Edinson Javier Gamba Martinez 10151144

Oscar Ivan Jaramillo Vargas 10151088

Catherine Prada Rodriguez 10152043

Primer punto

m1=matrix(c(1,sqrt(5),-2,0),nrow = 2)
m1
##          [,1] [,2]
## [1,] 1.000000   -2
## [2,] 2.236068    0
m2=matrix(1:6,nrow =3)
m2
##      [,1] [,2]
## [1,]    1    4
## [2,]    2    5
## [3,]    3    6
m3=matrix(0,nrow =3,ncol=3)
m3
##      [,1] [,2] [,3]
## [1,]    0    0    0
## [2,]    0    0    0
## [3,]    0    0    0
m4=diag(1,3,3)
m4
##      [,1] [,2] [,3]
## [1,]    1    0    0
## [2,]    0    1    0
## [3,]    0    0    1

Segundo punto

A=matrix(c(4,-5,-0.3,2.7),nrow = 2)
rownames(A)=c("f1","f2")
colnames(A)=c("c1","c2")
A
##    c1   c2
## f1  4 -0.3
## f2 -5  2.7
B=matrix(c(3,-8,1,-0.5,1.7,3,0.8,1.25,2),nrow = 3)
rownames(B)=c("cuatro","cinco","seis")
colnames(B)=c("uno","dos","tres")
B
##        uno  dos tres
## cuatro   3 -0.5 0.80
## cinco   -8  1.7 1.25
## seis     1  3.0 2.00

Tercer punto

x=1:200
length(A)
## [1] 4

Imprime el numero de elementos en el vector

dim(A)
## [1] 2 2

Imprime el tamaño de La matriz: 2x2

det(A)
## [1] 9.3

Calcula el determinante.

diag(A)
## [1] 4.0 2.7

Imprime los números que aparecen en la diagonal

prod(A)
## [1] 16.2

Es la multiplicación de los numeros que comoponen la matriz

min(A)
## [1] -5

Imprime el menor numero que contiene la matriz

max(A)
## [1] 4

Imprime el numero máximo que tiene la matriz

mean(A)
## [1] 0.35

Imprime el promedio de los numeros que componen la matriz

sd(A)
## [1] 3.995414

Imprime la desviación estandar de la matriz

var(A)
##       c1    c2
## c1  40.5 -13.5
## c2 -13.5   4.5

Imprime la varianza

t(A)
##      f1   f2
## c1  4.0 -5.0
## c2 -0.3  2.7

Imprime la transpuesta de la matriz

solve(A)
##           f1         f2
## c1 0.2903226 0.03225806
## c2 0.5376344 0.43010753

Imprime la inversa de la matriz

eigen(A)
## eigen() decomposition
## $values
## [1] 4.736542 1.963458
## 
## $vectors
##            [,1]      [,2]
## [1,]  0.3772183 0.1457358
## [2,] -0.9261244 0.9893236

Busca los valores propios de la matriz

Cuarto punto

m2 <- numeric(9)
m2
## [1] 0 0 0 0 0 0 0 0 0
is.vector(m2)
## [1] TRUE
attributes(m2)
## NULL

Imprime un vector númerico de ceros. El codigo is.vector(m2) me responde TRUE Si es un vector El codigo attributes(m2) me responde con un FALSE si el vector no tiene atributos

dim(m2)<-c(3,3)
m2
##      [,1] [,2] [,3]
## [1,]    0    0    0
## [2,]    0    0    0
## [3,]    0    0    0

El codigo dim(m2) <- c(3,3) convierte el vector de ceros en una matriz 3 x 3

attributes(m2)
## $dim
## [1] 3 3

El codigo dim(m2) Imprime la dimensión de la matriz

m3<-matrix(0,4,4)
m3
##      [,1] [,2] [,3] [,4]
## [1,]    0    0    0    0
## [2,]    0    0    0    0
## [3,]    0    0    0    0
## [4,]    0    0    0    0

El codigo m3 <- matrix(0,4,4) crea una matriz de ceros con tamaño 4x4

Quinto punto

z<-matrix(1:6,3,2)
y<-matrix(2:7,3,2)
z;y
##      [,1] [,2]
## [1,]    1    4
## [2,]    2    5
## [3,]    3    6
##      [,1] [,2]
## [1,]    2    5
## [2,]    3    6
## [3,]    4    7
cbind(z,y)
##      [,1] [,2] [,3] [,4]
## [1,]    1    4    2    5
## [2,]    2    5    3    6
## [3,]    3    6    4    7
rbind(z,y)
##      [,1] [,2]
## [1,]    1    4
## [2,]    2    5
## [3,]    3    6
## [4,]    2    5
## [5,]    3    6
## [6,]    4    7

El codigo cbind(z,y) une las matrices, sin alterar el número de filas

El codigo rbind(z,y) une las matrices, sin alterar el número de columnas

Sexto punto

W=matrix(1:16,4,4)
W
##      [,1] [,2] [,3] [,4]
## [1,]    1    5    9   13
## [2,]    2    6   10   14
## [3,]    3    7   11   15
## [4,]    4    8   12   16
W[2, 3]
## [1] 10
W[c(which(W=="11") , which(W=="12"))]
## [1] 11 12
W[2,]
## [1]  2  6 10 14
W[,3]
## [1]  9 10 11 12
W[,c(1,4)]
##      [,1] [,2]
## [1,]    1   13
## [2,]    2   14
## [3,]    3   15
## [4,]    4   16
W[2:3,]
##      [,1] [,2] [,3] [,4]
## [1,]    2    6   10   14
## [2,]    3    7   11   15
W[1:2,3:4]
##      [,1] [,2]
## [1,]    9   13
## [2,]   10   14

Septimo punto

A=matrix(1:16,4,4)
A
##      [,1] [,2] [,3] [,4]
## [1,]    1    5    9   13
## [2,]    2    6   10   14
## [3,]    3    7   11   15
## [4,]    4    8   12   16
A[c(13,14)]
## [1] 13 14

Extrae los valores trece y catorce

A[4,]
## [1]  4  8 12 16

Extrae los numeros que estan en la fila cuatro de la matriz A

A[,2]
## [1] 5 6 7 8

Extrae los numeros que estan en la columna dos de la matriz A

A[c(1,2),c(3,4)]
##      [,1] [,2]
## [1,]    9   13
## [2,]   10   14

Extrae los numeros que estan en las filas 1 y 2 en las columnas 3 y 4 de la matriz A

Octavo punto

A=matrix(c(1,-3,2,3,2,4,0,-1.5,-0.5,-1.5,-1,2),4,3)
A
##      [,1] [,2] [,3]
## [1,]    1  2.0 -0.5
## [2,]   -3  4.0 -1.5
## [3,]    2  0.0 -1.0
## [4,]    3 -1.5  2.0
B=matrix(c(1,0.2,4,-1.5,1.1,-0.7,1.1,-1,1.1,1.6,0.3,-0.5),3,4)
B
##      [,1] [,2] [,3] [,4]
## [1,]  1.0 -1.5  1.1  1.6
## [2,]  0.2  1.1 -1.0  0.3
## [3,]  4.0 -0.7  1.1 -0.5
A%*%B
##      [,1]  [,2]  [,3]  [,4]
## [1,] -0.6  1.05 -1.45  2.45
## [2,] -8.2  9.95 -8.95 -2.85
## [3,] -2.0 -2.30  1.10  3.70
## [4,] 10.7 -7.55  7.00  3.35
t(A)
##      [,1] [,2] [,3] [,4]
## [1,]  1.0 -3.0    2  3.0
## [2,]  2.0  4.0    0 -1.5
## [3,] -0.5 -1.5   -1  2.0
t(A)%*%t(B)
##       [,1]  [,2]  [,3]
## [1,] 12.50 -4.20  6.80
## [2,] -6.40  4.35  5.95
## [3,]  3.85 -0.15 -3.05
solve(t(A)%*%A)
##             [,1]       [,2]        [,3]
## [1,]  0.07801108 0.03353747 -0.03849519
## [2,]  0.03353747 0.12656751  0.13298338
## [3,] -0.03849519 0.13298338  0.35170604
(B%*%t(B))+(t(A)%*%A)
##        [,1]   [,2]   [,3]
## [1,]  30.02 -16.57  13.46
## [2,] -16.57  24.59 -11.22
## [3,]  13.46 -11.22  25.45

Noveno Punto

A=matrix(c(3,1,1,-1),2,2)
B=matrix(c(11,-1),2)
solve(A,B)
##      [,1]
## [1,]  2.5
## [2,]  3.5
lista1 <- list(persona="Carlos",vector=c(pi,exp(1)), matriz=matrix(16:1,4,4), arreglo=array(24:1,c(2,3,4)))
lista1[[3]][2,2]
## [1] 11
lista1[[4]][2,2,2]
## [1] 15
lista1[[1]]
## [1] "Carlos"

El comando lista1[[1]] extrae el elelmento que compone el primer elemento de la lista.

lista1[[3]][3,3]
## [1] 6

El comando lista1[[3]][3,3] extrae el elemento ubicado en la fila 3 y la columna 3 del tercer elemento de la lista (que es una matriz).

lista1$arreglo
## , , 1
## 
##      [,1] [,2] [,3]
## [1,]   24   22   20
## [2,]   23   21   19
## 
## , , 2
## 
##      [,1] [,2] [,3]
## [1,]   18   16   14
## [2,]   17   15   13
## 
## , , 3
## 
##      [,1] [,2] [,3]
## [1,]   12   10    8
## [2,]   11    9    7
## 
## , , 4
## 
##      [,1] [,2] [,3]
## [1,]    6    4    2
## [2,]    5    3    1

El comando lista1$arreglo extrae el elemento con nombre “arreglo”

lista1[["matriz"]]
##      [,1] [,2] [,3] [,4]
## [1,]   16   12    8    4
## [2,]   15   11    7    3
## [3,]   14   10    6    2
## [4,]   13    9    5    1

El comando lista1[[“matriz”]] extrae el elemento con nombre “matriz”

Decimo punto

ip<-installed.packages()
aip<-attributes(ip)
naip<-aip[[2]][1]
rnip<-rownames(ip)
str(ip)
##  chr [1:52, 1:16] "backports" "base64enc" "bitops" "caTools" "digest" ...
##  - attr(*, "dimnames")=List of 2
##   ..$ : chr [1:52] "backports" "base64enc" "bitops" "caTools" ...
##   ..$ : chr [1:16] "Package" "LibPath" "Version" "Priority" ...
is.array(ip)
## [1] TRUE
is.vector(ip)
## [1] FALSE
is.matrix(ip)
## [1] TRUE
is.list(ip)
## [1] FALSE

Es una matriz de caracteres con 30 filas y 16 columnas

str(aip)
## List of 2
##  $ dim     : int [1:2] 52 16
##  $ dimnames:List of 2
##   ..$ : chr [1:52] "backports" "base64enc" "bitops" "caTools" ...
##   ..$ : chr [1:16] "Package" "LibPath" "Version" "Priority" ...
is.array(aip)
## [1] FALSE
is.vector(aip)
## [1] TRUE
is.matrix(aip)
## [1] FALSE
is.list(aip)
## [1] TRUE

Es una lista de dos vectores de caracteres, uno de 30 elementos y el otro de 16 elementos.

str(naip)
## List of 1
##  $ : chr [1:52] "backports" "base64enc" "bitops" "caTools" ...
is.array(naip)
## [1] FALSE
is.vector(naip)
## [1] TRUE
is.matrix(naip)
## [1] FALSE
is.list(naip)
## [1] TRUE

Es una lista de un vector

str(rnip)
##  chr [1:52] "backports" "base64enc" "bitops" "caTools" "digest" ...
is.array(rnip)
## [1] FALSE
is.vector(rnip)
## [1] TRUE
is.matrix(rnip)
## [1] FALSE
is.list(rnip)
## [1] FALSE

Es un vector con 30 caracteres.

Undecimo punto

dim(ip)
## [1] 52 16

RStudio tiene instalados 30 paquetes en este equipo.

Duodecimo punto

set.seed(123)
X<-1:10
Y<-rpois(10,3)
reg1<- lm(Y~X)
reg1
## 
## Call:
## lm(formula = Y ~ X)
## 
## Coefficients:
## (Intercept)            X  
##      3.1333       0.0303
str(reg1)
## List of 12
##  $ coefficients : Named num [1:2] 3.1333 0.0303
##   ..- attr(*, "names")= chr [1:2] "(Intercept)" "X"
##  $ residuals    : Named num [1:10] -1.164 0.806 -1.224 1.745 2.715 ...
##   ..- attr(*, "names")= chr [1:10] "1" "2" "3" "4" ...
##  $ effects      : Named num [1:10] -10.436 0.275 -1.079 1.985 3.05 ...
##   ..- attr(*, "names")= chr [1:10] "(Intercept)" "X" "" "" ...
##  $ rank         : int 2
##  $ fitted.values: Named num [1:10] 3.16 3.19 3.22 3.25 3.28 ...
##   ..- attr(*, "names")= chr [1:10] "1" "2" "3" "4" ...
##  $ assign       : int [1:2] 0 1
##  $ qr           :List of 5
##   ..$ qr   : num [1:10, 1:2] -3.162 0.316 0.316 0.316 0.316 ...
##   .. ..- attr(*, "dimnames")=List of 2
##   .. .. ..$ : chr [1:10] "1" "2" "3" "4" ...
##   .. .. ..$ : chr [1:2] "(Intercept)" "X"
##   .. ..- attr(*, "assign")= int [1:2] 0 1
##   ..$ qraux: num [1:2] 1.32 1.27
##   ..$ pivot: int [1:2] 1 2
##   ..$ tol  : num 1e-07
##   ..$ rank : int 2
##   ..- attr(*, "class")= chr "qr"
##  $ df.residual  : int 8
##  $ xlevels      : Named list()
##  $ call         : language lm(formula = Y ~ X)
##  $ terms        :Classes 'terms', 'formula'  language Y ~ X
##   .. ..- attr(*, "variables")= language list(Y, X)
##   .. ..- attr(*, "factors")= int [1:2, 1] 0 1
##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : chr [1:2] "Y" "X"
##   .. .. .. ..$ : chr "X"
##   .. ..- attr(*, "term.labels")= chr "X"
##   .. ..- attr(*, "order")= int 1
##   .. ..- attr(*, "intercept")= int 1
##   .. ..- attr(*, "response")= int 1
##   .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv> 
##   .. ..- attr(*, "predvars")= language list(Y, X)
##   .. ..- attr(*, "dataClasses")= Named chr [1:2] "numeric" "numeric"
##   .. .. ..- attr(*, "names")= chr [1:2] "Y" "X"
##  $ model        :'data.frame':   10 obs. of  2 variables:
##   ..$ Y: int [1:10] 2 4 2 5 6 0 3 5 3 3
##   ..$ X: int [1:10] 1 2 3 4 5 6 7 8 9 10
##   ..- attr(*, "terms")=Classes 'terms', 'formula'  language Y ~ X
##   .. .. ..- attr(*, "variables")= language list(Y, X)
##   .. .. ..- attr(*, "factors")= int [1:2, 1] 0 1
##   .. .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. .. ..$ : chr [1:2] "Y" "X"
##   .. .. .. .. ..$ : chr "X"
##   .. .. ..- attr(*, "term.labels")= chr "X"
##   .. .. ..- attr(*, "order")= int 1
##   .. .. ..- attr(*, "intercept")= int 1
##   .. .. ..- attr(*, "response")= int 1
##   .. .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv> 
##   .. .. ..- attr(*, "predvars")= language list(Y, X)
##   .. .. ..- attr(*, "dataClasses")= Named chr [1:2] "numeric" "numeric"
##   .. .. .. ..- attr(*, "names")= chr [1:2] "Y" "X"
##  - attr(*, "class")= chr "lm"
res<-summary(reg1)
str(res)
## List of 11
##  $ call         : language lm(formula = Y ~ X)
##  $ terms        :Classes 'terms', 'formula'  language Y ~ X
##   .. ..- attr(*, "variables")= language list(Y, X)
##   .. ..- attr(*, "factors")= int [1:2, 1] 0 1
##   .. .. ..- attr(*, "dimnames")=List of 2
##   .. .. .. ..$ : chr [1:2] "Y" "X"
##   .. .. .. ..$ : chr "X"
##   .. ..- attr(*, "term.labels")= chr "X"
##   .. ..- attr(*, "order")= int 1
##   .. ..- attr(*, "intercept")= int 1
##   .. ..- attr(*, "response")= int 1
##   .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv> 
##   .. ..- attr(*, "predvars")= language list(Y, X)
##   .. ..- attr(*, "dataClasses")= Named chr [1:2] "numeric" "numeric"
##   .. .. ..- attr(*, "names")= chr [1:2] "Y" "X"
##  $ residuals    : Named num [1:10] -1.164 0.806 -1.224 1.745 2.715 ...
##   ..- attr(*, "names")= chr [1:10] "1" "2" "3" "4" ...
##  $ coefficients : num [1:2, 1:4] 3.1333 0.0303 1.2786 0.2061 2.4506 ...
##   ..- attr(*, "dimnames")=List of 2
##   .. ..$ : chr [1:2] "(Intercept)" "X"
##   .. ..$ : chr [1:4] "Estimate" "Std. Error" "t value" "Pr(>|t|)"
##  $ aliased      : Named logi [1:2] FALSE FALSE
##   ..- attr(*, "names")= chr [1:2] "(Intercept)" "X"
##  $ sigma        : num 1.87
##  $ df           : int [1:3] 2 8 2
##  $ r.squared    : num 0.0027
##  $ adj.r.squared: num -0.122
##  $ fstatistic   : Named num [1:3] 0.0216 1 8
##   ..- attr(*, "names")= chr [1:3] "value" "numdf" "dendf"
##  $ cov.unscaled : num [1:2, 1:2] 0.4667 -0.0667 -0.0667 0.0121
##   ..- attr(*, "dimnames")=List of 2
##   .. ..$ : chr [1:2] "(Intercept)" "X"
##   .. ..$ : chr [1:2] "(Intercept)" "X"
##  - attr(*, "class")= chr "summary.lm"
plot(reg1)

3punto

ts(1:10, frequency = 4, start = c(2014,2))
##      Qtr1 Qtr2 Qtr3 Qtr4
## 2014         1    2    3
## 2015    4    5    6    7
## 2016    8    9   10
st1<- ts(1:38, start= c(2016,3), frequency = 12)
ts.plot(st1)

st1
##      Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 2016           1   2   3   4   5   6   7   8   9  10
## 2017  11  12  13  14  15  16  17  18  19  20  21  22
## 2018  23  24  25  26  27  28  29  30  31  32  33  34
## 2019  35  36  37  38
window(st1, c(2017,1), c(2017,12))
##      Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 2017  11  12  13  14  15  16  17  18  19  20  21  22

Treceavo punto

print(ts(1:20,start = c(2011,1),frequency=2),calendar=TRUE)
##      p1 p2
## 2011  1  2
## 2012  3  4
## 2013  5  6
## 2014  7  8
## 2015  9 10
## 2016 11 12
## 2017 13 14
## 2018 15 16
## 2019 17 18
## 2020 19 20
print(ts(1:15,start = c(2014,1),frequency=0.5),calendar=TRUE)
## 2014 2016 2018 2020 2022 2024 2026 2028 2030 2032 2034 2036 2038 2040 2042 
##    1    2    3    4    5    6    7    8    9   10   11   12   13   14   15
coima<-ts(1:48, start = c(2015,1), frequency = 12)
print(coima, calendar = TRUE)
##      Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 2015   1   2   3   4   5   6   7   8   9  10  11  12
## 2016  13  14  15  16  17  18  19  20  21  22  23  24
## 2017  25  26  27  28  29  30  31  32  33  34  35  36
## 2018  37  38  39  40  41  42  43  44  45  46  47  48
window(coima, c(2017,1), c(2017,12))
##      Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 2017  25  26  27  28  29  30  31  32  33  34  35  36

Catorceavo punto

month.abb
##  [1] "Jan" "Feb" "Mar" "Apr" "May" "Jun" "Jul" "Aug" "Sep" "Oct" "Nov"
## [12] "Dec"
month.name
##  [1] "January"   "February"  "March"     "April"     "May"      
##  [6] "June"      "July"      "August"    "September" "October"  
## [11] "November"  "December"

El codigo month.abb tiene el abreviado de los nombres de los meses en ingles

El codigo month.name tiene los nombres de los meses en ingles