# 2. Luku # Havaintoaineiston käsittelyä ################################# firmat<-read.table("C:\\Kurssit\\Mmm\\mmm03\\Datat\\firmat.dat", header = T) summary(firmat) varat ntulot parvo Min. : 7.70 Min. :0.200 Min. : 2.900 1st Qu.:14.35 1st Qu.:0.925 1st Qu.: 7.375 Median :18.95 Median :1.050 Median : 8.300 Mean :19.32 Mean :1.510 Mean : 9.760 3rd Qu.:20.25 3rd Qu.:2.225 3rd Qu.:11.800 Max. :38.40 Max. :3.300 Max. :19.500 mean(varat); mean(ntulot);mean(parvo) #[1] 19.32 #[1] 1.51 #[1] 9.76 col.means <- apply(firmat, 2, mean) col.means varat ntulot parvo 19.32 1.51 9.76 col.min<- apply(firmat, 2, min) col.min varat ntulot parvo 7.7 0.2 2.9 yks<-rep(1,10) yks # [1] 1 1 1 1 1 1 1 1 1 1 yks<-as.matrix(yks) yks dim(yks) #[1] 10 1 Y<-as.matrix(firmat) Y dim(Y) # [1] 10 3 n<-dim(Y)[1] n #[1] 10 t(Y)%*%yks/n # [,1] # varat 19.32 # ntulot 1.51 # parvo 9.76 # Kovarianssi ja korrelaatio ############################ cor(firmat) varat ntulot parvo varat 1.0000000 0.7107028 0.9492063 ntulot 0.7107028 1.0000000 0.8518937 parvo 0.9492063 0.8518937 1.0000000 cov(varat,ntulot) # [1] 5.873111 cov(varat,ntulot); cor(ntulot,parvo) #[1] 5.873111 #[1] 0.8518937 cor(firmat)[1,2] #[1] 0.7107028 S<-cov(firmat) diag(S) # varat ntulot parvo # 70.4106667 0.9698889 24.0560000 sqrt(diag(S)) # varat ntulot parvo # 8.3911064 0.9848294 4.9046916 # Graafinen esitys ################## boxplot(firmat) pairs(firmat) stars(firmat,full = FALSE) # Kaksi muuttujaryhmää apply(hinnatr[,1:3], 2, mean) apply(hinnatr[,4:5], 2, mean) hinnatr<-read.table("C:\\Kurssit\\Mmm\\mmm03\\Datat\\hinnatr.dat", header = T, skip=6) hinnatr leipa hampuril voi appels tomaatti Anchorage 70.9 135.6 155.00 63.9 100.1 Atlanta 36.4 111.5 144.30 53.9 95.9 Baltimore 28.9 108.8 151.00 47.5 104.5 Boston 43.2 119.3 142.00 41.1 96.5 Buffalo 34.5 109.9 124.80 35.6 75.9 Chicago 37.1 107.5 145.40 65.1 94.2 Cincinnati 37.1 118.1 149.60 45.6 90.8 Cleveland 38.5 107.7 142.70 50.3 83.2 Dallas 35.5 116.8 142.50 62.4 90.7 Detroit 40.8 108.8 140.10 39.7 96.1 Honolulu 50.9 131.7 154.40 65.0 93.9 Houston 35.1 102.3 150.30 59.3 84.5 Kansas_City 35.1 99.8 162.30 42.6 87.9 Los_Angeles 36.9 96.2 140.40 54.7 79.3 Milwaukee 33.3 109.1 123.20 57.7 87.7 Minneapolis 32.5 116.7 135.10 48.0 89.1 New_York 42.7 130.8 148.70 47.6 92.1 Philadelphia 42.9 126.9 153.80 51.9 101.5 Pittsburgh 36.9 115.4 138.90 43.8 91.9 St._Louis 36.9 109.8 140.00 46.7 79.0 San_Diego 32.5 84.5 145.90 48.5 82.3 San_Francisco 40.0 104.6 139.10 59.2 81.9 Seattle 32.2 105.4 136.80 54.0 88.6 Washington 31.8 116.7 154.81 57.6 86.6 cor(hinnatr[,1:3]) leipa hampuril voi leipa 1.0000000 0.6490532 0.3301770 hampuril 0.6490532 1.0000000 0.2447778 voi 0.3301770 0.2447778 1.0000000 cor(hinnatr[,4:5]) appels tomaatti appels 1.0000000 0.1333844 tomaatti 0.1333844 1.0000000 cor(hinnatr[,1:3],hinnatr[,4:5]) appels tomaatti leipa 0.3187031 0.3620681 hampuril 0.1908956 0.5557993 voi 0.2351424 0.4361291 # Lineaariset yhdisteet ####################### a1<-c(1/5,2/5,1/10,1/10,1/5) a2<-c(1/5,1/10,2/10,3/10,1/5) Y<-as.matrix(hinnatr) a1<-as.matrix(a1) a2<-as.matrix(a2) z1<-Y%*%a1; z2<-Y%*%a2 # tai A<-rbind(t(a1),t(a2)) Z<-Y%*%t(A) hinnat<-transform(hinnatr,z1=Y%*%a1,z2=Y%*%a2) cov(hinnat[,6:7]) z1 z2 z1 55.12915 38.53941 z2 38.53941 34.69713 A<-rbind(t(a1),t(a2)) A%*%S%*%t(A) [,1] [,2] [1,] 55.12915 38.53941 [2,] 38.53941 34.69713 # Kokonaisvaihtelun mitat ######################## hinnatr<-read.table("C:\\Kurssit\\Mmm\\mmm03\\Datat\\hinnatr.dat", header = T, skip=6) S<-cov(hinnatr) diag(S) leipa hampuril voi appels tomaatti 69.99906 135.33042 85.13557 69.87288 54.74341 sum(diag(S)) [1] 415.0813 det(cor(hinnatr)) #[1] 0.2667545 prod(diag(S))