variable Diametre), ˆ la note de densité de peuplement (variable Densite), ˆ l orientation de la placette (variable Orient), allant de 1 (sud) à 2 (autre), ˆ la hauteur des arbres dominants (variable HautMax), ˆ le nombre de strates de végétation (variable NbStrat), ˆ le mélange du peuplement (variable Melange), allant de 1 (pas mélangé) à 2 (mélangé). 2 Données observées > rm(list=ls()) #on vide l'environnement > chenilles=read.table("chenilles.txt",sep="",header=true) > head(chenilles,15) Altitude Pente NbPins Hauteur Diametre Densite Orient HautMax NbStrat 1 1200 22 1 4.0 14.8 1.0 1.1 5. 1.4 2 1342 28 8 4.4 18.0 1.5 1.5 6.4 1.7 3 1231 28 5 2.4 7.8 1.3 1.6 4.3 1.5 4 1254 28 18 3.0.2 2.3 1.7 6. 2.3 5 1357 32 7 3.7 10.7 1.4 1.7 6.6 1.8 6 1250 27 1 4.4 14.8 1.0 1.7 5.8 1.3 7 1422 37 22 3.0 8.1 2.7 1. 8.3 2.5 8 130 46 7 5.7 1.6 1.5 1.3 7.8 1.8 1127 24 2 3.5 12.6 1.0 1.7 4. 1.5 10 1075 34 4.3 12.0 1.6 1.8 6.8 2.0 11 1166 24 17 5.5 16.7 2.4 1.5 11.5 2. 12 1182 41 32 5.4 21.6 3.3 1.4 11.3 2.8 13 117 15 0 3.2 10.5 1.0 1.7 4.0 1.1 14 1256 21 0 5.1 1.5 1.0 1.8 5.8 1.1 15 1251 26 2 4.2 16.4 1.1 1.7 6.2 1.3 Melange NbNids LogNids 1 1.4 2.37 0.8628 2 1.7 1.47 0.38526 1

3 1.7 1.13 0.12222 4 1.6 0.85-0.16252 5 1.3 0.24-1.42712 6 1.4 1.4 0.3878 7 2.0 0.30-1.2037 8 1.6 0.07-2.6526 2.0 3.00 1.0861 10 2.0 1.21 0.1062 11 1.7 0.38-0.6758 12 2.0 0.70-0.35667 13 1.6 2.64 0.7078 14 1.4 2.05 0.71784 15 1.8 1.75 0.5562 > dim(chenilles) [1] 33 12 3 Influence de NbStrat sur le nombre de Nids 3.1 Analyse descriptive > par(mfrow=c(1,2)) > plot(chenilles$nbstrat,chenilles$nbnids) > plot(chenilles$nbstrat,chenilles$lognids) chenilles$nbnids 0.0 0.5 1.0 1.5 2.0 2.5 3.0 chenilles$lognids 3 2 1 0 1 1.5 2.0 2.5 chenilles$nbstrat 1.5 2.0 2.5 chenilles$nbstrat 2

3.2 Régression linéaire simple sur le NbNids > chenilles.bis=chenilles[names(chenilles) %in% c("nbstrat","lognids","nbnids")] > head(chenilles.bis) NbStrat NbNids LogNids 1 1.4 2.37 0.8628 2 1.7 1.47 0.38526 3 1.5 1.13 0.12222 4 2.3 0.85-0.16252 5 1.8 0.24-1.42712 6 1.3 1.4 0.3878 > chenilles.bis=chenilles.bis[order(chenilles.bis$nbstrat),] Graphes de diagnostic. > Nids.lm=lm(NbNids~NbStrat,data=chenilles.bis) > par(mfrow=c(2,2)) > plot(nids.lm) Residuals vs Fitted Normal Q Q Residuals 1.5 0.5 0.5 1.5 1 28 2 0 1 2 3 28 13 0.0 0.5 1.0 1.5 2 1 0 1 2 Theoretical Quantiles 0.0 0.5 1.0 1.5 Scale Location 28 13 2 0 1 2 3 Residuals vs Leverage 13 Cook's distance 28 0.5 0.0 0.5 1.0 1.5 0.00 0.04 0.08 Leverage 3.3 Régression linéaire simple sur le log du NbNids Graphes de diagnostic. > log.nids.lm=lm(lognids~nbstrat,data=chenilles.bis) > par(mfrow=c(2,2)) > plot(log.nids.lm) 3

Residuals vs Fitted Normal Q Q Residuals 2 1 0 1 33 8 28 2 1 0 1 2 8 3328 2.0 1.0 0.0 2 1 0 1 2 Theoretical Quantiles 0.0 0.5 1.0 1.5 Scale Location 8 33 28 2 1 0 1 2 Residuals vs Leverage 28 Cook's distance 33 12 2.0 1.0 0.0 0.00 0.04 0.08 Leverage Résultats de l analyse. > summary(log.nids.lm) Call: lm(formula = LogNids ~ NbStrat, data = chenilles.bis) Residuals: Min 1Q Median 3Q Max -2.0833-0.8512 0.2844 0.167 1.5247 Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) 1.7737 0.6537 2.713 0.010780 * NbStrat -1.3054 0.3175-4.111 0.000268 *** --- Signif. codes: 0 *** 0.001 ** 0.01 * 0.05. 0.1 1 Residual standard error: 1.018 on 31 degrees of freedom Multiple R-squared: 0.3528, Adjusted R-squared: 0.331 F-statistic: 16. on 1 and 31 DF, p-value: 0.0002681 > #test du modèle > log.nids.lm.0=lm(lognids~1,data=chenilles.bis) > anova(log.nids.lm.0,log.nids.lm) Analysis of Variance Table 4

Model 1: LogNids ~ 1 Model 2: LogNids ~ NbStrat Res.Df RSS Df Sum of Sq F Pr(>F) 1 32 4.56 2 31 32.07 1 17.4 16. 0.0002681 *** --- Signif. codes: 0 *** 0.001 ** 0.01 * 0.05. 0.1 1 Intervalle de confiance et de prédiction > par(mfrow=c(1,1)) > p.conf<-predict(log.nids.lm,interval="confidence",level=0.5) > p.int<-predict(log.nids.lm,interval="prediction", level=0.5) > matplot(chenilles.bis$nbstrat,cbind(p.conf,p.int[,-1]),col = 1, type="l",ylab="lognids",xlab="nbstrat" > points(chenilles.bis$nbstrat,chenilles$lognids,col="blue",pch=20) > legende<-c('fit','confl5','confu5','predl5','predu5') > n <- length(legende) > legend("bottomright",legend = paste(legende[1:n]), xpd = NA, bg = grey(0.),cex=0.7,text.col=1,lty=1:5 2 1 0 LogNids 1 2 3 4 fit ConfL5 ConfU5 PredL5 PredU5 1.5 2.0 2.5 NbStrat Regression lineaire simple 4 Influence de toutes les variables sur le nombre de Nids 4.1 Etude descriptive des données Graphe entre la variable explicative et les variables à expliquer. > par(mfrow=c(2,2)) > plot(chenilles$nbstrat,chenilles$nbnids) > plot(chenilles$pente,chenilles$nbnids) 5

> plot(chenilles$hauteur,chenilles$nbnids) > plot(chenilles$diametre,chenilles$nbnids) chenilles$nbnids 0.0 1.0 2.0 3.0 chenilles$nbnids 0.0 1.0 2.0 3.0 1.5 2.0 2.5 chenilles$nbstrat 15 20 25 30 35 40 45 chenilles$pente chenilles$nbnids 0.0 1.0 2.0 3.0 chenilles$nbnids 0.0 1.0 2.0 3.0 3 4 5 6 chenilles$hauteur 10 15 20 chenilles$diametre Statistiques simples (moyenne, écart-type, corrélations). ˆ Moyennes. > colmeans(chenilles) Altitude Pente NbPins Hauteur Diametre Densite 1315.3333333 2.0303030 11.4545455 4.4515152 15.2515152 1.7001 Orient HautMax NbStrat Melange NbNids LogNids 1.6575758 7.5333 1.818182 1.7606061 0.8112121-0.8132803 ˆ Ecart-type. > sapply(chenilles, sd) Altitude Pente NbPins Hauteur Diametre Densite 12.03677 7.3036158.5364135 1.040763 4.3025517 0.7173578 Orient HautMax NbStrat Melange NbNids LogNids 0.1871335 2.351852 0.5664884 0.2486707 0.8062287 1.244406 ˆ Corrélations entre variables > cor(chenilles) Altitude Pente NbPins Hauteur Diametre Densite Altitude 1.0000000 0.120520 0.5375645 0.32105284 0.28377386 0.5146683 Pente 0.120520 1.0000000 0.321411 0.13668772 0.11341631 0.3006666 6

NbPins 0.5375645 0.321411 1.0000000 0.4144343 0.24203 0.75521 Hauteur 0.3210528 0.1366877 0.414434 1.00000000 0.0465522 0.4327 Diametre 0.283773 0.1134163 0.24204 0.0465522 1.00000000 0.3062303 Densite 0.5146683 0.3006666 0.75521 0.43274 0.30623032 1.0000000 Orient 0.268428-0.1522218 0.1284678 0.0581023-0.0787071 0.1506780 HautMax 0.3601466 0.261061 0.75860 0.7712534 0.561783 0.8102161 NbStrat 0.3637243 0.3256728 0.8767888 0.4558851 0.26746450 0.08531 Melange -0.127644 0.1280044 0.1870038-0.12111138-0.0063278 0.108243 NbNids -0.5302188-0.4554582-0.563008-0.3570141-0.15777120-0.5702405 LogNids -0.5336138-0.42436-0.5177880-0.4252455-0.2003786-0.5282782 Orient HautMax NbStrat Melange NbNids LogNids Altitude 0.2684282 0.36014656 0.3637242-0.1276440-0.5302188-0.53361382 Pente -0.15222176 0.2610610 0.32567283 0.12800444-0.4554582-0.424363 NbPins 0.12846781 0.758602 0.87678882 0.18700384-0.563008-0.5177875 Hauteur 0.0581023 0.7712534 0.4558851-0.12111138-0.357014-0.4252455 Diametre -0.0787071 0.561783 0.26746450-0.0063278-0.1577712-0.2003786 Densite 0.15067805 0.81021606 0.085310 0.1082434-0.5702405-0.52827817 Orient 1.00000000 0.060001 0.0632450 0.1308416-0.2117483-0.2268178 HautMax 0.060001 1.00000000 0.8536311 0.0032707-0.5511316-0.5413705 NbStrat 0.0632450 0.8536311 1.00000000 0.14782424-0.6358716-0.53865 Melange 0.1308416 0.0032707 0.14782424 1.00000000-0.1127613-0.03644182 NbNids -0.2117482-0.55113165-0.63587161-0.11276133 1.0000000 0.87615265 LogNids -0.2268178-0.5413705-0.53865-0.03644182 0.8761526 1.00000000 > cor.test(chenilles$hauteur,chenilles$diametre) Pearson's product-moment correlation data: chenilles$hauteur and chenilles$diametre t = 11.82, df = 31, p-value = 5.125e-13 alternative hypothesis: true correlation is not equal to 0 5 percent confidence interval: 0.8142253 0.522256 sample estimates: cor 0.046552 > cor.test(chenilles$densite,chenilles$nbstrat) Pearson's product-moment correlation data: chenilles$densite and chenilles$nbstrat t = 12.107, df = 31, p-value = 2.768e-13 alternative hypothesis: true correlation is not equal to 0 5 percent confidence interval: 0.8214341 0.542145 sample estimates: cor 0.08531 ˆ Corrélations partielles entre toutes les variables (conditionnellement aux autres) > library(ppcor) > pcor(chenilles)$estimate Altitude Pente NbPins Hauteur Diametre Altitude 1.000000000-0.2600632 0.3174782-0.2241607 0.32040785 Pente -0.26006325 1.00000000 0.1481651-0.167515 0.21217545 NbPins 0.31747820 0.1481651 1.00000000 0.34335104-0.25143160 Hauteur -0.2241606-0.167515 0.34335104 1.00000000 0.87615184 Diametre 0.320407851 0.21217545-0.25143160 0.87615184 1.00000000 Densite -0.11137684-0.07426884 0.1506636-0.4185082 0.31040664 7

Orient 0.212124771-0.16077342-0.32176 0.3856777-0.4082872 HautMax -0.0088088 0.05751548-0.3563150 0.60343420-0.24086221 NbStrat -0.21366800-0.0051463-0.02545177 0.01211458-0.1878280 Melange -0.375307807-0.0422753 0.532133-0.35008751 0.34547134 NbNids -0.23011348-0.128141 0.0140487 0.0421584 0.024138 LogNids -0.243445082-0.2208412 0.11066058-0.36813458 0.31372475 Densite Orient HautMax NbStrat Melange Altitude -0.1113768 0.212124771-0.0088088-0.2136680-0.37530781 Pente -0.07426884-0.160773423 0.057515481-0.0051463-0.0422753 NbPins 0.1506636-0.3217687-0.35631501-0.02545177 0.532133 Hauteur -0.4185082 0.38567773 0.6034341 0.01211458-0.35008751 Diametre 0.31040664-0.40828722-0.240862212-0.1878280 0.34547134 Densite 1.00000000 0.40221780 0.43184664 0.2831618-0.4084273 Orient 0.4022178 1.000000000-0.17701177-0.25228882 0.38605261 HautMax 0.4318466-0.17701177 1.000000000 0.3653322 0.11460045 NbStrat 0.2831618-0.252288821 0.36533218 1.00000000 0.16560578 Melange -0.4084273 0.386052611 0.114600446 0.16560578 1.00000000 NbNids 0.04227516-0.051324563-0.08847134-0.14808280-0.11651361 LogNids -0.0738864 0.00248821 0.18270387-0.13201643-0.036431 NbNids LogNids Altitude -0.2301135-0.243445082 Pente -0.128141-0.22084123 NbPins 0.0140487 0.110660581 Hauteur 0.0421584-0.368134583 Diametre 0.024138 0.313724754 Densite 0.04227516-0.07388643 Orient -0.05132456 0.00248821 HautMax -0.0884713 0.18270387 NbStrat -0.14808280-0.132016433 Melange -0.11651361-0.0364305 NbNids 1.00000000 0.64114407 LogNids 0.6411441 1.000000000 4.2 Régression linéaire multiple sur le NbNids Graphes de diagnostic > Nids.lm=lm(NbNids~Altitude+Pente+NbPins+Hauteur+Diametre+Densite+Orient+HautMax+NbStrat+Melange,data=c > par(mfrow=c(2,2)) > plot(nids.lm) 8

Residuals vs Fitted Normal Q Q Residuals 1.0 0.0 1.0 20 31 2 0 1 2 3 31 20 0.5 0.5 1.0 1.5 2.0 2 1 0 1 2 Theoretical Quantiles 0.0 0.5 1.0 1.5 Scale Location 31 20 2 0 1 2 3 Residuals vs Leverage Cook's distance 1 31 12 1 0.5 0.5 0.5 0.5 1.0 1.5 2.0 0.0 0.2 0.4 0.6 Leverage 4.3 Régression linéaire multiple le log du NbNids Graphes de diagnostic. > log.nids.lm=lm(log(nbnids)~altitude+pente+nbpins+hauteur+diametre+densite+orient+hautmax+nbstrat+melan > par(mfrow=c(2,2)) > plot(log.nids.lm)

Residuals vs Fitted Normal Q Q Residuals 2 1 0 1 2 20 33 22 2 0 1 2 33 10 20 3 2 1 0 1 2 1 0 1 2 Theoretical Quantiles 0.0 0.5 1.0 1.5 Scale Location 2033 10 2 0 1 2 Residuals vs Leverage Cook's distance 33 10 8 1 0.5 0.5 1 3 2 1 0 1 0.0 0.2 0.4 0.6 Leverage Résultats de l analyse. > summary(log.nids.lm) Call: lm(formula = log(nbnids) ~ Altitude + Pente + NbPins + Hauteur + Diametre + Densite + Orient + HautMax + NbStrat + Melange, data = chenilles) Residuals: Min 1Q Median 3Q Max -1.6082-0.27556-0.02122 0.31358 1.74750 Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) 11.30012 3.156550 3.580 0.00167 ** Altitude -0.004505 0.001563-2.882 0.00865 ** Pente -0.053606 0.021843-2.454 0.02250 * NbPins 0.074581 0.100233 0.744 0.46470 Hauteur -1.328277 0.570061-2.330 0.0238 * Diametre 0.236101 0.104611 2.257 0.03428 * Densite -0.451118 1.57216-0.287 0.7765 Orient -0.187810 1.00750-0.186 0.8538 HautMax 0.185636 0.236344 0.785 0.44057 NbStrat -1.266028 0.861235-1.470 0.15572 Melange -0.537203 0.773372-0.65 0.4456 --- Signif. codes: 0 *** 0.001 ** 0.01 * 0.05. 0.1 1 10

Residual standard error: 0.8268 on 22 degrees of freedom Multiple R-squared: 0.668, Adjusted R-squared: 0.558 F-statistic: 5.055 on 10 and 22 DF, p-value: 0.0007441 > #test du modèle > log.nids.lm.0=lm(log(nbnids)~1,data=chenilles) > anova(log.nids.lm.0,log.nids.lm) Analysis of Variance Table Model 1: log(nbnids) ~ 1 Model 2: log(nbnids) ~ Altitude + Pente + NbPins + Hauteur + Diametre + Densite + Orient + HautMax + NbStrat + Melange Res.Df RSS Df Sum of Sq F Pr(>F) 1 32 4.56 2 22 15.03 10 34.557 5.0553 0.0007441 *** --- Signif. codes: 0 *** 0.001 ** 0.01 * 0.05. 0.1 1 > #tests de type I > anova(log.nids.lm) Analysis of Variance Table Response: log(nbnids) Df Sum Sq Mean Sq F value Pr(>F) Altitude 1 14.1222 14.1222 20.658 0.000153 *** Pente 1 6.705 6.705.8152 0.0048376 ** NbPins 1 1.4175 1.4175 2.0736 0.163516 Hauteur 1 1.8035 1.8035 2.6383 0.1185567 Diametre 1 8.0480 8.0480 11.7732 0.0023866 ** Densite 1 0.1353 0.1353 0.17 0.6608026 Orient 1 0.0385 0.0385 0.0563 0.8146664 HautMax 1 0.0001 0.0001 0.0001 0.10625 NbStrat 1 1.528 1.528 2.8567 0.1051153 Melange 1 0.328 0.328 0.4825 0.44561 Residuals 22 15.038 0.6836 --- Signif. codes: 0 *** 0.001 ** 0.01 * 0.05. 0.1 1 > #tests de type II > library(car) > Anova(log.Nids.lm) Anova Table (Type II tests) Response: log(nbnids) Sum Sq Df F value Pr(>F) Altitude 5.674 1 8.3082 0.008648 ** Pente 4.1173 1 6.0231 0.022502 * NbPins 0.3785 1 0.5537 0.464703 Hauteur 3.7113 1 5.422 0.02376 * Diametre 3.4820 1 5.038 0.034281 * Densite 0.0562 1 0.0823 0.77646 Orient 0.0237 1 0.0347 0.85385 HautMax 0.4217 1 0.616 0.440567 NbStrat 1.4772 1 2.160 0.155715 Melange 0.328 1 0.4825 0.44562 Residuals 15.038 22 --- Signif. codes: 0 *** 0.001 ** 0.01 * 0.05. 0.1 1 11

SCR = 15.038 SCM = 14.1222 + 6.705 +. + 0.328 = 34.55712 SCT = SCM + SCR = 4.5603 Vérification: F = (SCM/10)/(SCR/22) = 5.0552 Sélection de variables. > ##Forward > #select.variables.forward=step(log.nids.lm.0,scope=~altitude+pente+nbpins+hauteur+diametre+densite+ori > #summary(select.variables.forward) > ##Backward > #select.variables.backward=step(nids.log.lm,direction="backward") > #summary(select.variables.backward) > #Stepwise > select.variables.stepwise=step(log.nids.lm.0,scope=~altitude+pente+nbpins+hauteur+diametre+densite+ori Start: AIC=15.44 log(nbnids) ~ 1 Df Sum of Sq RSS AIC + NbStrat 1 17.487 32.07 3.0848 + HautMax 1 14.5358 35.060 5.85 + Altitude 1 14.1222 35.474 6.3855 + Densite 1 13.8412 35.755 6.645 + NbPins 1 13.26 36.2 7.1444 + Pente 1.1464 40.450 10.7171 + Hauteur 1 8.707 40.625 10.8602 <none> 4.56 15.4443 + Orient 1 2.6164 46.80 15.6558 + Diametre 1 2.0025 47.54 16.0842 + Melange 1 0.065 4.530 17.4004 Step: AIC=3.08 log(nbnids) ~ NbStrat Df Sum of Sq RSS AIC + Altitude 1 5.7642 26.333-1.4474 + Pente 1 3.08 2.007 1.7445 <none> 32.07 3.0848 + Orient 1 1.8378 30.260 3.130 + Hauteur 1 1.4585 30.63 3.5501 + HautMax 1 0.2153 31.882 4.8627 + Melange 1 0.1338 31.64 4.470 + Diametre 1 0.045 32.003 4.874 + Densite 1 0.0368 32.061 5.046 + NbPins 1 0.0020 32.05 5.0828 - NbStrat 1 17.487 4.56 15.4443 Step: AIC=-1.45 log(nbnids) ~ NbStrat + Altitude Df Sum of Sq RSS AIC + Pente 1 3.0701 23.263-3.5382 + Densite 1 2.2734 24.060-2.426 + NbPins 1 1.416 24.32-1.74 <none> 26.333-1.4474 + Hauteur 1 0.6000 25.733-0.2081 + Orient 1 0.55 25.773-0.1566 + HautMax 1 0.0482 26.285 0.422 + Diametre 1 0.0383 26.25 0.5046 + Melange 1 0.011 26.321 0.5376 12

- Altitude 1 5.7642 32.07 3.0848 - NbStrat 1.1407 35.474 6.3855 Step: AIC=-3.54 log(nbnids) ~ NbStrat + Altitude + Pente Df Sum of Sq RSS AIC + NbPins 1 2.4280 20.835-5.1757 + Densite 1 2.3402 20.23-5.0370 <none> 23.263-3.5382 + Orient 1 1.2150 22.048-3.3084 + Hauteur 1 0.644 22.618-2.4660 + HautMax 1 0.0771 23.186-1.6477 + Diametre 1 0.0608 23.202-1.6246 + Melange 1 0.0020 23.261-1.5410 - Pente 1 3.0701 26.333-1.4474 - NbStrat 1 5.5013 28.764 1.4668 - Altitude 1 5.7445 2.008 1.7445 Step: AIC=-5.18 log(nbnids) ~ NbStrat + Altitude + Pente + NbPins Df Sum of Sq RSS AIC + Orient 1 1.3806 1.454-5.4382 <none> 20.835-5.1757 + Hauteur 1 0.476 20.358-3.38 - NbPins 1 2.4280 23.263-3.5382 + Melange 1 0.123 20.711-3.3725 + Densite 1 0.102 20.732-3.331 + HautMax 1 0.0717 20.763-3.285 + Diametre 1 0.031 20.76-3.2377 - Pente 1 3.5565 24.32-1.74 - NbStrat 1 6.5118 27.347 1.71 - Altitude 1 8.1380 28.73 3.7054 Step: AIC=-5.44 log(nbnids) ~ NbStrat + Altitude + Pente + NbPins + Orient Df Sum of Sq RSS AIC <none> 1.454-5.4382 - Orient 1 1.3806 20.835-5.1757 + Hauteur 1 0.5057 18.4-4.3074 + Densite 1 0.2830 1.172-3.218 + HautMax 1 0.0867 1.368-3.5855 + Melange 1 0.0138 1.441-3.4616 + Diametre 1 0.0000 1.454-3.4382 - NbPins 1 2.535 22.048-3.3084 - Pente 1 4.3177 23.772-0.8237 - Altitude 1 6.4076 25.862 1.570 - NbStrat 1 6.6742 26.12 2.254 > summary(select.variables.stepwise) Call: lm(formula = log(nbnids) ~ NbStrat + Altitude + Pente + NbPins + Orient, data = chenilles) Residuals: Min 1Q Median 3Q Max -1.366-0.3635-0.05672 0.5826 1.63851 Coefficients: 13

Estimate Std. Error t value Pr(> t ) (Intercept) 11.107708 2.477481 4.483 0.000122 *** NbStrat -1.745233 0.573431-3.043 0.005163 ** Altitude -0.004373 0.001466-2.82 0.006003 ** Pente -0.054446 0.022242-2.448 0.021152 * NbPins 0.07148 0.037686 1.87 0.068544. Orient -1.175853 0.84483-1.384 0.177633 --- Signif. codes: 0 *** 0.001 ** 0.01 * 0.05. 0.1 1 Residual standard error: 0.8488 on 27 degrees of freedom Multiple R-squared: 0.6077, Adjusted R-squared: 0.5351 F-statistic: 8.366 on 5 and 27 DF, p-value: 7.028e-05 14