matrizY<-matrix(data=c(6.1,9.1,7.2,7.5,6.9,11.5,10.3,9.5,9.2,10.6,12.5,12.9,13.6,12.8,16.5,17.1,15,16.2,15.8,19,19.4,19.1,18,20.2),nrow = 24,ncol=1,byrow=FALSE)
colnames(matrizY) <-c("matrizY")
print(matrizY)
## matrizY
## [1,] 6.1
## [2,] 9.1
## [3,] 7.2
## [4,] 7.5
## [5,] 6.9
## [6,] 11.5
## [7,] 10.3
## [8,] 9.5
## [9,] 9.2
## [10,] 10.6
## [11,] 12.5
## [12,] 12.9
## [13,] 13.6
## [14,] 12.8
## [15,] 16.5
## [16,] 17.1
## [17,] 15.0
## [18,] 16.2
## [19,] 15.8
## [20,] 19.0
## [21,] 19.4
## [22,] 19.1
## [23,] 18.0
## [24,] 20.2
matrizX<-cbind(rep(x = 1,24),
matrix(data = c(216,283,237,203,259,374,342,301,365,384,404,426,432,409,553,572,506,528,501,628,677,602,630,652),nrow = 24,ncol = 1,byrow = FALSE))
colnames(matrizX)<-c("Cte","X1")
print(matrizX)
## Cte X1
## [1,] 1 216
## [2,] 1 283
## [3,] 1 237
## [4,] 1 203
## [5,] 1 259
## [6,] 1 374
## [7,] 1 342
## [8,] 1 301
## [9,] 1 365
## [10,] 1 384
## [11,] 1 404
## [12,] 1 426
## [13,] 1 432
## [14,] 1 409
## [15,] 1 553
## [16,] 1 572
## [17,] 1 506
## [18,] 1 528
## [19,] 1 501
## [20,] 1 628
## [21,] 1 677
## [22,] 1 602
## [23,] 1 630
## [24,] 1 652
Parametros del modelo
sigmaMat<- t(matrizX)%*% matrizX
invSig<- solve(sigmaMat)
matProdCruz<- t(matrizX) %*% matrizY
Beta<- invSig %*% matProdCruz
Matrices
XX_transpuesta<- t(matrizX)%*%matrizX
inversaxtranspuesta <- solve(XX_transpuesta)
xtranspuestaY <- t(matrizX)%*%matrizY
##Matriz A
matrizA <- inversaxtranspuesta%*% t(matrizX)
print(matrizA)
## [,1] [,2] [,3] [,4] [,5]
## Cte 0.236906257 0.1776713023 0.2183400774 0.2483996068 0.1988897936
## X1 -0.000446943 -0.0003113422 -0.0004044412 -0.0004732536 -0.0003599156
## [,6] [,7] [,8] [,9] [,10]
## Cte 0.0972178559 0.1255091777 0.1617574338 0.105174790 0.088376818
## X1 -0.0001271679 -0.0001919325 -0.0002749121 -0.000145383 -0.000106929
## [,11] [,12] [,13] [,14] [,15]
## Cte 7.069474e-02 0.0512444579 4.593984e-02 6.627422e-02 -0.0610367256
## X1 -6.645114e-05 -0.0000219255 -9.782148e-06 -5.633168e-05 0.0002351089
## [,16] [,17] [,18] [,19] [,20]
## Cte -0.0778346979 -0.0194838466 -0.0389341304 -0.0150633276 -0.1273445111
## X1 0.0002735628 0.0001399859 0.0001845116 0.0001298665 0.0003869008
## [,21] [,22] [,23] [,24]
## Cte -0.1706655976 -0.1043578121 -0.1291127187 -0.1485630024
## X1 0.0004860716 0.0003342796 0.0003909486 0.0004354743
##Matriz P
matrizP <- matrizX%*%matrizA
print(matrizP)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.1403665742 0.1104213947 0.130980772 0.146176833 0.1211480262
## [2,] 0.1104213947 0.0895614697 0.103883209 0.114468843 0.0970336816
## [3,] 0.1309807717 0.1038832092 0.122487506 0.136238508 0.1135897988
## [4,] 0.1461768329 0.1144688428 0.136238508 0.152329129 0.1258269288
## [5,] 0.1211480262 0.0970336816 0.113589799 0.125826929 0.1056716558
## [6,] 0.0697495838 0.0612293327 0.067079057 0.071402767 0.0642813629
## [7,] 0.0840517590 0.0711922820 0.080021177 0.086546881 0.0757986618
## [8,] 0.1023764211 0.0839573107 0.096603267 0.105950278 0.0905552010
## [9,] 0.0737720706 0.0640314122 0.070719028 0.075662049 0.0675206032
## [10,] 0.0652801540 0.0581159110 0.063034645 0.066670231 0.0606822070
## [11,] 0.0563412944 0.0518890677 0.054945820 0.057205159 0.0534838952
## [12,] 0.0465085489 0.0450395401 0.046048113 0.046793580 0.0455657522
## [13,] 0.0438268911 0.0431714871 0.043621466 0.043954059 0.0434062587
## [14,] 0.0541065795 0.0503323569 0.052923614 0.054838891 0.0516843173
## [15,] -0.0102532092 0.0054990852 -0.005315923 -0.013309625 -0.0001435277
## [16,] -0.0187451258 -0.0004164159 -0.013000306 -0.022301443 -0.0069819239
## [17,] 0.0107531107 0.0201321669 0.013692815 0.008933294 0.0167725050
## [18,] 0.0009203652 0.0132826393 0.004795108 -0.001478285 0.0088543620
## [19,] 0.0129878256 0.0216888778 0.015715021 0.011299562 0.0185720830
## [20,] -0.0437739325 -0.0178515772 -0.035649015 -0.048803643 -0.0271371970
## [21,] -0.0656741384 -0.0331073432 -0.055466635 -0.071993069 -0.0447730609
## [22,] -0.0321534151 -0.0097566809 -0.025133543 -0.036499050 -0.0177793916
## [23,] -0.0446678185 -0.0184742615 -0.036457898 -0.049750150 -0.0278570282
## [24,] -0.0545005640 -0.0253237891 -0.045355605 -0.060161729 -0.0357751712
## [,6] [,7] [,8] [,9] [,10]
## [1,] 0.06974958 0.0840517590 0.102376421 0.073772071 0.06528015
## [2,] 0.06122933 0.0711922820 0.083957311 0.064031412 0.05811591
## [3,] 0.06707906 0.0800211767 0.096603267 0.070719028 0.06303464
## [4,] 0.07140277 0.0865468815 0.105950278 0.075662049 0.06667023
## [5,] 0.06428136 0.0757986618 0.090555201 0.067520603 0.06068221
## [6,] 0.04965705 0.0537264250 0.058940310 0.050801563 0.04838537
## [7,] 0.05372643 0.0598682648 0.067737497 0.055453817 0.05180710
## [8,] 0.05894031 0.0677374971 0.079008893 0.061414519 0.05619119
## [9,] 0.05080156 0.0554538175 0.061414519 0.052110009 0.04934773
## [10,] 0.04838537 0.0518071001 0.056191189 0.049347733 0.04731608
## [11,] 0.04584201 0.0479684502 0.050692947 0.046440074 0.04517750
## [12,] 0.04304432 0.0437459353 0.044644881 0.043241649 0.04282506
## [13,] 0.04228131 0.0425943404 0.042995408 0.042369351 0.04218349
## [14,] 0.04520617 0.0470087877 0.049318387 0.045713159 0.04464286
## [15,] 0.02689399 0.0193705086 0.009731045 0.024778013 0.02924508
## [16,] 0.02447780 0.0157237913 0.004507715 0.022015736 0.02721343
## [17,] 0.03287089 0.0283913359 0.022651913 0.031611012 0.03427074
## [18,] 0.03007319 0.0241688210 0.016603847 0.028412587 0.03191831
## [19,] 0.03350672 0.0293509983 0.024026474 0.032337927 0.03480539
## [20,] 0.01735640 0.0049755716 -0.010887362 0.013874291 0.02122541
## [21,] 0.01112517 -0.0044291206 -0.024358055 0.006750526 0.01598589
## [22,] 0.02066276 0.0099658165 -0.003739648 0.017654248 0.02400556
## [23,] 0.01710206 0.0045917066 -0.011437186 0.013583525 0.02101155
## [24,] 0.01430437 0.0003691918 -0.017485253 0.010385100 0.01865911
## [,11] [,12] [,13] [,14] [,15]
## [1,] 0.05634129 0.04650855 0.04382689 0.05410658 -0.0102532092
## [2,] 0.05188907 0.04503954 0.04317149 0.05033236 0.0054990852
## [3,] 0.05494582 0.04604811 0.04362147 0.05292361 -0.0053159229
## [4,] 0.05720516 0.04679358 0.04395406 0.05483889 -0.0133096246
## [5,] 0.05348390 0.04556575 0.04340626 0.05168432 -0.0001435277
## [6,] 0.04584201 0.04304432 0.04228131 0.04520617 0.0268939925
## [7,] 0.04796845 0.04374594 0.04259434 0.04700879 0.0193705086
## [8,] 0.05069295 0.04464488 0.04299541 0.04931839 0.0097310449
## [9,] 0.04644007 0.04324165 0.04236935 0.04571316 0.0247780127
## [10,] 0.04517750 0.04282506 0.04218349 0.04464286 0.0292450813
## [11,] 0.04384848 0.04238655 0.04198785 0.04351622 0.0339472587
## [12,] 0.04238655 0.04190419 0.04177264 0.04227693 0.0391196539
## [13,] 0.04198785 0.04177264 0.04171395 0.04193894 0.0405303071
## [14,] 0.04351622 0.04227693 0.04193894 0.04323457 0.0351228031
## [15,] 0.03394726 0.03911965 0.04053031 0.03512280 0.0689784806
## [16,] 0.03268469 0.03870307 0.04034445 0.03405250 0.0734455492
## [17,] 0.03707046 0.04015015 0.04099007 0.03777039 0.0579283636
## [18,] 0.03560854 0.03966779 0.04077486 0.03653110 0.0631007588
## [19,] 0.03740272 0.04025978 0.04103898 0.03805205 0.0567528193
## [20,] 0.02896342 0.03747524 0.03979665 0.03089793 0.0866116460
## [21,] 0.02570732 0.03640089 0.03931732 0.02813767 0.0981319807
## [22,] 0.03069115 0.03804530 0.04005098 0.03236255 0.0804988153
## [23,] 0.02883052 0.03743139 0.03977708 0.03078526 0.0870818638
## [24,] 0.02736860 0.03694903 0.03956187 0.02954597 0.0922542589
## [,16] [,17] [,18] [,19] [,20]
## [1,] -0.0187451258 0.010753111 0.0009203652 0.01298783 -0.043773933
## [2,] -0.0004164159 0.020132167 0.0132826393 0.02168888 -0.017851577
## [3,] -0.0130003063 0.013692815 0.0047951078 0.01571502 -0.035649015
## [4,] -0.0223014426 0.008933294 -0.0014782850 0.01129956 -0.048803643
## [5,] -0.0069819239 0.016772505 0.0088543620 0.01857208 -0.027137197
## [6,] 0.0244778019 0.032870885 0.0300731907 0.03350672 0.017356398
## [7,] 0.0157237913 0.028391336 0.0241688210 0.02935100 0.004975572
## [8,] 0.0045077151 0.022651913 0.0166038473 0.02402647 -0.010887362
## [9,] 0.0220157364 0.031611012 0.0284125867 0.03233793 0.013874291
## [10,] 0.0272134303 0.034270744 0.0319183062 0.03480539 0.021225406
## [11,] 0.0326846870 0.037070462 0.0356085373 0.03740272 0.028963423
## [12,] 0.0387030693 0.040150153 0.0396677915 0.04025978 0.037475241
## [13,] 0.0403444463 0.040990068 0.0407748608 0.04103898 0.039796646
## [14,] 0.0340525011 0.037770392 0.0365310951 0.03805205 0.030897927
## [15,] 0.0734455492 0.057928364 0.0631007588 0.05675282 0.086611646
## [16,] 0.0786432430 0.060588096 0.0666064783 0.05922028 0.093962762
## [17,] 0.0605880960 0.051349026 0.0544287158 0.05064910 0.068427307
## [18,] 0.0666064783 0.054428716 0.0584879700 0.05350616 0.076939125
## [19,] 0.0592202818 0.050649096 0.0535061580 0.04999976 0.066492803
## [20,] 0.0939627617 0.068427307 0.0769391254 0.06649280 0.115629208
## [21,] 0.1073673406 0.075286617 0.0859801915 0.07285626 0.134587349
## [22,] 0.0868501280 0.064787673 0.0721418250 0.06311628 0.105569787
## [23,] 0.0945098874 0.068707279 0.0773081485 0.06675254 0.116403010
## [24,] 0.1005282697 0.071786969 0.0813674026 0.06960960 0.124914828
## [,21] [,22] [,23] [,24]
## [1,] -0.065674138 -0.032153415 -0.044667818 -0.0545005640
## [2,] -0.033107343 -0.009756681 -0.018474261 -0.0253237891
## [3,] -0.055466635 -0.025133543 -0.036457898 -0.0453556047
## [4,] -0.071993069 -0.036499050 -0.049750150 -0.0601617293
## [5,] -0.044773061 -0.017779392 -0.027857028 -0.0357751712
## [6,] 0.011125170 0.020662764 0.017102062 0.0143043678
## [7,] -0.004429121 0.009965816 0.004591707 0.0003691918
## [8,] -0.024358055 -0.003739648 -0.011437186 -0.0174852526
## [9,] 0.006750526 0.017654248 0.013583525 0.0103850996
## [10,] 0.015985885 0.024005560 0.021011548 0.0186591104
## [11,] 0.025707317 0.030691153 0.028830521 0.0273685954
## [12,] 0.036400891 0.038045304 0.037431390 0.0369490289
## [13,] 0.039317321 0.040050982 0.039777082 0.0395618744
## [14,] 0.028137675 0.032362551 0.030785264 0.0295459667
## [15,] 0.098131981 0.080498815 0.087081864 0.0922542589
## [16,] 0.107367341 0.086850128 0.094509887 0.1005282697
## [17,] 0.075286617 0.064787673 0.068707279 0.0717869691
## [18,] 0.085980191 0.072141825 0.077308148 0.0813674026
## [19,] 0.072856259 0.063116275 0.066752536 0.0696095978
## [20,] 0.134587349 0.105569787 0.116403010 0.1249148278
## [21,] 0.158404855 0.121949488 0.135559492 0.1462530662
## [22,] 0.121949488 0.096878517 0.106238346 0.1135924973
## [23,] 0.135559492 0.106238346 0.117184907 0.1257857764
## [24,] 0.146253066 0.113592497 0.125785776 0.1353662099
##Matriz M
identidad <- diag(1, 24)
matrizM <- identidad - matrizP
print(matrizM)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.8596334258 -0.1104213947 -0.130980772 -0.146176833 -0.1211480262
## [2,] -0.1104213947 0.9104385303 -0.103883209 -0.114468843 -0.0970336816
## [3,] -0.1309807717 -0.1038832092 0.877512494 -0.136238508 -0.1135897988
## [4,] -0.1461768329 -0.1144688428 -0.136238508 0.847670871 -0.1258269288
## [5,] -0.1211480262 -0.0970336816 -0.113589799 -0.125826929 0.8943283442
## [6,] -0.0697495838 -0.0612293327 -0.067079057 -0.071402767 -0.0642813629
## [7,] -0.0840517590 -0.0711922820 -0.080021177 -0.086546881 -0.0757986618
## [8,] -0.1023764211 -0.0839573107 -0.096603267 -0.105950278 -0.0905552010
## [9,] -0.0737720706 -0.0640314122 -0.070719028 -0.075662049 -0.0675206032
## [10,] -0.0652801540 -0.0581159110 -0.063034645 -0.066670231 -0.0606822070
## [11,] -0.0563412944 -0.0518890677 -0.054945820 -0.057205159 -0.0534838952
## [12,] -0.0465085489 -0.0450395401 -0.046048113 -0.046793580 -0.0455657522
## [13,] -0.0438268911 -0.0431714871 -0.043621466 -0.043954059 -0.0434062587
## [14,] -0.0541065795 -0.0503323569 -0.052923614 -0.054838891 -0.0516843173
## [15,] 0.0102532092 -0.0054990852 0.005315923 0.013309625 0.0001435277
## [16,] 0.0187451258 0.0004164159 0.013000306 0.022301443 0.0069819239
## [17,] -0.0107531107 -0.0201321669 -0.013692815 -0.008933294 -0.0167725050
## [18,] -0.0009203652 -0.0132826393 -0.004795108 0.001478285 -0.0088543620
## [19,] -0.0129878256 -0.0216888778 -0.015715021 -0.011299562 -0.0185720830
## [20,] 0.0437739325 0.0178515772 0.035649015 0.048803643 0.0271371970
## [21,] 0.0656741384 0.0331073432 0.055466635 0.071993069 0.0447730609
## [22,] 0.0321534151 0.0097566809 0.025133543 0.036499050 0.0177793916
## [23,] 0.0446678185 0.0184742615 0.036457898 0.049750150 0.0278570282
## [24,] 0.0545005640 0.0253237891 0.045355605 0.060161729 0.0357751712
## [,6] [,7] [,8] [,9] [,10]
## [1,] -0.06974958 -0.0840517590 -0.102376421 -0.073772071 -0.06528015
## [2,] -0.06122933 -0.0711922820 -0.083957311 -0.064031412 -0.05811591
## [3,] -0.06707906 -0.0800211767 -0.096603267 -0.070719028 -0.06303464
## [4,] -0.07140277 -0.0865468815 -0.105950278 -0.075662049 -0.06667023
## [5,] -0.06428136 -0.0757986618 -0.090555201 -0.067520603 -0.06068221
## [6,] 0.95034295 -0.0537264250 -0.058940310 -0.050801563 -0.04838537
## [7,] -0.05372643 0.9401317352 -0.067737497 -0.055453817 -0.05180710
## [8,] -0.05894031 -0.0677374971 0.920991107 -0.061414519 -0.05619119
## [9,] -0.05080156 -0.0554538175 -0.061414519 0.947889991 -0.04934773
## [10,] -0.04838537 -0.0518071001 -0.056191189 -0.049347733 0.95268392
## [11,] -0.04584201 -0.0479684502 -0.050692947 -0.046440074 -0.04517750
## [12,] -0.04304432 -0.0437459353 -0.044644881 -0.043241649 -0.04282506
## [13,] -0.04228131 -0.0425943404 -0.042995408 -0.042369351 -0.04218349
## [14,] -0.04520617 -0.0470087877 -0.049318387 -0.045713159 -0.04464286
## [15,] -0.02689399 -0.0193705086 -0.009731045 -0.024778013 -0.02924508
## [16,] -0.02447780 -0.0157237913 -0.004507715 -0.022015736 -0.02721343
## [17,] -0.03287089 -0.0283913359 -0.022651913 -0.031611012 -0.03427074
## [18,] -0.03007319 -0.0241688210 -0.016603847 -0.028412587 -0.03191831
## [19,] -0.03350672 -0.0293509983 -0.024026474 -0.032337927 -0.03480539
## [20,] -0.01735640 -0.0049755716 0.010887362 -0.013874291 -0.02122541
## [21,] -0.01112517 0.0044291206 0.024358055 -0.006750526 -0.01598589
## [22,] -0.02066276 -0.0099658165 0.003739648 -0.017654248 -0.02400556
## [23,] -0.01710206 -0.0045917066 0.011437186 -0.013583525 -0.02101155
## [24,] -0.01430437 -0.0003691918 0.017485253 -0.010385100 -0.01865911
## [,11] [,12] [,13] [,14] [,15]
## [1,] -0.05634129 -0.04650855 -0.04382689 -0.05410658 0.0102532092
## [2,] -0.05188907 -0.04503954 -0.04317149 -0.05033236 -0.0054990852
## [3,] -0.05494582 -0.04604811 -0.04362147 -0.05292361 0.0053159229
## [4,] -0.05720516 -0.04679358 -0.04395406 -0.05483889 0.0133096246
## [5,] -0.05348390 -0.04556575 -0.04340626 -0.05168432 0.0001435277
## [6,] -0.04584201 -0.04304432 -0.04228131 -0.04520617 -0.0268939925
## [7,] -0.04796845 -0.04374594 -0.04259434 -0.04700879 -0.0193705086
## [8,] -0.05069295 -0.04464488 -0.04299541 -0.04931839 -0.0097310449
## [9,] -0.04644007 -0.04324165 -0.04236935 -0.04571316 -0.0247780127
## [10,] -0.04517750 -0.04282506 -0.04218349 -0.04464286 -0.0292450813
## [11,] 0.95615152 -0.04238655 -0.04198785 -0.04351622 -0.0339472587
## [12,] -0.04238655 0.95809581 -0.04177264 -0.04227693 -0.0391196539
## [13,] -0.04198785 -0.04177264 0.95828605 -0.04193894 -0.0405303071
## [14,] -0.04351622 -0.04227693 -0.04193894 0.95676543 -0.0351228031
## [15,] -0.03394726 -0.03911965 -0.04053031 -0.03512280 0.9310215194
## [16,] -0.03268469 -0.03870307 -0.04034445 -0.03405250 -0.0734455492
## [17,] -0.03707046 -0.04015015 -0.04099007 -0.03777039 -0.0579283636
## [18,] -0.03560854 -0.03966779 -0.04077486 -0.03653110 -0.0631007588
## [19,] -0.03740272 -0.04025978 -0.04103898 -0.03805205 -0.0567528193
## [20,] -0.02896342 -0.03747524 -0.03979665 -0.03089793 -0.0866116460
## [21,] -0.02570732 -0.03640089 -0.03931732 -0.02813767 -0.0981319807
## [22,] -0.03069115 -0.03804530 -0.04005098 -0.03236255 -0.0804988153
## [23,] -0.02883052 -0.03743139 -0.03977708 -0.03078526 -0.0870818638
## [24,] -0.02736860 -0.03694903 -0.03956187 -0.02954597 -0.0922542589
## [,16] [,17] [,18] [,19] [,20]
## [1,] 0.0187451258 -0.010753111 -0.0009203652 -0.01298783 0.043773933
## [2,] 0.0004164159 -0.020132167 -0.0132826393 -0.02168888 0.017851577
## [3,] 0.0130003063 -0.013692815 -0.0047951078 -0.01571502 0.035649015
## [4,] 0.0223014426 -0.008933294 0.0014782850 -0.01129956 0.048803643
## [5,] 0.0069819239 -0.016772505 -0.0088543620 -0.01857208 0.027137197
## [6,] -0.0244778019 -0.032870885 -0.0300731907 -0.03350672 -0.017356398
## [7,] -0.0157237913 -0.028391336 -0.0241688210 -0.02935100 -0.004975572
## [8,] -0.0045077151 -0.022651913 -0.0166038473 -0.02402647 0.010887362
## [9,] -0.0220157364 -0.031611012 -0.0284125867 -0.03233793 -0.013874291
## [10,] -0.0272134303 -0.034270744 -0.0319183062 -0.03480539 -0.021225406
## [11,] -0.0326846870 -0.037070462 -0.0356085373 -0.03740272 -0.028963423
## [12,] -0.0387030693 -0.040150153 -0.0396677915 -0.04025978 -0.037475241
## [13,] -0.0403444463 -0.040990068 -0.0407748608 -0.04103898 -0.039796646
## [14,] -0.0340525011 -0.037770392 -0.0365310951 -0.03805205 -0.030897927
## [15,] -0.0734455492 -0.057928364 -0.0631007588 -0.05675282 -0.086611646
## [16,] 0.9213567570 -0.060588096 -0.0666064783 -0.05922028 -0.093962762
## [17,] -0.0605880960 0.948650974 -0.0544287158 -0.05064910 -0.068427307
## [18,] -0.0666064783 -0.054428716 0.9415120300 -0.05350616 -0.076939125
## [19,] -0.0592202818 -0.050649096 -0.0535061580 0.95000024 -0.066492803
## [20,] -0.0939627617 -0.068427307 -0.0769391254 -0.06649280 0.884370792
## [21,] -0.1073673406 -0.075286617 -0.0859801915 -0.07285626 -0.134587349
## [22,] -0.0868501280 -0.064787673 -0.0721418250 -0.06311628 -0.105569787
## [23,] -0.0945098874 -0.068707279 -0.0773081485 -0.06675254 -0.116403010
## [24,] -0.1005282697 -0.071786969 -0.0813674026 -0.06960960 -0.124914828
## [,21] [,22] [,23] [,24]
## [1,] 0.065674138 0.032153415 0.044667818 0.0545005640
## [2,] 0.033107343 0.009756681 0.018474261 0.0253237891
## [3,] 0.055466635 0.025133543 0.036457898 0.0453556047
## [4,] 0.071993069 0.036499050 0.049750150 0.0601617293
## [5,] 0.044773061 0.017779392 0.027857028 0.0357751712
## [6,] -0.011125170 -0.020662764 -0.017102062 -0.0143043678
## [7,] 0.004429121 -0.009965816 -0.004591707 -0.0003691918
## [8,] 0.024358055 0.003739648 0.011437186 0.0174852526
## [9,] -0.006750526 -0.017654248 -0.013583525 -0.0103850996
## [10,] -0.015985885 -0.024005560 -0.021011548 -0.0186591104
## [11,] -0.025707317 -0.030691153 -0.028830521 -0.0273685954
## [12,] -0.036400891 -0.038045304 -0.037431390 -0.0369490289
## [13,] -0.039317321 -0.040050982 -0.039777082 -0.0395618744
## [14,] -0.028137675 -0.032362551 -0.030785264 -0.0295459667
## [15,] -0.098131981 -0.080498815 -0.087081864 -0.0922542589
## [16,] -0.107367341 -0.086850128 -0.094509887 -0.1005282697
## [17,] -0.075286617 -0.064787673 -0.068707279 -0.0717869691
## [18,] -0.085980191 -0.072141825 -0.077308148 -0.0813674026
## [19,] -0.072856259 -0.063116275 -0.066752536 -0.0696095978
## [20,] -0.134587349 -0.105569787 -0.116403010 -0.1249148278
## [21,] 0.841595145 -0.121949488 -0.135559492 -0.1462530662
## [22,] -0.121949488 0.903121483 -0.106238346 -0.1135924973
## [23,] -0.135559492 -0.106238346 0.882815093 -0.1257857764
## [24,] -0.146253066 -0.113592497 -0.125785776 0.8646337901
Residuos del modelo
Ygorro<- matrizX %*% Beta
Residuos<- matrizY - Ygorro
print(Residuos)
## matrizY
## [1,] -0.50716765
## [2,] 0.50270510
## [3,] -0.03093888
## [4,] 1.27897644
## [5,] -0.98441350
## [6,] 0.19969645
## [7,] -0.04979501
## [8,] 0.36804405
## [9,] -1.83297302
## [10,] -0.99733747
## [11,] 0.30859470
## [12,] 0.05512008
## [13,] 0.57689973
## [14,] 0.46007774
## [15,] -0.11721068
## [16,] -0.08157512
## [17,] -0.22115126
## [18,] 0.32537412
## [19,] 0.72736569
## [20,] 0.15503494
## [21,] -0.90043126
## [22,] 1.02732313
## [23,] -0.90437184
## [24,] 0.64215354
Aplicando Pruebas de normalidad
Jarque Bera
library(normtest)
jb.norm.test(Residuos)
##
## Jarque-Bera test for normality
##
## data: Residuos
## JB = 1.5606, p-value = 0.2385
#El P value es mayor al 5%, no rechazamos la hipotesis nula y concluimos que los residuos tienen una districucion normal
Kolmogorov-Smirnov
library(nortest)
lillie.test(Residuos)
##
## Lilliefors (Kolmogorov-Smirnov) normality test
##
## data: Residuos
## D = 0.14418, p-value = 0.2209
#El P value es mayor al 5%, no rechazamos la hipotesis nula y concluimos que los residuos tienen una distribucion normal.
Shapiro-Wilk
shapiro.test(Residuos)
##
## Shapiro-Wilk normality test
##
## data: Residuos
## W = 0.95746, p-value = 0.3895
#El P value es mayot al 5%, no rechazamos la hipotesis nula y concluimos que los residuos tienen una distribucion normal.
EJERCICIO 2: matriz de correlacion de los regresores:
R<-matrix(data = c(1,-0.8,0.68,0.74,-0.57,-0.75,-0.8,1,-0.71,-0.87,
0.69,0.80,0.68,-0.71,1,0.81,-0.77,-0.82,0.74,-0.87,
0.81,1,-0.8,-0.84,-0.57,0.69,-0.77,-0.80,1,0.64,-0.75,
0.8,-0.82,-0.84,0.64,1),
nrow = 6,
ncol = 6,
byrow = TRUE)
colnames(R)<-c("porcentajeprn","porcentajepac","rezago","nini","educ_superior","ips")
rownames(R)<-c("porcentajeprn","porcentajepac","rezago","nini","educ_superior","ips")
print(R)
## porcentajeprn porcentajepac rezago nini educ_superior ips
## porcentajeprn 1.00 -0.80 0.68 0.74 -0.57 -0.75
## porcentajepac -0.80 1.00 -0.71 -0.87 0.69 0.80
## rezago 0.68 -0.71 1.00 0.81 -0.77 -0.82
## nini 0.74 -0.87 0.81 1.00 -0.80 -0.84
## educ_superior -0.57 0.69 -0.77 -0.80 1.00 0.64
## ips -0.75 0.80 -0.82 -0.84 0.64 1.00
Calcular \(|R|\)
determinante_R<-det(R)
print(determinante_R)
## [1] 0.001684439
Aplicando la prueba de Farrer Glaubar (Bartlett)
Estadistico \(X^2_{FG}\)
m<-ncol(R)
n<-nrow(R)
chi_FG<--(n-1-(2*m+5)/6)*log(determinante_R)
print(chi_FG)
## [1] 13.83703
Valor critico.
gl<-m*(m-1)/2
VC<-qchisq(p = 0.95,df = gl)
print(VC)
## [1] 24.99579
como el valor de Farrer Glaubar es menor que el valor critico, no se rechaza Ho, por lo tanto no hay colinealidad en los regresores.
Cálculando VIF’s para el modelo estimado
##Inversa: matriz de correlación $R^{-1}$:
options(scipen = 999)
inversa_R<-solve(R)
print(inversa_R)
## porcentajeprn porcentajepac rezago nini
## porcentajeprn 3.12989194 1.8066302 -0.5430948 0.01312674
## porcentajepac 1.80663016 5.5207504 -0.8728955 3.04065276
## rezago -0.54309484 -0.8728955 4.6100427 -0.68684569
## nini 0.01312674 3.0406528 -0.6868457 7.70048852
## educ_superior -0.28728369 -0.4001754 1.7897206 2.22245739
## ips 0.65166508 -0.9671414 2.3488587 2.06014702
## educ_superior ips
## porcentajeprn -0.2872837 0.6516651
## porcentajepac -0.4001754 -0.9671414
## rezago 1.7897206 2.3488587
## nini 2.2224574 2.0601470
## educ_superior 3.5016734 1.1980416
## ips 1.1980416 5.1523030
VIF’s para el modelo estimado:
VIFs<-diag(inversa_R)
print(VIFs)
## porcentajeprn porcentajepac rezago nini educ_superior
## 3.129892 5.520750 4.610043 7.700489 3.501673
## ips
## 5.152303
si tomamos en cuenta que a partir de 2 las variables representan un grando de colinealidad, significa en este caso que todas las variables poseen colinealidad.