Ejemplo de regresion lineal multiple
Mayra Gil
2025-03-11
Carga de datos
#Archivo CSV
library(readr)
ejemplo_regresion <- read_csv("E:/Archivos para importar/ejemplo_regresion.csv")
head(ejemplo_regresion,n=5)## # A tibble: 5 × 3
## X1 X2 Y
## <dbl> <dbl> <dbl>
## 1 3.92 7298 0.75
## 2 3.61 6855 0.71
## 3 3.32 6636 0.66
## 4 3.07 6506 0.61
## 5 3.06 6450 0.7#Archivo Excel
library(readxl)
ejemplo_regresion <- read_excel("E:/Archivos para importar/ejemplo_regresion.xlsx",
col_types = c("numeric", "numeric", "numeric"))Ejemplo de regresion lineal
library(stargazer)
Modelo_lineal <- lm(formula = Y~X1 + X2, data = ejemplo_regresion)
#Usando summary
summary(Modelo_lineal)Call: lm(formula = Y ~ X1 + X2, data = ejemplo_regresion)
Residuals: Min 1Q Median 3Q Max -0.111071 -0.044467 -0.001806 0.060543 0.104058
Coefficients: Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.576e+00 1.023e-01 15.412 2.84e-13 X1
-1.269e-06 7.428e-07 -1.708 0.102
X2 -1.229e-04 1.386e-05 -8.866 1.03e-08 — Signif. codes:
0 ‘’ 0.001 ’’ 0.01 ’’ 0.05 ‘.’ 0.1 ’ ’ 1
Residual standard error: 0.06773 on 22 degrees of freedom Multiple R-squared: 0.7825, Adjusted R-squared: 0.7628 F-statistic: 39.58 on 2 and 22 DF, p-value: 5.144e-08
#Usando stargazer
stargazer(Modelo_lineal,title = "Ejemplo de Regresion Multiple",type = "html",digits = 8)| Dependent variable: | |
| Y | |
| X1 | -0.00000127 |
| (0.00000074) | |
| X2 | -0.00012289*** |
| (0.00001386) | |
| Constant | 1.57619400*** |
| (0.10227100) | |
| Observations | 25 |
| R2 | 0.78253320 |
| Adjusted R2 | 0.76276350 |
| Residual Std. Error | 0.06772541 (df = 22) |
| F Statistic | 39.58243000*** (df = 2; 22) |
| Note: | p<0.1; p<0.05; p<0.01 |
Objetos dentro del modelo lineal
Vector de coeficientes estimados
options(scipen = 999999)
Modelo_lineal$coefficients## (Intercept) X1 X2
## 1.576193987405 -0.000001268749 -0.000122892962Matriz de varianza-covarianza delos parametros
var_covar <- vcov(Modelo_lineal)
print(var_covar)## (Intercept) X1 X2
## (Intercept) 0.01045935002566 -0.0000000131410842007 -0.000001402024153188
## X1 -0.00000001314108 0.0000000000005517899 0.000000000001115281
## X2 -0.00000140202415 0.0000000000011152812 0.000000000192148255Intervalos de confianza
confint(object = Modelo_lineal,level = .95)## 2.5 % 97.5 %
## (Intercept) 1.364096990062 1.7882909847476
## X1 -0.000002809275 0.0000002717773
## X2 -0.000151640483 -0.0000941454413Valores ajustado Y
library(magrittr)## Warning: package 'magrittr' was built under R version 4.4.3plot(Modelo_lineal$fitted.values,main = "valores ajustados",ylab = "Y", xlab ="casos")
Modelo_lineal$fitted.values %>% as.matrix()## [,1]
## 1 0.6793162
## 2 0.7337582
## 3 0.7606721
## 4 0.7184917
## 5 0.7254117
## 6 0.7311165
## 7 0.7936075
## 8 0.7970485
## 9 0.7959422
## 10 0.7955736
## 11 0.7944675
## 12 0.7934842
## 13 0.7717320
## 14 0.7562473
## 15 0.7294566
## 16 0.7018055
## 17 0.6175953
## 18 0.6488383
## 19 0.6015243
## 20 0.5811240
## 21 0.4773744
## 22 0.5049302
## 23 0.4712574
## 24 0.4481535
## 25 0.4310713Residuos del modelo E
library(magrittr)
plot(Modelo_lineal$residuals,main = "Residuos",ylab = "Residuos",xlab = "casos")
Modelo_lineal$residuals %>% matrix() ## [,1]
## [1,] 0.070683822
## [2,] -0.023758153
## [3,] -0.100672080
## [4,] -0.108491668
## [5,] -0.025411736
## [6,] -0.011116480
## [7,] -0.023607533
## [8,] -0.057048473
## [9,] 0.104057767
## [10,] 0.024426446
## [11,] -0.044467479
## [12,] -0.023484171
## [13,] 0.008267985
## [14,] 0.083752651
## [15,] 0.060543367
## [16,] -0.001805526
## [17,] 0.062404723
## [18,] 0.071161696
## [19,] -0.051524311
## [20,] 0.048876022
## [21,] 0.082625592
## [22,] -0.094930227
## [23,] 0.038742584
## [24,] 0.021846486
## [25,] -0.111071303Matrices A,P & M
#Matriz X
matriz_X <- model.matrix(Modelo_lineal)
#Matriz XX
matriz_XX <- t(matriz_X) %*% matriz_X
print(matriz_XX)## (Intercept) X1 X2
## (Intercept) 25.0 229378.3 181083
## X1 229378.3 10515712538.2 1612640105
## X2 181083.0 1612640105.2 1335796275#Matriz A
matriz_A <- solve(matriz_XX) %*% t(matriz_X)
print(matriz_A)## 1 2 3 4
## (Intercept) 0.04956171280968 0.184974227481 0.251916697630 0.160327791267
## X1 -0.00000109001358 -0.000001197768 -0.000001251054 0.000004231671
## X2 0.00000006064994 -0.000018497670 -0.000027672133 -0.000021972512
## 5 6 7 8
## (Intercept) 0.177531238726 0.19176503051 0.333836461779 0.342395066931
## X1 0.000004214445 0.00000422118 -0.000001316232 -0.000001323034
## X2 -0.000024325770 -0.00002629939 -0.000038899270 -0.000040072239
## 9 10 11 12
## (Intercept) 0.339643582255 0.338726573498 0.335975461275 0.333529732135
## X1 -0.000001320827 -0.000001320097 -0.000001317905 -0.000001315944
## X2 -0.000039695170 -0.000039569494 -0.000039192457 -0.000038857287
## 13 14 15 16
## (Intercept) 0.279425986245 0.240911274630 0.174275190323 0.105499103762
## X1 -0.000001272897 -0.000001242245 -0.000001189232 -0.000001134505
## X2 -0.000031442348 -0.000026163902 -0.000017031392 -0.000007605611
## 17 18 19 20
## (Intercept) -0.09062980371 -0.026245289929 -0.1439285388693 -0.1946699193157
## X1 0.00000443142 -0.000001029672 -0.0000009360383 -0.0000008956651
## X2 0.00001242123 0.000010449996 0.0000265785323 0.0000335326571
## 21 22 23 24
## (Intercept) -0.439398801116 -0.3841853203704 -0.4679391020350 -0.5254050414679
## X1 0.000004708859 -0.0000007448989 -0.0000006782615 -0.0000006325462
## X2 0.000060220230 0.0000595058436 0.0000709843334 0.0000788600720
## 25
## (Intercept) -0.5678933144472
## X1 -0.0000005987394
## X2 0.0000846831050#Matriz_P
matriz_P <- matriz_X %*% matriz_A
print(matriz_P)## 1 2 3 4 5
## 1 0.05000006325 0.049973533 0.049960567 -0.00001101108 0.00001829293
## 2 0.04997353323 0.058168373 0.062219710 0.00972149979 0.01079330238
## 3 0.04996056700 0.062219710 0.068280270 0.01453225267 0.01611942373
## 4 -0.00001101108 0.009721500 0.014532253 0.21135864640 0.21246215694
## 5 0.00001829293 0.010793302 0.016119424 0.21246215694 0.21369796668
## 6 -0.00015139035 0.011497932 0.017256275 0.21416428311 0.21551041371
## 7 0.04994443272 0.067177217 0.075696539 0.02042042033 0.02263826639
## 8 0.04994268002 0.067695092 0.076471296 0.02103586224 0.02331959866
## 9 0.04994305146 0.067528421 0.076222047 0.02083878670 0.02310134104
## 10 0.04994323341 0.067472928 0.076139030 0.02077286917 0.02302836373
## 11 0.04994374656 0.067306413 0.075889944 0.02057524351 0.02280955824
## 12 0.04994409006 0.067158276 0.075668404 0.02040001353 0.02261549996
## 13 0.04995473790 0.063884093 0.070770336 0.01651121749 0.01831017590
## 14 0.04996224899 0.061553243 0.067283497 0.01374318882 0.01524563467
## 15 0.04997542708 0.057520703 0.061250922 0.00895335053 0.00994278547
## 16 0.04998890981 0.053358547 0.055024505 0.00401017015 0.00447011949
## 17 0.00003769251 -0.005466285 -0.008187820 0.19332344595 0.19249491455
## 18 0.05001474474 0.045385716 0.043097465 -0.00545879754 -0.00601310716
## 19 0.05003792056 0.038263921 0.032443494 -0.01391753748 -0.01537785414
## 20 0.05004790125 0.035193212 0.027849820 -0.01756463589 -0.01941559473
## 21 0.00010689410 -0.026572127 -0.039761723 0.16825281009 0.16473921146
## 22 0.05008540612 0.023724548 0.010692985 -0.03118721230 -0.03449719258
## 23 0.05010190430 0.018656055 0.003110683 -0.03720721503 -0.04116198985
## 24 0.05011328469 0.015178469 -0.002091703 -0.04133796260 -0.04573515025
## 25 0.05012163873 0.012607209 -0.005938218 -0.04439184551 -0.04911613721
## 6 7 8 9 10 11
## 1 -0.0001513903 0.04994443 0.04994268 0.049943051 0.049943233 0.049943747
## 2 0.0114979321 0.06717722 0.06769509 0.067528421 0.067472928 0.067306413
## 3 0.0172562749 0.07569654 0.07647130 0.076222047 0.076139030 0.075889944
## 4 0.2141642831 0.02042042 0.02103586 0.020838787 0.020772869 0.020575244
## 5 0.2155104137 0.02263827 0.02331960 0.023101341 0.023028364 0.022809558
## 6 0.2174186251 0.02430405 0.02504064 0.024804623 0.024725725 0.024489157
## 7 0.0243040478 0.08612169 0.08721080 0.086860498 0.086743800 0.086393667
## 8 0.0250406419 0.08721080 0.08833276 0.087971896 0.087851680 0.087490990
## 9 0.0248046227 0.08686050 0.08797190 0.087614429 0.087495343 0.087138047
## 10 0.0247257246 0.08674380 0.08785168 0.087495343 0.087376635 0.087020469
## 11 0.0244891567 0.08639367 0.08749099 0.087138047 0.087020469 0.086667698
## 12 0.0242793103 0.08608230 0.08717024 0.086820314 0.086703742 0.086353987
## 13 0.0196246555 0.07919703 0.08007735 0.079794163 0.079699836 0.079416817
## 14 0.0163114385 0.07429556 0.07502809 0.074792413 0.074713921 0.074478409
## 15 0.0105783398 0.06581547 0.06629229 0.066138813 0.066087719 0.065934401
## 16 0.0046616096 0.05706293 0.05727583 0.057207202 0.057184385 0.057115900
## 17 0.1925767029 -0.01151720 -0.01186477 -0.011752269 -0.011715005 -0.011603081
## 18 -0.0066722467 0.04029698 0.04000433 0.040098213 0.040129563 0.040223582
## 19 -0.0167968375 0.02532055 0.02457630 0.024815361 0.024895097 0.025134276
## 20 -0.0211621990 0.01886317 0.01792421 0.018225857 0.018326455 0.018628223
## 21 0.1625690958 -0.05590126 -0.05758719 -0.057044458 -0.056863798 -0.056321674
## 22 -0.0374674426 -0.00525450 -0.00692070 -0.006385267 -0.006206749 -0.005671219
## 23 -0.0446730119 -0.01591304 -0.01790064 -0.017261889 -0.017048936 -0.016410097
## 24 -0.0496172133 -0.02322613 -0.02543425 -0.024724607 -0.024488027 -0.023778306
## 25 -0.0532725334 -0.02863322 -0.03100438 -0.030242329 -0.029988279 -0.029226149
## 12 13 14 15 16
## 1 0.049944090 0.049954738 0.0499622490 0.049975427 0.049988910
## 2 0.067158276 0.063884093 0.0615532426 0.057520703 0.053358547
## 3 0.075668404 0.070770336 0.0672834974 0.061250922 0.055024505
## 4 0.020400014 0.016511217 0.0137431888 0.008953351 0.004010170
## 5 0.022615500 0.018310176 0.0152456347 0.009942785 0.004470119
## 6 0.024279310 0.019624655 0.0163114385 0.010578340 0.004661610
## 7 0.086082302 0.079197026 0.0742955597 0.065815466 0.057062933
## 8 0.087170240 0.080077348 0.0750280869 0.066292286 0.057275834
## 9 0.086820314 0.079794163 0.0747924130 0.066138813 0.057207202
## 10 0.086703742 0.079699836 0.0747139213 0.066087719 0.057184385
## 11 0.086353987 0.079416817 0.0744784089 0.065934401 0.057115900
## 12 0.086042957 0.079165112 0.0742689362 0.065797995 0.057054908
## 13 0.079165112 0.073599715 0.0696378262 0.062783343 0.055708624
## 14 0.074268936 0.069637826 0.0663410255 0.060637245 0.054750181
## 15 0.065797995 0.062783343 0.0606372452 0.056924354 0.053092112
## 16 0.057054908 0.055708624 0.0547501809 0.053092112 0.051380680
## 17 -0.011503135 -0.009304223 -0.0077386169 -0.005030612 -0.002235171
## 18 0.040307049 0.042156615 0.0434731914 0.045751249 0.048102344
## 19 0.025346782 0.030051108 0.0333998904 0.039193973 0.045174002
## 20 0.018896367 0.024831576 0.0290565833 0.036366667 0.043911380
## 21 -0.055839300 -0.045179943 -0.0375916289 -0.024463431 -0.010913172
## 22 -0.005195269 0.005337205 0.0128348523 0.025807096 0.039195799
## 23 -0.015842311 -0.003278138 0.0056658066 0.021140364 0.037111737
## 24 -0.023147507 -0.009189325 0.0007469682 0.017938439 0.035681860
## 25 -0.028548762 -0.013559901 -0.0028899012 0.015570992 0.034624601
## 17 18 19 20 21
## 1 0.00003769251 0.050014745 0.050037921 0.05004790 0.0001068941
## 2 -0.00546628542 0.045385716 0.038263921 0.03519321 -0.0265721274
## 3 -0.00818781956 0.043097465 0.032443494 0.02784982 -0.0397617233
## 4 0.19332344595 -0.005458798 -0.013917537 -0.01756464 0.1682528101
## 5 0.19249491455 -0.006013107 -0.015377854 -0.01941559 0.1647392115
## 6 0.19257670289 -0.006672247 -0.016796838 -0.02116220 0.1625690958
## 7 -0.01151719623 0.040296980 0.025320550 0.01886317 -0.0559012628
## 8 -0.01186476906 0.040004328 0.024576304 0.01792421 -0.0575871938
## 9 -0.01175226898 0.040098213 0.024815361 0.01822586 -0.0570444583
## 10 -0.01171500529 0.040129563 0.024895097 0.01832646 -0.0568637976
## 11 -0.01160308129 0.040223582 0.025134276 0.01862822 -0.0563216743
## 12 -0.01150313538 0.040307049 0.025346782 0.01889637 -0.0558393003
## 13 -0.00930422344 0.042156615 0.030051108 0.02483158 -0.0451799430
## 14 -0.00773861688 0.043473191 0.033399890 0.02905658 -0.0375916289
## 15 -0.00503061183 0.045751249 0.039193973 0.03636667 -0.0244634305
## 16 -0.00223517072 0.048102344 0.045174002 0.04391138 -0.0109131725
## 17 0.20352570591 0.003119620 0.007902501 0.00996478 0.2176983275
## 18 0.00311961953 0.052606004 0.056629088 0.05836370 0.0150430650
## 19 0.00790250150 0.056629088 0.066861673 0.07127363 0.0382286068
## 20 0.00996477993 0.058363705 0.071273634 0.07683998 0.0482255417
## 21 0.21769832754 0.015043065 0.038228607 0.04822554 0.2864096097
## 22 0.01766634038 0.064842610 0.087752240 0.09763015 0.0855625079
## 23 0.02107024443 0.067705795 0.095034655 0.10681800 0.1020633688
## 24 0.02340552400 0.069670374 0.100031400 0.11312212 0.1133848662
## 25 0.02513238495 0.071122851 0.103725751 0.11778310 0.1217558077
## 22 23 24 25
## 1 0.050085406 0.050101904 0.0501132847 0.050121639
## 2 0.023724548 0.018656055 0.0151784689 0.012607209
## 3 0.010692985 0.003110683 -0.0020917035 -0.005938218
## 4 -0.031187212 -0.037207215 -0.0413379626 -0.044391846
## 5 -0.034497193 -0.041161990 -0.0457351502 -0.049116137
## 6 -0.037467443 -0.044673012 -0.0496172133 -0.053272533
## 7 -0.005254500 -0.015913044 -0.0232261332 -0.028633224
## 8 -0.006920700 -0.017900639 -0.0254342468 -0.031004381
## 9 -0.006385267 -0.017261889 -0.0247246074 -0.030242329
## 10 -0.006206749 -0.017048936 -0.0244880272 -0.029988279
## 11 -0.005671219 -0.016410097 -0.0237783055 -0.029226149
## 12 -0.005195269 -0.015842311 -0.0231475072 -0.028548762
## 13 0.005337205 -0.003278138 -0.0091893250 -0.013559901
## 14 0.012834852 0.005665807 0.0007469682 -0.002889901
## 15 0.025807096 0.021140364 0.0179384386 0.015570992
## 16 0.039195799 0.037111737 0.0356818599 0.034624601
## 17 0.017666340 0.021070244 0.0234055240 0.025132385
## 18 0.064842610 0.067705795 0.0696703738 0.071122851
## 19 0.087752240 0.095034655 0.1000314003 0.103725751
## 20 0.097630151 0.106818000 0.1131221217 0.117783098
## 21 0.085562508 0.102063369 0.1133848662 0.121755808
## 22 0.134523707 0.150828226 0.1620153094 0.170286570
## 23 0.150828226 0.170277858 0.1836228996 0.193489674
## 24 0.162015309 0.183622900 0.1984485805 0.209410086
## 25 0.170286570 0.193489674 0.2094100862 0.221180996#Matriz M
matriz_M <- diag(25) - matriz_P
print(matriz_M)## 1 2 3 4 5
## 1 0.94999993675 -0.049973533 -0.049960567 0.00001101108 -0.00001829293
## 2 -0.04997353323 0.941831627 -0.062219710 -0.00972149979 -0.01079330238
## 3 -0.04996056700 -0.062219710 0.931719730 -0.01453225267 -0.01611942373
## 4 0.00001101108 -0.009721500 -0.014532253 0.78864135360 -0.21246215694
## 5 -0.00001829293 -0.010793302 -0.016119424 -0.21246215694 0.78630203332
## 6 0.00015139035 -0.011497932 -0.017256275 -0.21416428311 -0.21551041371
## 7 -0.04994443272 -0.067177217 -0.075696539 -0.02042042033 -0.02263826639
## 8 -0.04994268002 -0.067695092 -0.076471296 -0.02103586224 -0.02331959866
## 9 -0.04994305146 -0.067528421 -0.076222047 -0.02083878670 -0.02310134104
## 10 -0.04994323341 -0.067472928 -0.076139030 -0.02077286917 -0.02302836373
## 11 -0.04994374656 -0.067306413 -0.075889944 -0.02057524351 -0.02280955824
## 12 -0.04994409006 -0.067158276 -0.075668404 -0.02040001353 -0.02261549996
## 13 -0.04995473790 -0.063884093 -0.070770336 -0.01651121749 -0.01831017590
## 14 -0.04996224899 -0.061553243 -0.067283497 -0.01374318882 -0.01524563467
## 15 -0.04997542708 -0.057520703 -0.061250922 -0.00895335053 -0.00994278547
## 16 -0.04998890981 -0.053358547 -0.055024505 -0.00401017015 -0.00447011949
## 17 -0.00003769251 0.005466285 0.008187820 -0.19332344595 -0.19249491455
## 18 -0.05001474474 -0.045385716 -0.043097465 0.00545879754 0.00601310716
## 19 -0.05003792056 -0.038263921 -0.032443494 0.01391753748 0.01537785414
## 20 -0.05004790125 -0.035193212 -0.027849820 0.01756463589 0.01941559473
## 21 -0.00010689410 0.026572127 0.039761723 -0.16825281009 -0.16473921146
## 22 -0.05008540612 -0.023724548 -0.010692985 0.03118721230 0.03449719258
## 23 -0.05010190430 -0.018656055 -0.003110683 0.03720721503 0.04116198985
## 24 -0.05011328469 -0.015178469 0.002091703 0.04133796260 0.04573515025
## 25 -0.05012163873 -0.012607209 0.005938218 0.04439184551 0.04911613721
## 6 7 8 9 10 11
## 1 0.0001513903 -0.04994443 -0.04994268 -0.049943051 -0.049943233 -0.049943747
## 2 -0.0114979321 -0.06717722 -0.06769509 -0.067528421 -0.067472928 -0.067306413
## 3 -0.0172562749 -0.07569654 -0.07647130 -0.076222047 -0.076139030 -0.075889944
## 4 -0.2141642831 -0.02042042 -0.02103586 -0.020838787 -0.020772869 -0.020575244
## 5 -0.2155104137 -0.02263827 -0.02331960 -0.023101341 -0.023028364 -0.022809558
## 6 0.7825813749 -0.02430405 -0.02504064 -0.024804623 -0.024725725 -0.024489157
## 7 -0.0243040478 0.91387831 -0.08721080 -0.086860498 -0.086743800 -0.086393667
## 8 -0.0250406419 -0.08721080 0.91166724 -0.087971896 -0.087851680 -0.087490990
## 9 -0.0248046227 -0.08686050 -0.08797190 0.912385571 -0.087495343 -0.087138047
## 10 -0.0247257246 -0.08674380 -0.08785168 -0.087495343 0.912623365 -0.087020469
## 11 -0.0244891567 -0.08639367 -0.08749099 -0.087138047 -0.087020469 0.913332302
## 12 -0.0242793103 -0.08608230 -0.08717024 -0.086820314 -0.086703742 -0.086353987
## 13 -0.0196246555 -0.07919703 -0.08007735 -0.079794163 -0.079699836 -0.079416817
## 14 -0.0163114385 -0.07429556 -0.07502809 -0.074792413 -0.074713921 -0.074478409
## 15 -0.0105783398 -0.06581547 -0.06629229 -0.066138813 -0.066087719 -0.065934401
## 16 -0.0046616096 -0.05706293 -0.05727583 -0.057207202 -0.057184385 -0.057115900
## 17 -0.1925767029 0.01151720 0.01186477 0.011752269 0.011715005 0.011603081
## 18 0.0066722467 -0.04029698 -0.04000433 -0.040098213 -0.040129563 -0.040223582
## 19 0.0167968375 -0.02532055 -0.02457630 -0.024815361 -0.024895097 -0.025134276
## 20 0.0211621990 -0.01886317 -0.01792421 -0.018225857 -0.018326455 -0.018628223
## 21 -0.1625690958 0.05590126 0.05758719 0.057044458 0.056863798 0.056321674
## 22 0.0374674426 0.00525450 0.00692070 0.006385267 0.006206749 0.005671219
## 23 0.0446730119 0.01591304 0.01790064 0.017261889 0.017048936 0.016410097
## 24 0.0496172133 0.02322613 0.02543425 0.024724607 0.024488027 0.023778306
## 25 0.0532725334 0.02863322 0.03100438 0.030242329 0.029988279 0.029226149
## 12 13 14 15 16
## 1 -0.049944090 -0.049954738 -0.0499622490 -0.049975427 -0.049988910
## 2 -0.067158276 -0.063884093 -0.0615532426 -0.057520703 -0.053358547
## 3 -0.075668404 -0.070770336 -0.0672834974 -0.061250922 -0.055024505
## 4 -0.020400014 -0.016511217 -0.0137431888 -0.008953351 -0.004010170
## 5 -0.022615500 -0.018310176 -0.0152456347 -0.009942785 -0.004470119
## 6 -0.024279310 -0.019624655 -0.0163114385 -0.010578340 -0.004661610
## 7 -0.086082302 -0.079197026 -0.0742955597 -0.065815466 -0.057062933
## 8 -0.087170240 -0.080077348 -0.0750280869 -0.066292286 -0.057275834
## 9 -0.086820314 -0.079794163 -0.0747924130 -0.066138813 -0.057207202
## 10 -0.086703742 -0.079699836 -0.0747139213 -0.066087719 -0.057184385
## 11 -0.086353987 -0.079416817 -0.0744784089 -0.065934401 -0.057115900
## 12 0.913957043 -0.079165112 -0.0742689362 -0.065797995 -0.057054908
## 13 -0.079165112 0.926400285 -0.0696378262 -0.062783343 -0.055708624
## 14 -0.074268936 -0.069637826 0.9336589745 -0.060637245 -0.054750181
## 15 -0.065797995 -0.062783343 -0.0606372452 0.943075646 -0.053092112
## 16 -0.057054908 -0.055708624 -0.0547501809 -0.053092112 0.948619320
## 17 0.011503135 0.009304223 0.0077386169 0.005030612 0.002235171
## 18 -0.040307049 -0.042156615 -0.0434731914 -0.045751249 -0.048102344
## 19 -0.025346782 -0.030051108 -0.0333998904 -0.039193973 -0.045174002
## 20 -0.018896367 -0.024831576 -0.0290565833 -0.036366667 -0.043911380
## 21 0.055839300 0.045179943 0.0375916289 0.024463431 0.010913172
## 22 0.005195269 -0.005337205 -0.0128348523 -0.025807096 -0.039195799
## 23 0.015842311 0.003278138 -0.0056658066 -0.021140364 -0.037111737
## 24 0.023147507 0.009189325 -0.0007469682 -0.017938439 -0.035681860
## 25 0.028548762 0.013559901 0.0028899012 -0.015570992 -0.034624601
## 17 18 19 20 21
## 1 -0.00003769251 -0.050014745 -0.050037921 -0.05004790 -0.0001068941
## 2 0.00546628542 -0.045385716 -0.038263921 -0.03519321 0.0265721274
## 3 0.00818781956 -0.043097465 -0.032443494 -0.02784982 0.0397617233
## 4 -0.19332344595 0.005458798 0.013917537 0.01756464 -0.1682528101
## 5 -0.19249491455 0.006013107 0.015377854 0.01941559 -0.1647392115
## 6 -0.19257670289 0.006672247 0.016796838 0.02116220 -0.1625690958
## 7 0.01151719623 -0.040296980 -0.025320550 -0.01886317 0.0559012628
## 8 0.01186476906 -0.040004328 -0.024576304 -0.01792421 0.0575871938
## 9 0.01175226898 -0.040098213 -0.024815361 -0.01822586 0.0570444583
## 10 0.01171500529 -0.040129563 -0.024895097 -0.01832646 0.0568637976
## 11 0.01160308129 -0.040223582 -0.025134276 -0.01862822 0.0563216743
## 12 0.01150313538 -0.040307049 -0.025346782 -0.01889637 0.0558393003
## 13 0.00930422344 -0.042156615 -0.030051108 -0.02483158 0.0451799430
## 14 0.00773861688 -0.043473191 -0.033399890 -0.02905658 0.0375916289
## 15 0.00503061183 -0.045751249 -0.039193973 -0.03636667 0.0244634305
## 16 0.00223517072 -0.048102344 -0.045174002 -0.04391138 0.0109131725
## 17 0.79647429409 -0.003119620 -0.007902501 -0.00996478 -0.2176983275
## 18 -0.00311961953 0.947393996 -0.056629088 -0.05836370 -0.0150430650
## 19 -0.00790250150 -0.056629088 0.933138327 -0.07127363 -0.0382286068
## 20 -0.00996477993 -0.058363705 -0.071273634 0.92316002 -0.0482255417
## 21 -0.21769832754 -0.015043065 -0.038228607 -0.04822554 0.7135903903
## 22 -0.01766634038 -0.064842610 -0.087752240 -0.09763015 -0.0855625079
## 23 -0.02107024443 -0.067705795 -0.095034655 -0.10681800 -0.1020633688
## 24 -0.02340552400 -0.069670374 -0.100031400 -0.11312212 -0.1133848662
## 25 -0.02513238495 -0.071122851 -0.103725751 -0.11778310 -0.1217558077
## 22 23 24 25
## 1 -0.050085406 -0.050101904 -0.0501132847 -0.050121639
## 2 -0.023724548 -0.018656055 -0.0151784689 -0.012607209
## 3 -0.010692985 -0.003110683 0.0020917035 0.005938218
## 4 0.031187212 0.037207215 0.0413379626 0.044391846
## 5 0.034497193 0.041161990 0.0457351502 0.049116137
## 6 0.037467443 0.044673012 0.0496172133 0.053272533
## 7 0.005254500 0.015913044 0.0232261332 0.028633224
## 8 0.006920700 0.017900639 0.0254342468 0.031004381
## 9 0.006385267 0.017261889 0.0247246074 0.030242329
## 10 0.006206749 0.017048936 0.0244880272 0.029988279
## 11 0.005671219 0.016410097 0.0237783055 0.029226149
## 12 0.005195269 0.015842311 0.0231475072 0.028548762
## 13 -0.005337205 0.003278138 0.0091893250 0.013559901
## 14 -0.012834852 -0.005665807 -0.0007469682 0.002889901
## 15 -0.025807096 -0.021140364 -0.0179384386 -0.015570992
## 16 -0.039195799 -0.037111737 -0.0356818599 -0.034624601
## 17 -0.017666340 -0.021070244 -0.0234055240 -0.025132385
## 18 -0.064842610 -0.067705795 -0.0696703738 -0.071122851
## 19 -0.087752240 -0.095034655 -0.1000314003 -0.103725751
## 20 -0.097630151 -0.106818000 -0.1131221217 -0.117783098
## 21 -0.085562508 -0.102063369 -0.1133848662 -0.121755808
## 22 0.865476293 -0.150828226 -0.1620153094 -0.170286570
## 23 -0.150828226 0.829722142 -0.1836228996 -0.193489674
## 24 -0.162015309 -0.183622900 0.8015514195 -0.209410086
## 25 -0.170286570 -0.193489674 -0.2094100862 0.778819004Practica 2
Introduccion de la matriz
matriz_completa <- matrix(data = c(320,50,7.4,450,53,5.1,370,60,4.2,470,63,3.9,420,69,1.4,500,82,2.2,
570,100,7.0,640,104,5.7,670,113,13.1,780,130,16.4,690,150,5.1,
700,181,2.9,910,202,4.5,930,217,6.2,940,229,3.2,1070,240,2.4,
1160,243,4.9,1210,247,8.8,1450,249,10.1,1220,254,6.7),
nrow = 20, ncol = 3, byrow = TRUE)
colnames(matriz_completa) <- c("Y","X1","X2")
print(matriz_completa)## Y X1 X2
## [1,] 320 50 7.4
## [2,] 450 53 5.1
## [3,] 370 60 4.2
## [4,] 470 63 3.9
## [5,] 420 69 1.4
## [6,] 500 82 2.2
## [7,] 570 100 7.0
## [8,] 640 104 5.7
## [9,] 670 113 13.1
## [10,] 780 130 16.4
## [11,] 690 150 5.1
## [12,] 700 181 2.9
## [13,] 910 202 4.5
## [14,] 930 217 6.2
## [15,] 940 229 3.2
## [16,] 1070 240 2.4
## [17,] 1160 243 4.9
## [18,] 1210 247 8.8
## [19,] 1450 249 10.1
## [20,] 1220 254 6.7Ejemplo de regresion lineal
library(stargazer)
Modelo_lineal <- lm(formula = Y~X1 + X2, data = ejemplo_regresion)
#Usando summary
summary(Modelo_lineal)Call: lm(formula = Y ~ X1 + X2, data = ejemplo_regresion)
Residuals: Min 1Q Median 3Q Max -0.111071 -0.044467 -0.001806 0.060543 0.104058
Coefficients: Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.5761939874 0.1022709637 15.412 0.000000000000284
X1 -0.0000012687 0.0000007428 -1.708 0.102
X2 -0.0001228930 0.0000138618 -8.866 0.000000010293448 —
Signif. codes: 0 ‘’ 0.001 ’’ 0.01 ’’ 0.05 ‘.’
0.1 ’ ’ 1
Residual standard error: 0.06773 on 22 degrees of freedom Multiple R-squared: 0.7825, Adjusted R-squared: 0.7628 F-statistic: 39.58 on 2 and 22 DF, p-value: 0.00000005144
#Usando stargazer
stargazer(Modelo_lineal,title = "Ejemplo de Regresion Multiple",type = "html",digits = 8)| Dependent variable: | |
| Y | |
| X1 | -0.00000127 |
| (0.00000074) | |
| X2 | -0.00012289*** |
| (0.00001386) | |
| Constant | 1.57619400*** |
| (0.10227100) | |
| Observations | 25 |
| R2 | 0.78253320 |
| Adjusted R2 | 0.76276350 |
| Residual Std. Error | 0.06772541 (df = 22) |
| F Statistic | 39.58243000*** (df = 2; 22) |
| Note: | p<0.1; p<0.05; p<0.01 |
Objetos dentro del modelo lineal
Vector de coeficientes estimados
options(scipen = 999999)
Modelo_lineal$coefficients## (Intercept) X1 X2
## 1.576193987405 -0.000001268749 -0.000122892962Matriz de varianza-covarianza de los parametros
var_covar <- vcov(Modelo_lineal)
print(var_covar)## (Intercept) X1 X2
## (Intercept) 0.01045935002566 -0.0000000131410842007 -0.000001402024153188
## X1 -0.00000001314108 0.0000000000005517899 0.000000000001115281
## X2 -0.00000140202415 0.0000000000011152812 0.000000000192148255Intervalos de confianza
confint(object = Modelo_lineal,level = .95)## 2.5 % 97.5 %
## (Intercept) 1.364096990062 1.7882909847476
## X1 -0.000002809275 0.0000002717773
## X2 -0.000151640483 -0.0000941454413Valores ajustados Y
library(magrittr)
plot(Modelo_lineal$fitted.values,main = "valores ajustados",ylab = "Y", xlab ="casos")
Modelo_lineal$fitted.values %>% as.matrix()## [,1]
## 1 0.6793162
## 2 0.7337582
## 3 0.7606721
## 4 0.7184917
## 5 0.7254117
## 6 0.7311165
## 7 0.7936075
## 8 0.7970485
## 9 0.7959422
## 10 0.7955736
## 11 0.7944675
## 12 0.7934842
## 13 0.7717320
## 14 0.7562473
## 15 0.7294566
## 16 0.7018055
## 17 0.6175953
## 18 0.6488383
## 19 0.6015243
## 20 0.5811240
## 21 0.4773744
## 22 0.5049302
## 23 0.4712574
## 24 0.4481535
## 25 0.4310713Residuos del modelo E
library(magrittr)
plot(Modelo_lineal$residuals,main = "Residuos",ylab = "Residuos",xlab = "casos")
Modelo_lineal$residuals %>% matrix() ## [,1]
## [1,] 0.070683822
## [2,] -0.023758153
## [3,] -0.100672080
## [4,] -0.108491668
## [5,] -0.025411736
## [6,] -0.011116480
## [7,] -0.023607533
## [8,] -0.057048473
## [9,] 0.104057767
## [10,] 0.024426446
## [11,] -0.044467479
## [12,] -0.023484171
## [13,] 0.008267985
## [14,] 0.083752651
## [15,] 0.060543367
## [16,] -0.001805526
## [17,] 0.062404723
## [18,] 0.071161696
## [19,] -0.051524311
## [20,] 0.048876022
## [21,] 0.082625592
## [22,] -0.094930227
## [23,] 0.038742584
## [24,] 0.021846486
## [25,] -0.111071303