Štatistika - cviko v R

Created: 2012-03-31 - 19:18


R version 2.13.1 Patched (2011-07-22 r56481)
Copyright (C) 2011 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i386-pc-mingw32/i386 (32-bit)

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Loading required package: rcom
Loading required package: rscproxy
> utils:::menuInstallPkgs()
--- Please select a CRAN mirror for use in this session ---
Error in contrib.url(repos, type) :
  trying to use CRAN without setting a mirror
> x = rnorm(100)
> min(x)
[1] -2.214016
> max(x)
[1] 3.21365
> x
  [1] -0.94722393  0.26114322  1.21136948  1.24876620  1.62121428 -1.65436597  1.09504437  0.55328724  0.26781693  0.88449261 -0.52192671  0.75450917 -0.01096783 -0.15491704
 [15] -0.45119001 -0.02777787  0.86946711  0.78728977 -0.27691471 -0.50251016  3.21364982  0.99616221 -0.75544204  0.72113035  0.06771297 -1.21470654 -0.14194687 -0.21776183
 [29]  0.80296853 -0.78796429  0.44638858  0.25615215 -0.48397229  0.82682828 -0.98061042  0.09826682 -0.33951689 -0.78669167 -0.07223029 -0.64335980 -0.10680862  1.88865068
 [43] -2.21401604 -0.46350949  0.43889553 -1.07273778 -0.97999941 -1.63440144  0.59110821  0.85800290  0.92513254  1.88726570 -1.56524564 -0.32039809 -2.19154929  0.91349004
 [57]  0.52479162  0.57548224  0.29499456  1.59831611 -0.12642759  1.29541787  2.04131531  1.37062340  1.05269502 -0.29097545  1.34737414  0.80685092  0.65192730  0.99055427
 [71] -0.60621055 -1.58646413  0.25580931  0.80146002  0.04579534  0.99375433 -0.11053758 -0.21005887  0.13120021  0.35940287  0.17311264  1.09093131  0.44041842 -0.30593590
 [85] -0.91882202 -0.32876722 -1.10254861 -1.26079882 -0.14850136  0.90597316 -1.53368851 -0.69193030  0.19492055 -0.99924244  0.78108644 -0.57499383  1.86240090  0.64761823
 [99]  1.12685042 -0.52939044
> sum(x)
[1] 14.00133
> plot(x)
> mean(x)
[1] 0.1400133
> var(x)
[1] 0.9658413
> sd(x)
[1] 0.9827722
> help sd
Error: unexpected symbol in "help sd"
> help(sd)
starting httpd help server ... done
> sd(x)*sd(x)
[1] 0.9658413
> cummax(x)
  [1] -0.9472239  0.2611432  1.2113695  1.2487662  1.6212143  1.6212143  1.6212143
  [8]  1.6212143  1.6212143  1.6212143  1.6212143  1.6212143  1.6212143  1.6212143
 [15]  1.6212143  1.6212143  1.6212143  1.6212143  1.6212143  1.6212143  3.2136498
 [22]  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498
 [29]  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498
 [36]  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498
 [43]  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498
 [50]  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498
 [57]  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498
 [64]  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498
 [71]  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498
 [78]  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498
 [85]  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498
 [92]  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498  3.2136498
 [99]  3.2136498  3.2136498
> diff(x)
 [1]  1.20836715  0.95022626  0.03739672  0.37244808 -3.27558025  2.74941034
 [7] -0.54175713 -0.28547031  0.61667568 -1.40641932  1.27643588 -0.76547701
[13] -0.14394921 -0.29627298  0.42341214  0.89724499 -0.08217734 -1.06420448
[19] -0.22559545  3.71615999 -2.21748761 -1.75160426  1.47657239 -0.65341738
[25] -1.28241951  1.07275967 -0.07581496  1.02073035 -1.59093282  1.23435287
[31] -0.19023643 -0.74012444  1.31080057 -1.80743871  1.07887724 -0.43778371
[37] -0.44717478  0.71446138 -0.57112951  0.53655118  1.99545930 -4.10266672
[43]  1.75050655  0.90240503 -1.51163331  0.09273836 -0.65440203  2.22550965
[49]  0.26689469  0.06712964  0.96213316 -3.45251134  1.24484755 -1.87115120
[55]  3.10503932 -0.38869842  0.05069062 -0.28048768  1.30332155 -1.72474370
[61]  1.42184546  0.74589744 -0.67069191 -0.31792838 -1.34367047  1.63834959
[67] -0.54052322 -0.15492362  0.33862696 -1.59676481 -0.98025358  1.84227344
[73]  0.54565072 -0.75566468  0.94795899 -1.10429191 -0.09952130  0.34125908
[79]  0.22820266 -0.18629022  0.91781866 -0.65051289 -0.74635432 -0.61288612
[85]  0.59005480 -0.77378139 -0.15825020  1.11229746  1.05447451 -2.43966166
[91]  0.84175820  0.88685086 -1.19416299  1.78032887 -1.35608027  2.43739473
[97] -1.21478267  0.47923219 -1.65624086
> x=c(1,2,4,7)
> diff(x)
[1] 1 2 3
> order(x)
[1] 1 2 3 4
> x=c(1,2,4,7,0)
> order(x)
[1] 5 1 2 3 4
> x[order(x)]
[1] 0 1 2 4 7
> x=1:10;\
Error: unexpected input in "\"
> x=1:10;
> cbind(x, cumsum(x))
       x  
 [1,]  1  1
 [2,]  2  3
 [3,]  3  6
 [4,]  4 10
 [5,]  5 15
 [6,]  6 21
 [7,]  7 28
 [8,]  8 36
 [9,]  9 45
[10,] 10 55
> cumsum(x)
 [1]  1  3  6 10 15 21 28 36 45 55
> a = matrix(a,2,sum)
Error in matrix(a, 2, sum) : object 'a' not found
> a = matrix(1:8,2,4)
> a
     [,1] [,2] [,3] [,4]
[1,]    1    3    5    7
[2,]    2    4    6    8
> apply(a,2,sum)
[1]  3  7 11 15
> length(x)
[1] 10
> sum((x-mean(x)) ^ 2) / (length(x) -1)
[1] 9.166667
> var(x)
[1] 9.166667
> x = c(0,1)
> sum((x-mean(x)) ^ 2) / (length(x) -1)
[1] 0.5
> var(x)
[1] 0.5
> var(x)*(length(x)-1)*length(x))
Error: unexpected ')' in "var(x)*(length(x)-1)*length(x))"
> var(x)*(length(x)-1)*length(x)
[1] 1
> x
[1] 0 1
> var(x)*(length(x)-1)*length(x)
[1] 1
> var(x)*(length(x)-1)/length(x)
[1] 0.25
> var(x)*((length(x)-1)/length(x))
[1] 0.25
> x = rnorm(100)
> x
  [1]  0.78821160 -0.34141601 -0.07118281 -0.81201389  0.26874703  0.40554476
  [7] -1.11694181 -0.19933451 -1.29289183 -0.55480136 -1.03333939  1.46018686
 [13]  0.67552120 -0.42380821 -0.05398014  0.22887773  0.09455121  0.76003883
 [19]  1.41872096  0.67029670  0.56177064 -0.32080959 -0.88749787 -0.40123754
 [25]  1.96633308 -1.43774795 -1.85778523  0.94505757 -0.69617967  0.06200773
 [31] -0.62744976  1.07270896  0.23929145 -0.13430310 -1.78934393  1.35698066
 [37] -0.07239580  0.80122640 -1.47458190 -0.02868427  0.27760466 -1.05483148
 [43]  0.24081589 -0.06147058  0.48091098 -1.01116158  0.54015487 -0.53456427
 [49] -1.61545444 -1.92256937  0.32554970 -0.43367975 -0.42654656  0.66419550
 [55]  1.15840604  0.76196264 -0.34744312  0.74916561  0.29587967 -1.01951437
 [61] -1.17184571  0.18792459 -1.89407322 -0.32492129  0.97818688 -0.01554742
 [67]  0.80625017 -0.16599103  1.05229013  0.27521208  0.20096005 -0.46024458
 [73] -0.02534390 -1.43035488  0.88041532 -0.30755242  0.95139204  0.42419925
 [79]  0.23959115  2.57858413 -0.91977888  0.02105786 -0.52366533 -0.01550240
 [85] -0.22794635  0.07509667  0.68688054  1.04639559  0.44950427 -0.67035977
 [91]  1.55770837  2.17103451  0.55390713  1.64566988  0.97634989  0.02244066
 [97] -0.28195868  0.84729316  1.61858689 -0.75336858
> corr(x)
Error: could not find function "corr"
> cor(x)
Error in cor(x) : supply both 'x' and 'y' or a matrix-like 'x'
> cor(x,2*x)
[1] 1
> cor(x,-2*x)
[1] -1
> cor(x,2/x)
[1] 0.08945048
> plot(cor(x,2/x))
> plot(x,2/x)
> plot(x,2*x)
> x = rnorm(100); y = rnorm(100);
> plot(x,y)
> cor(x,y)
[1] -0.05883529
> hist(x)
> hist(y)
> hist(rnorm(1000))
> hist(rnorm(100000000))
Error: cannot allocate vector of size 381.5 Mb
In addition: Warning messages:
1: In hist.default(rnorm(1e+08)) :
  Reached total allocation of 1535Mb: see help(memory.size)
2: In hist.default(rnorm(1e+08)) :
  Reached total allocation of 1535Mb: see help(memory.size)
3: In hist.default(rnorm(1e+08)) :
  Reached total allocation of 1535Mb: see help(memory.size)
4: In hist.default(rnorm(1e+08)) :
  Reached total allocation of 1535Mb: see help(memory.size)
> hist(rnorm(1000000))
> set.seed(123)
> #upravime generator nah cisel
> x = rnorm(100); y = x+rnorm(100);
> corr(x,y)
Error: could not find function "corr"
> cor(x,y)
[1] 0.66713
> x = rnorm(100); y = x+rnorm(100); cor(x,y);
[1] 0.656549
> x = rnorm(100); y = x+rnorm(100); cor(x,y);
[1] 0.7899585
> set.seed(123); x = rnorm(100); y = x+rnorm(100); cor(x,y);
[1] 0.66713
> set.seed(123); x = rnorm(100); y = x+rnorm(100); cor(x,y);
[1] 0.66713
> set.seed(123); x = rnorm(100); y = x+rnorm(100); cor(x,y);
[1] 0.66713
> set.seed(123); x = rnorm(100); y = x+rnorm(100); cor(x,y);
[1] 0.66713
> y
  [1] -1.270882210  0.026706220  1.312016436 -0.277034208 -0.822330832  1.670037262
  [7] -0.323988263 -2.933003171 -1.067079372  0.473334639  0.648734835  0.967778149
 [13] -1.217111258  0.055120750 -0.036433931  2.088066499  0.603526672 -2.607323165
 [19] -0.148348444 -1.496920198 -0.950177109 -1.165449529 -1.516561892 -0.984983421
 [25]  1.218822737 -2.338643212  1.073173617  0.231333967 -2.099993571  1.182506835
 [31]  1.871015080  0.156432570  0.936358583  0.455636655 -1.231666140  1.819977468
 [37] -0.906722417  0.678035800  1.603140905 -1.824364162  0.007077356 -0.470114767
 [43] -2.837540511  0.654288312 -0.393574175 -1.654015105 -1.864640420  0.221261419
 [49]  2.880074059 -1.370399543  1.041057361  0.740495486  0.289332122  0.360225676
 [55] -0.345223592  1.236075269 -0.985763271  0.212174994  1.100827631 -0.158639289
 [61]  1.432350948 -1.551500460 -1.593362628  2.222464552 -1.488648815  0.601756233
 [67]  1.084779453 -0.430776399  1.439129512  2.419049213 -0.706411674 -2.243875842
 [73]  0.971671271  1.419251136 -1.429344713 -0.070424897 -0.246984608 -0.910236963
 [79]  0.617826959 -0.597256695 -1.057561948  1.648465577 -0.720310420 -0.221136314
 [85] -0.456766131  0.134606070  2.206759303  0.519918783  0.428122200  0.649515601
 [91]  1.207949166  0.223711048  0.333315263 -1.523269434  0.049850915  1.396953798
 [97]  2.788041817  0.281339265 -0.846866276 -2.211900985
> plot(y~x)
> abline(lm(y~x));
> cor(x,y);
[1] 0.66713
> #lm je linearny model
> #d -density/p,, p-CDF/F, q - quantile, r -randorm
> rnorm(1,5)
[1] 7.19881
> pnorm(1,5)
[1] 3.167124e-05
> rnorm(1,5,0.01)
[1] 5.013124
> seq(-3,5,length.out=100)
  [1] -3.00000000 -2.91919192 -2.83838384 -2.75757576 -2.67676768 -2.59595960
  [7] -2.51515152 -2.43434343 -2.35353535 -2.27272727 -2.19191919 -2.11111111
 [13] -2.03030303 -1.94949495 -1.86868687 -1.78787879 -1.70707071 -1.62626263
 [19] -1.54545455 -1.46464646 -1.38383838 -1.30303030 -1.22222222 -1.14141414
 [25] -1.06060606 -0.97979798 -0.89898990 -0.81818182 -0.73737374 -0.65656566
 [31] -0.57575758 -0.49494949 -0.41414141 -0.33333333 -0.25252525 -0.17171717
 [37] -0.09090909 -0.01010101  0.07070707  0.15151515  0.23232323  0.31313131
 [43]  0.39393939  0.47474747  0.55555556  0.63636364  0.71717172  0.79797980
 [49]  0.87878788  0.95959596  1.04040404  1.12121212  1.20202020  1.28282828
 [55]  1.36363636  1.44444444  1.52525253  1.60606061  1.68686869  1.76767677
 [61]  1.84848485  1.92929293  2.01010101  2.09090909  2.17171717  2.25252525
 [67]  2.33333333  2.41414141  2.49494949  2.57575758  2.65656566  2.73737374
 [73]  2.81818182  2.89898990  2.97979798  3.06060606  3.14141414  3.22222222
 [79]  3.30303030  3.38383838  3.46464646  3.54545455  3.62626263  3.70707071
 [85]  3.78787879  3.86868687  3.94949495  4.03030303  4.11111111  4.19191919
 [91]  4.27272727  4.35353535  4.43434343  4.51515152  4.59595960  4.67676768
 [97]  4.75757576  4.83838384  4.91919192  5.00000000
> x = seq(-3,5,length.out=100)
> y = dnorm(x,1,1);
> y
  [1] 0.0001338302 0.0001842953 0.0002521381 0.0003427099 0.0004627846 0.0006208623
  [7] 0.0008275148 0.0010957722 0.0014415473 0.0018840898 0.0024464615 0.0031560163
 [13] 0.0040448664 0.0051503080 0.0065151783 0.0081881065 0.0102236211 0.0126820683
 [19] 0.0156292995 0.0191360817 0.0232771927 0.0281301641 0.0337736510 0.0402854146
 [25] 0.0477399263 0.0562056185 0.0657418315 0.0763955298 0.0881978860 0.1011608535
 [31] 0.1152738702 0.1305008512 0.1467776382 0.1640100747 0.1820728700 0.2008093962
 [37] 0.2200325354 0.2395266587 0.2590507715 0.2783428081 0.2971250031 0.3151102096
 [43] 0.3320089800 0.3475371752 0.3614238299 0.3734189738 0.3833010942 0.3908839312
 [49] 0.3960223134 0.3986167793 0.3986167793 0.3960223134 0.3908839312 0.3833010942
 [55] 0.3734189738 0.3614238299 0.3475371752 0.3320089800 0.3151102096 0.2971250031
 [61] 0.2783428081 0.2590507715 0.2395266587 0.2200325354 0.2008093962 0.1820728700
 [67] 0.1640100747 0.1467776382 0.1305008512 0.1152738702 0.1011608535 0.0881978860
 [73] 0.0763955298 0.0657418315 0.0562056185 0.0477399263 0.0402854146 0.0337736510
 [79] 0.0281301641 0.0232771927 0.0191360817 0.0156292995 0.0126820683 0.0102236211
 [85] 0.0081881065 0.0065151783 0.0051503080 0.0040448664 0.0031560163 0.0024464615
 [91] 0.0018840898 0.0014415473 0.0010957722 0.0008275148 0.0006208623 0.0004627846
 [97] 0.0003427099 0.0002521381 0.0001842953 0.0001338302
> plot(x,y)
> y1 = dnorm(x,1/100,1);
> plot(x,y1);
> screen(2);
[1] FALSE
> help(plot)
> help(screen)
> split.screen(2)
Error in seq.int(0, 1, length.out = nc + 1) :
  'length.out' must be a non-negative number
> split.screen(0,2)
Error in split.screen(0, 2) : invalid screen number
> split.screen(1,2)
Error in split.screen(1, 2) : invalid screen number
> split.screen(c(1,2))
[1] 1 2
> screen(1);
> plot(x,y);
> screen(2);
> plot(x,y1);
> y1 = dnorm(x,1,0.5);
> plot(x,y1);
> split.screen(c(2,1));
[1] 3 4
> screen(1);
> plot(x,y);
> f = pnorm(x,mean=15,sd=1); plot(rnorm(100),f);
> x = seq(-3,5, length.out = 100);
> f = pnorm(x,mean=1,sd=1);
> plot(x,f);
> split.screen(1);
Error in seq.int(0, 1, length.out = nc + 1) :
  'length.out' must be a non-negative number
> split.screen(c(1));
Error in seq.int(0, 1, length.out = nc + 1) :
  'length.out' must be a non-negative number
> split.screen(c(1,1));
[1] 5
> plot(x,f);
> #quantil urovne 0.5 je 0: overenie
> qnorm(0.5,0,1)
[1] 0
> qt(0.95,df=25)
[1] 1.708141
> qchisq(0.95,df=25)
[1] 37.65248
> qf(0.07,10,5)
[1] 0.3420626
> qnorm(0.95,0,1)
[1] 1.644854
> qf(0.975,10,5)
[1] 6.619154
>

 

EXCEL:

 

HODNOTA
VZOREC EXCEL
PRIKAZ R
1,644853627
 =NORMINV(0,95;0;1)
qnorm(0.95,0,1)
1,708140761
 =TINV(2*(1-0,95);25)
qt(0.95,df=25)
37,65248413
 =CHIINV(1-0,95;25)
qchisq(0.95,df=25)
6,619154331
 =FINV(1-0,975;10;5)
qf(0.975,10,5)