Analyse du prix des maisons
> x
[1] 168000 182700 205000 135000 158167 184000 234000 165000 380000 148000
[11] 140000 180000 174000 169000 140000 165000 157000 170000 300000 475000
[21] 255000 125000 140070 177380 180000 127000 133000 215000 175000 135000
[31] 160000 500000
> mean(x)
[1] 198509.9
> sqrt(var(x)/length(x))
[1] 16297.25
> qt(.025,length(x)-1)
[1] -2.039513
> qt(.975,length(x)-1)
[1] 2.039513
> c(mean(x)-qt(.975,length(x)-1)*sqrt(var(x)/length(x)),
+ mean(x)-qt(.025,length(x)-1)*sqrt(var(x)/length(x)))
[1] 165271.4 231748.4
> t.test(x)
One-sample t-Test
data: x
t = 12.1806, df = 31, p-value = 0
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
165271.4 231748.4
sample estimates:
mean of x
198509.9
> qqnorm(x,main="Graphique quantiles normaux de x")
> maison.1999
Ahunstic Anjou Beaconsfield Beloeil Blainville Boucherville Brossard
168000 182700 205000 135000 158167 184000 234000
Chomedey Cote St-Luc Dorval Fabreville Hudson Kirkland Lachine Lasalle
165000 380000 148000 140000 180000 174000 169000 140000
Laval-Des-Rapides Longueuil Lorraine Montreal Ouest Mont-Royal
165000 157000 170000 3e+05 475000
Notre-Dame-de Grace Pierrefonds Repentigny Rosemere St-Bruno St-Eustache
255000 125000 140070 177380 180000 127000
St-Hubert St-Lambert St-Laurent Ste-Therese Vimont Westmount
133000 215000 175000 135000 160000 5e+05
> stem(maison.1999)
N = 32 Median = 169500
Quartiles = 144035, 194500
Decimal point is 4 places to the right of the colon
12 : 57
13 : 355
14 : 0008
15 : 78
16 : 05589
17 : 0457
18 : 0034
19 :
20 : 5
21 : 5
22 :
23 : 4
24 :
25 : 5
High: 300000 380000 475000 500000
> hist(maison.1999,main="Histogramme du prix des maisons",
+ sub="Prix en octobre 1999")
> maison.1999.analyse_bootstrap(maison.1999,median,B=999)
Forming replications 1 to 100
Forming replications 101 to 200
Forming replications 201 to 300
Forming replications 301 to 400
Forming replications 401 to 500
Forming replications 501 to 600
Forming replications 601 to 700
Forming replications 701 to 800
Forming replications 801 to 900
Forming replications 901 to 999
> maison.1999.analyse
Call:
bootstrap(data = maison.1999, statistic = median, B = 999)
Number of Replications: 999
Summary Statistics:
Observed Bias Mean SE
median 169500 552.5 170052 5505
> summary(maison.1999.analyse)
Call:
bootstrap(data = maison.1999, statistic = median, B = 999)
Number of Replications: 999
Summary Statistics:
Observed Bias Mean SE
median 169500 552.5 170052 5505
Empirical Percentiles:
2.5% 5% 95% 97.5%
median 158483 160000 180000 180002
BCa Confidence Limits:
2.5% 5% 95% 97.5%
median 157584 159084 178690 180000
> plot(maison.1999.analyse)
> qqnorm(maison.1999.analyse)
> maison.1999.analyse4_bootstrap(maison.1999,mean,B=999)
Forming replications 1 to 100
Forming replications 101 to 200
Forming replications 201 to 300
Forming replications 301 to 400
Forming replications 401 to 500
Forming replications 501 to 600
Forming replications 601 to 700
Forming replications 701 to 800
Forming replications 801 to 900
Forming replications 901 to 999
> maison.1999.analyse4
Call:
bootstrap(data = maison.1999, statistic = mean, B = 999)
Number of Replications: 999
Summary Statistics:
Observed Bias Mean SE
mean 198510 471.2 198981 16035
> summary(maison.1999.analyse4)
Call:
bootstrap(data = maison.1999, statistic = mean, B = 999)
Number of Replications: 999
Summary Statistics:
Observed Bias Mean SE
mean 198510 471.2 198981 16035
Empirical Percentiles:
2.5% 5% 95% 97.5%
mean 171526 174396 227512 232473
BCa Confidence Limits:
2.5% 5% 95% 97.5%
mean 173861 176702 231987 242395
> sqrt(var(maison.1999)/length(maison.1999))
[1] 16297.25
> sqrt(31/32)*16297.25
[1] 16040.58
> plot(maison.1999.analyse4)
> qqnorm(maison.1999.analyse4)
> tempo1_as.numeric(length=263)
> for(i in 1:length(tempo))
+ tempo1[i]_mean(dnorm(tempo[i],maison.1999,15625/2))
> tempo2_as.numeric(length=263)
> for(i in 1:length(tempo))
+ tempo2[i]_mean(dnorm(tempo[i],maison.1999,20000))
> tempo3_as.numeric(length=263)
> for(i in 1:length(tempo))
+ tempo3[i]_mean(dnorm(tempo[i],maison.1999,30000))
> plot(tempo,tempo1)
> lines(tempo,tempo2)
> lines(tempo,tempo3,lty=3)
> par(mfrow=c(3,1))
> plot(tempo,tempo1,type="l")
> plot(tempo,tempo2,type="l")
> plot(tempo,tempo3,type="l")
> tempo1[73]
[1] 1.477673e-05
> tempo2[73]
[1] 1.0213e-05
> tempo3[73]
[1] 8.37587e-06
> 1/(4*32*tempo1[73]^2)
[1] 35779426
> sqrt(1/(4*32*tempo1[73]^2))
[1] 5981.591
> sqrt(1/(4*32*tempo2[73]^2))
[1] 8654.497
> sqrt(1/(4*32*tempo3[73]^2))
[1] 10552.74
> densite.maison99_list(x=tempo,y7812.5=tempo1,y20000=tempo2,y30000=tempo3)
> par(mfrow=c(3,1))
> plot(densite.maison99$x,densite.maison99$y30000,
+ main="Fenêtre = 30 000; Écart type de la médiane = 10 552,74",xlab="Prix",
+ ylab="Densité",type="l")
> plot(densite.maison99$x,densite.maison99$y20000,
+ main="Fenêtre = 20 000; Écart type de la médiane = 8 654,497",xlab="Prix",
+ ylab="Densité",type="l")
> plot(densite.maison99$x,densite.maison99$y7812.5,
+ main="Fenêtre par défaut (7 812,5); Écart type de la médiane = 5 981,591",
+ xlab="Prix",ylab="Densité",type="l")
> par(mfrow=c(1,1))
> plot(c(0,600000),c(0,1),type="n",xlab="Prix",ylab="Probabilité",
+ main="Fonction de répartition expérimentale du prix des maisons",
+ sub="Octobre 1999")
> lines(c(0,min(maison.1999)),c(0,0))
> lines(c(max(maison.1999),600000),c(1,1))
> for(i in 2:length(maison.1999))
+ lines(c(sort(maison.1999)[i-1],sort(maison.1999)[i]),
+ c((i-1)/length(maison.1999),(i-1)/length(maison.1999)))