Carga de datos
library(readr)
ejemplo_regresion <- read_csv("ejemplo_regresion.csv")
head(ejemplo_regresion, n=6)
## # A tibble: 6 × 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
## 6 3.11 6402 0.72
Correr el modelo
library(stargazer)
modelo_clase <- lm(formula = Y~X1+X2,data = ejemplo_regresion)
#summary
summary(modelo_clase)
##
## Call:
## lm(formula = Y ~ X1 + X2, data = ejemplo_regresion)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.085090 -0.039102 -0.003341 0.030236 0.105692
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.564e+00 7.940e-02 19.705 1.82e-15 ***
## X1 2.372e-01 5.556e-02 4.269 0.000313 ***
## X2 -2.491e-04 3.205e-05 -7.772 9.51e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0533 on 22 degrees of freedom
## Multiple R-squared: 0.8653, Adjusted R-squared: 0.8531
## F-statistic: 70.66 on 2 and 22 DF, p-value: 2.65e-10
#stargazer
stargazer(modelo_clase, title = "Modelo de Regresión", type = "text", digits = 6)
##
## Modelo de Regresión
## ===============================================
## Dependent variable:
## ---------------------------
## Y
## -----------------------------------------------
## X1 0.237197***
## (0.055559)
##
## X2 -0.000249***
## (0.000032)
##
## Constant 1.564497***
## (0.079396)
##
## -----------------------------------------------
## Observations 25
## R2 0.865296
## Adjusted R2 0.853050
## Residual Std. Error 0.053302 (df = 22)
## F Statistic 70.660570*** (df = 2; 22)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01
Matrices A P ^ M
mat_x<-model.matrix(modelo_clase)
# Matrix X'X
mat_xx<-t(mat_x)%*%mat_x
print(mat_xx)
## (Intercept) X1 X2
## (Intercept) 25.00 96.3400 181083.0
## X1 96.34 379.2928 710932.3
## X2 181083.00 710932.3200 1335796275.0
# Matrix A
mat_A<-solve(mat_xx)%*%t(mat_x)
print(mat_A)
## 1 2 3 4
## (Intercept) 2.671735e-02 1.536650e-01 2.048227e-01 0.2285864559
## X1 3.989544e-02 -3.565847e-02 -2.215854e-01 -0.4165400478
## X2 -1.939144e-05 3.278674e-06 9.513298e-05 0.0001955722
## 5 6 7 8
## (Intercept) 0.2471098101 0.267955249 2.881990e-01 3.021260e-01
## X1 -0.3943792324 -0.311747228 -1.830474e-01 -1.122102e-01
## X2 0.0001812249 0.000134385 6.311916e-05 2.350957e-05
## 9 10 11 12
## (Intercept) 3.125846e-01 3.115468e-01 3.109783e-01 0.3192380551
## X1 5.631978e-02 5.455055e-02 8.183743e-02 0.2183626148
## X2 -6.759587e-05 -6.651133e-05 -8.095003e-05 -0.0001547247
## 13 14 15 16
## (Intercept) 0.2647959132 0.2313887316 0.1593708433 0.0942621738
## X1 0.2008967572 0.2569672798 0.1718624834 0.2021429065
## X2 -0.0001379163 -0.0001631348 -0.0001079146 -0.0001150357
## 17 18 19 20
## (Intercept) 2.940927e-02 -0.0310791444 -0.1506869905 -2.013240e-01
## X1 1.857657e-01 0.2521791772 0.1989653933 1.879867e-01
## X2 -9.736917e-05 -0.0001243516 -0.0000795279 -6.669616e-05
## 21 22 23 24
## (Intercept) -3.118477e-01 -0.4081610633 -0.4936128503 -0.556949583
## X1 1.973536e-01 -0.0798709381 -0.1219474069 -0.211089593
## X2 -5.642085e-05 0.0001043654 0.0001385483 0.000194718
## 25
## (Intercept) -0.5990949550
## X1 -0.2170100301
## X2 0.0002036863
# Matrix P
mat_P<-mat_x%*%mat_A
print(mat_P)
## 1 2 3 4 5 6
## 1 0.04158873 0.03781156 3.048860e-02 0.02303563 0.02372260 0.026648158
## 2 0.03781156 0.04741323 5.703616e-02 0.06552455 0.06569752 0.063757225
## 3 0.03048860 0.05703616 1.004618e-01 0.14349084 0.14037925 0.124733596
## 4 0.02303563 0.06552455 1.434908e-01 0.22220146 0.21541482 0.185200348
## 5 0.02372260 0.06569752 1.403792e-01 0.21541482 0.20921001 0.180792258
## 6 0.02664816 0.06375722 1.247336e-01 0.18520035 0.18079226 0.158754414
## 7 0.03129701 0.06007990 9.934054e-02 0.13689689 0.13519269 0.123010600
## 8 0.03383474 0.05820518 8.559755e-02 0.11059386 0.11039943 0.103660458
## 9 0.04004349 0.05252933 5.100009e-02 0.04570760 0.04892978 0.054990366
## 10 0.03998532 0.05253917 5.128549e-02 0.04629432 0.04947345 0.055393522
## 11 0.04100766 0.05149892 4.549412e-02 0.03555827 0.03927310 0.047250570
## 12 0.04603893 0.04688955 1.744909e-02 -0.01702736 -0.01054640 0.007798511
## 13 0.04579828 0.04461719 1.656080e-02 -0.01573428 -0.01001993 0.006644885
## 14 0.04814241 0.04075129 1.957310e-03 -0.04107698 -0.03451110 -0.013832267
## 15 0.04551090 0.04003970 1.383288e-02 -0.01510384 -0.01077924 0.002993784
## 16 0.04713214 0.03542863 2.000001e-03 -0.03358109 -0.02916052 -0.013531666
## 17 0.04701070 0.03255787 9.655854e-06 -0.03377378 -0.03017877 -0.016216760
## 18 0.04994515 0.02685737 -1.904159e-02 -0.06592067 -0.06147877 -0.042900936
## 19 0.04886272 0.02241431 -1.786905e-02 -0.05727177 -0.05480786 -0.041042251
## 20 0.04883537 0.02010589 -1.980380e-02 -0.05812998 -0.05627486 -0.043674112
## 21 0.05001919 0.01383400 -3.104239e-02 -0.07304609 -0.07186006 -0.059284179
## 22 0.04040327 0.01892940 1.923596e-02 0.02563620 0.02059045 0.011587364
## 23 0.03947851 0.01590533 2.092801e-02 0.03340359 0.02686436 0.014116670
## 24 0.03663083 0.01580855 3.438130e-02 0.06184036 0.05304706 0.033146114
## 25 0.03672810 0.01376819 3.209381e-02 0.05986710 0.05063077 0.030003329
## 7 8 9 10 11
## 1 3.129701e-02 0.033834744 0.040043491 0.039985317 0.04100766
## 2 6.007990e-02 0.058205176 0.052529329 0.052539165 0.05149892
## 3 9.934054e-02 0.085597548 0.051000087 0.051285486 0.04549412
## 4 1.368969e-01 0.110593862 0.045707605 0.046294321 0.03555827
## 5 1.351927e-01 0.110399429 0.048929776 0.049473450 0.03927310
## 6 1.230106e-01 0.103660458 0.054990366 0.055393522 0.04725057
## 7 1.025598e-01 0.091640109 0.062920604 0.063109962 0.05818661
## 8 9.164011e-02 0.085371329 0.067629278 0.067699807 0.06454509
## 9 6.292060e-02 0.067629278 0.076032081 0.075829293 0.07691052
## 10 6.310996e-02 0.067699807 0.075829293 0.075629759 0.07666767
## 11 5.818661e-02 0.064545086 0.076910524 0.076667674 0.07839425
## 12 3.489541e-02 0.050145832 0.083691329 0.083227155 0.08838551
## 13 3.142371e-02 0.045330207 0.076232442 0.075818693 0.08060435
## 14 1.741105e-02 0.034827185 0.074473737 0.073984332 0.08022514
## 15 2.384913e-02 0.035463862 0.061990628 0.061666884 0.06585153
## 16 1.059384e-02 0.023921981 0.055229525 0.054884418 0.05991338
## 17 5.670364e-03 0.017684986 0.046531179 0.046239071 0.05093572
## 18 -1.345506e-02 0.002635740 0.041865244 0.041492189 0.04793840
## 19 -1.844176e-02 -0.006266712 0.024852000 0.024613416 0.02986663
## 20 -2.260777e-02 -0.011340942 0.018136668 0.017936579 0.02297592
## 21 -3.763051e-02 -0.026183041 0.004885754 0.004716492 0.01012931
## 22 5.184751e-05 -0.006863930 -0.018703991 -0.018390895 -0.01984774
## 23 -2.788711e-03 -0.012765433 -0.031030084 -0.030614439 -0.03302593
## 24 5.416744e-03 -0.010589838 -0.042611712 -0.042027558 -0.04660778
## 25 1.376993e-03 -0.015176724 -0.048065153 -0.047454094 -0.05213122
## 12 13 14 15 16
## 1 0.046038933 0.045798283 0.04814241 0.045510898 0.047132139
## 2 0.046889547 0.044617195 0.04075129 0.040039703 0.035428634
## 3 0.017449090 0.016560798 0.00195731 0.013832885 0.002000001
## 4 -0.017027358 -0.015734277 -0.04107698 -0.015103836 -0.033581091
## 5 -0.010546403 -0.010019933 -0.03451110 -0.010779242 -0.029160523
## 6 0.007798511 0.006644885 -0.01383227 0.002993784 -0.013531666
## 7 0.034895411 0.031423714 0.01741105 0.023849129 0.010593837
## 8 0.050145832 0.045330207 0.03482719 0.035463862 0.023921981
## 9 0.083691329 0.076232442 0.07447374 0.061990628 0.055229525
## 10 0.083227155 0.075818693 0.07398433 0.061666884 0.054884418
## 11 0.088385511 0.080604350 0.08022514 0.065851527 0.059913384
## 12 0.115534854 0.105617598 0.11232580 0.087330333 0.085271677
## 13 0.105617598 0.097278159 0.10400832 0.081978444 0.081081798
## 14 0.112325805 0.104008320 0.11428940 0.089004701 0.090844454
## 15 0.087330333 0.081978444 0.08900470 0.072353813 0.073852397
## 16 0.085271677 0.081081798 0.09084445 0.073852397 0.078290810
## 17 0.074306310 0.071933225 0.08195660 0.068160746 0.074117541
## 18 0.079726880 0.077890979 0.09248418 0.075462692 0.085310455
## 19 0.055095904 0.056936697 0.07079203 0.061413561 0.073364592
## 20 0.046880620 0.050114337 0.06426903 0.057248734 0.070440106
## 21 0.035333920 0.041135721 0.05770913 0.053303532 0.070211887
## 22 -0.029396034 -0.017313040 -0.01374752 0.005809294 0.017310860
## 23 -0.047770704 -0.033003454 -0.03018006 -0.004854438 0.008026809
## 24 -0.072491687 -0.054913777 -0.05571007 -0.021705137 -0.009557036
## 25 -0.078713032 -0.060021365 -0.06039810 -0.024674895 -0.011396989
## 17 18 19 20 21
## 1 4.701070e-02 0.04994515 0.048862716 0.04883537 0.050019190
## 2 3.255787e-02 0.02685737 0.022414305 0.02010589 0.013833997
## 3 9.655854e-06 -0.01904159 -0.017869048 -0.01980380 -0.031042393
## 4 -3.377378e-02 -0.06592067 -0.057271769 -0.05812998 -0.073046093
## 5 -3.017877e-02 -0.06147877 -0.054807860 -0.05627486 -0.071860062
## 6 -1.621676e-02 -0.04290094 -0.041042251 -0.04367411 -0.059284179
## 7 5.670364e-03 -0.01345506 -0.018441763 -0.02260777 -0.037630506
## 8 1.768499e-02 0.00263574 -0.006266712 -0.01134094 -0.026183041
## 9 4.653118e-02 0.04186524 0.024852000 0.01813667 0.004885754
## 10 4.623907e-02 0.04149219 0.024613416 0.01793658 0.004716492
## 11 5.093572e-02 0.04793840 0.029866626 0.02297592 0.010129313
## 12 7.430631e-02 0.07972688 0.055095904 0.04688062 0.035333920
## 13 7.193323e-02 0.07789098 0.056936697 0.05011434 0.041135721
## 14 8.195660e-02 0.09248418 0.070792028 0.06426903 0.057709131
## 15 6.816075e-02 0.07546269 0.061413561 0.05724873 0.053303532
## 16 7.411754e-02 0.08531046 0.073364592 0.07044011 0.070211887
## 17 7.205185e-02 0.08416583 0.076401216 0.07509919 0.077986031
## 18 8.416583e-02 0.10232508 0.094798376 0.09433034 0.101153521
## 19 7.640122e-02 0.09479838 0.096014597 0.09873020 0.111008077
## 20 7.509919e-02 0.09433034 0.098730196 0.10269757 0.117430507
## 21 7.798603e-02 0.10115352 0.111008077 0.11743051 0.137942637
## 22 3.144922e-02 0.03992847 0.067329782 0.07826476 0.100211409
## 23 2.520430e-02 0.03359584 0.067425330 0.08066855 0.106460997
## 24 1.061421e-02 0.01526132 0.056453392 0.07188940 0.099800950
## 25 1.008350e-02 0.01562898 0.059326591 0.07577771 0.105773207
## 22 23 24 25
## 1 4.040327e-02 0.039478511 0.036630829 0.036728099
## 2 1.892940e-02 0.015905328 0.015808550 0.013768192
## 3 1.923596e-02 0.020928007 0.034381300 0.032093809
## 4 2.563620e-02 0.033403586 0.061840365 0.059867102
## 5 2.059045e-02 0.026864357 0.053047055 0.050630771
## 6 1.158736e-02 0.014116670 0.033146114 0.030003329
## 7 5.184751e-05 -0.002788711 0.005416744 0.001376993
## 8 -6.863930e-03 -0.012765433 -0.010589838 -0.015176724
## 9 -1.870399e-02 -0.031030084 -0.042611712 -0.048065153
## 10 -1.839090e-02 -0.030614439 -0.042027558 -0.047454094
## 11 -1.984774e-02 -0.033025927 -0.046607784 -0.052131218
## 12 -2.939603e-02 -0.047770704 -0.072491687 -0.078713032
## 13 -1.731304e-02 -0.033003454 -0.054913777 -0.060021365
## 14 -1.374752e-02 -0.030180062 -0.055710066 -0.060398099
## 15 5.809294e-03 -0.004854438 -0.021705137 -0.024674895
## 16 1.731086e-02 0.008026809 -0.009557036 -0.011396989
## 17 3.144922e-02 0.025204299 0.010614210 0.010083496
## 18 3.992847e-02 0.033595835 0.015261315 0.015628983
## 19 6.732978e-02 0.067425330 0.056453392 0.059326591
## 20 7.826476e-02 0.080668548 0.071889405 0.075777709
## 21 1.002114e-01 0.106460997 0.099800950 0.105773207
## 22 1.357829e-01 0.155593202 0.173616472 0.182532291
## 23 1.555932e-01 0.180141211 0.203749335 0.214471225
## 24 1.736165e-01 0.203749335 0.236134518 0.248424042
## 25 1.825323e-01 0.214471225 0.248424042 0.261545731
# Matrix M
mat_M<-diag(25)-mat_P
print(mat_M)
## 1 2 3 4 5 6
## 1 0.95841127 -0.03781156 -3.048860e-02 -0.02303563 -0.02372260 -0.026648158
## 2 -0.03781156 0.95258677 -5.703616e-02 -0.06552455 -0.06569752 -0.063757225
## 3 -0.03048860 -0.05703616 8.995382e-01 -0.14349084 -0.14037925 -0.124733596
## 4 -0.02303563 -0.06552455 -1.434908e-01 0.77779854 -0.21541482 -0.185200348
## 5 -0.02372260 -0.06569752 -1.403792e-01 -0.21541482 0.79078999 -0.180792258
## 6 -0.02664816 -0.06375722 -1.247336e-01 -0.18520035 -0.18079226 0.841245586
## 7 -0.03129701 -0.06007990 -9.934054e-02 -0.13689689 -0.13519269 -0.123010600
## 8 -0.03383474 -0.05820518 -8.559755e-02 -0.11059386 -0.11039943 -0.103660458
## 9 -0.04004349 -0.05252933 -5.100009e-02 -0.04570760 -0.04892978 -0.054990366
## 10 -0.03998532 -0.05253917 -5.128549e-02 -0.04629432 -0.04947345 -0.055393522
## 11 -0.04100766 -0.05149892 -4.549412e-02 -0.03555827 -0.03927310 -0.047250570
## 12 -0.04603893 -0.04688955 -1.744909e-02 0.01702736 0.01054640 -0.007798511
## 13 -0.04579828 -0.04461719 -1.656080e-02 0.01573428 0.01001993 -0.006644885
## 14 -0.04814241 -0.04075129 -1.957310e-03 0.04107698 0.03451110 0.013832267
## 15 -0.04551090 -0.04003970 -1.383288e-02 0.01510384 0.01077924 -0.002993784
## 16 -0.04713214 -0.03542863 -2.000001e-03 0.03358109 0.02916052 0.013531666
## 17 -0.04701070 -0.03255787 -9.655854e-06 0.03377378 0.03017877 0.016216760
## 18 -0.04994515 -0.02685737 1.904159e-02 0.06592067 0.06147877 0.042900936
## 19 -0.04886272 -0.02241431 1.786905e-02 0.05727177 0.05480786 0.041042251
## 20 -0.04883537 -0.02010589 1.980380e-02 0.05812998 0.05627486 0.043674112
## 21 -0.05001919 -0.01383400 3.104239e-02 0.07304609 0.07186006 0.059284179
## 22 -0.04040327 -0.01892940 -1.923596e-02 -0.02563620 -0.02059045 -0.011587364
## 23 -0.03947851 -0.01590533 -2.092801e-02 -0.03340359 -0.02686436 -0.014116670
## 24 -0.03663083 -0.01580855 -3.438130e-02 -0.06184036 -0.05304706 -0.033146114
## 25 -0.03672810 -0.01376819 -3.209381e-02 -0.05986710 -0.05063077 -0.030003329
## 7 8 9 10 11
## 1 -3.129701e-02 -0.033834744 -0.040043491 -0.039985317 -0.04100766
## 2 -6.007990e-02 -0.058205176 -0.052529329 -0.052539165 -0.05149892
## 3 -9.934054e-02 -0.085597548 -0.051000087 -0.051285486 -0.04549412
## 4 -1.368969e-01 -0.110593862 -0.045707605 -0.046294321 -0.03555827
## 5 -1.351927e-01 -0.110399429 -0.048929776 -0.049473450 -0.03927310
## 6 -1.230106e-01 -0.103660458 -0.054990366 -0.055393522 -0.04725057
## 7 8.974402e-01 -0.091640109 -0.062920604 -0.063109962 -0.05818661
## 8 -9.164011e-02 0.914628671 -0.067629278 -0.067699807 -0.06454509
## 9 -6.292060e-02 -0.067629278 0.923967919 -0.075829293 -0.07691052
## 10 -6.310996e-02 -0.067699807 -0.075829293 0.924370241 -0.07666767
## 11 -5.818661e-02 -0.064545086 -0.076910524 -0.076667674 0.92160575
## 12 -3.489541e-02 -0.050145832 -0.083691329 -0.083227155 -0.08838551
## 13 -3.142371e-02 -0.045330207 -0.076232442 -0.075818693 -0.08060435
## 14 -1.741105e-02 -0.034827185 -0.074473737 -0.073984332 -0.08022514
## 15 -2.384913e-02 -0.035463862 -0.061990628 -0.061666884 -0.06585153
## 16 -1.059384e-02 -0.023921981 -0.055229525 -0.054884418 -0.05991338
## 17 -5.670364e-03 -0.017684986 -0.046531179 -0.046239071 -0.05093572
## 18 1.345506e-02 -0.002635740 -0.041865244 -0.041492189 -0.04793840
## 19 1.844176e-02 0.006266712 -0.024852000 -0.024613416 -0.02986663
## 20 2.260777e-02 0.011340942 -0.018136668 -0.017936579 -0.02297592
## 21 3.763051e-02 0.026183041 -0.004885754 -0.004716492 -0.01012931
## 22 -5.184751e-05 0.006863930 0.018703991 0.018390895 0.01984774
## 23 2.788711e-03 0.012765433 0.031030084 0.030614439 0.03302593
## 24 -5.416744e-03 0.010589838 0.042611712 0.042027558 0.04660778
## 25 -1.376993e-03 0.015176724 0.048065153 0.047454094 0.05213122
## 12 13 14 15 16
## 1 -0.046038933 -0.045798283 -0.04814241 -0.045510898 -0.047132139
## 2 -0.046889547 -0.044617195 -0.04075129 -0.040039703 -0.035428634
## 3 -0.017449090 -0.016560798 -0.00195731 -0.013832885 -0.002000001
## 4 0.017027358 0.015734277 0.04107698 0.015103836 0.033581091
## 5 0.010546403 0.010019933 0.03451110 0.010779242 0.029160523
## 6 -0.007798511 -0.006644885 0.01383227 -0.002993784 0.013531666
## 7 -0.034895411 -0.031423714 -0.01741105 -0.023849129 -0.010593837
## 8 -0.050145832 -0.045330207 -0.03482719 -0.035463862 -0.023921981
## 9 -0.083691329 -0.076232442 -0.07447374 -0.061990628 -0.055229525
## 10 -0.083227155 -0.075818693 -0.07398433 -0.061666884 -0.054884418
## 11 -0.088385511 -0.080604350 -0.08022514 -0.065851527 -0.059913384
## 12 0.884465146 -0.105617598 -0.11232580 -0.087330333 -0.085271677
## 13 -0.105617598 0.902721841 -0.10400832 -0.081978444 -0.081081798
## 14 -0.112325805 -0.104008320 0.88571060 -0.089004701 -0.090844454
## 15 -0.087330333 -0.081978444 -0.08900470 0.927646187 -0.073852397
## 16 -0.085271677 -0.081081798 -0.09084445 -0.073852397 0.921709190
## 17 -0.074306310 -0.071933225 -0.08195660 -0.068160746 -0.074117541
## 18 -0.079726880 -0.077890979 -0.09248418 -0.075462692 -0.085310455
## 19 -0.055095904 -0.056936697 -0.07079203 -0.061413561 -0.073364592
## 20 -0.046880620 -0.050114337 -0.06426903 -0.057248734 -0.070440106
## 21 -0.035333920 -0.041135721 -0.05770913 -0.053303532 -0.070211887
## 22 0.029396034 0.017313040 0.01374752 -0.005809294 -0.017310860
## 23 0.047770704 0.033003454 0.03018006 0.004854438 -0.008026809
## 24 0.072491687 0.054913777 0.05571007 0.021705137 0.009557036
## 25 0.078713032 0.060021365 0.06039810 0.024674895 0.011396989
## 17 18 19 20 21
## 1 -4.701070e-02 -0.04994515 -0.048862716 -0.04883537 -0.050019190
## 2 -3.255787e-02 -0.02685737 -0.022414305 -0.02010589 -0.013833997
## 3 -9.655854e-06 0.01904159 0.017869048 0.01980380 0.031042393
## 4 3.377378e-02 0.06592067 0.057271769 0.05812998 0.073046093
## 5 3.017877e-02 0.06147877 0.054807860 0.05627486 0.071860062
## 6 1.621676e-02 0.04290094 0.041042251 0.04367411 0.059284179
## 7 -5.670364e-03 0.01345506 0.018441763 0.02260777 0.037630506
## 8 -1.768499e-02 -0.00263574 0.006266712 0.01134094 0.026183041
## 9 -4.653118e-02 -0.04186524 -0.024852000 -0.01813667 -0.004885754
## 10 -4.623907e-02 -0.04149219 -0.024613416 -0.01793658 -0.004716492
## 11 -5.093572e-02 -0.04793840 -0.029866626 -0.02297592 -0.010129313
## 12 -7.430631e-02 -0.07972688 -0.055095904 -0.04688062 -0.035333920
## 13 -7.193323e-02 -0.07789098 -0.056936697 -0.05011434 -0.041135721
## 14 -8.195660e-02 -0.09248418 -0.070792028 -0.06426903 -0.057709131
## 15 -6.816075e-02 -0.07546269 -0.061413561 -0.05724873 -0.053303532
## 16 -7.411754e-02 -0.08531046 -0.073364592 -0.07044011 -0.070211887
## 17 9.279482e-01 -0.08416583 -0.076401216 -0.07509919 -0.077986031
## 18 -8.416583e-02 0.89767492 -0.094798376 -0.09433034 -0.101153521
## 19 -7.640122e-02 -0.09479838 0.903985403 -0.09873020 -0.111008077
## 20 -7.509919e-02 -0.09433034 -0.098730196 0.89730243 -0.117430507
## 21 -7.798603e-02 -0.10115352 -0.111008077 -0.11743051 0.862057363
## 22 -3.144922e-02 -0.03992847 -0.067329782 -0.07826476 -0.100211409
## 23 -2.520430e-02 -0.03359584 -0.067425330 -0.08066855 -0.106460997
## 24 -1.061421e-02 -0.01526132 -0.056453392 -0.07188940 -0.099800950
## 25 -1.008350e-02 -0.01562898 -0.059326591 -0.07577771 -0.105773207
## 22 23 24 25
## 1 -4.040327e-02 -0.039478511 -0.036630829 -0.036728099
## 2 -1.892940e-02 -0.015905328 -0.015808550 -0.013768192
## 3 -1.923596e-02 -0.020928007 -0.034381300 -0.032093809
## 4 -2.563620e-02 -0.033403586 -0.061840365 -0.059867102
## 5 -2.059045e-02 -0.026864357 -0.053047055 -0.050630771
## 6 -1.158736e-02 -0.014116670 -0.033146114 -0.030003329
## 7 -5.184751e-05 0.002788711 -0.005416744 -0.001376993
## 8 6.863930e-03 0.012765433 0.010589838 0.015176724
## 9 1.870399e-02 0.031030084 0.042611712 0.048065153
## 10 1.839090e-02 0.030614439 0.042027558 0.047454094
## 11 1.984774e-02 0.033025927 0.046607784 0.052131218
## 12 2.939603e-02 0.047770704 0.072491687 0.078713032
## 13 1.731304e-02 0.033003454 0.054913777 0.060021365
## 14 1.374752e-02 0.030180062 0.055710066 0.060398099
## 15 -5.809294e-03 0.004854438 0.021705137 0.024674895
## 16 -1.731086e-02 -0.008026809 0.009557036 0.011396989
## 17 -3.144922e-02 -0.025204299 -0.010614210 -0.010083496
## 18 -3.992847e-02 -0.033595835 -0.015261315 -0.015628983
## 19 -6.732978e-02 -0.067425330 -0.056453392 -0.059326591
## 20 -7.826476e-02 -0.080668548 -0.071889405 -0.075777709
## 21 -1.002114e-01 -0.106460997 -0.099800950 -0.105773207
## 22 8.642171e-01 -0.155593202 -0.173616472 -0.182532291
## 23 -1.555932e-01 0.819858789 -0.203749335 -0.214471225
## 24 -1.736165e-01 -0.203749335 0.763865482 -0.248424042
## 25 -1.825323e-01 -0.214471225 -0.248424042 0.738454269
Vector de Coeficientes estimados
options(scipen = 999999)
modelo_clase$coefficients
## (Intercept) X1 X2
## 1.5644967711 0.2371974748 -0.0002490793
Matriz de Varianza-Covarianza de los parámetros
var_cov <- vcov(modelo_clase)
print(var_cov)
## (Intercept) X1 X2
## (Intercept) 0.0063037218732 0.000240996434 -0.000000982806321
## X1 0.0002409964344 0.003086843196 -0.000001675537651
## X2 -0.0000009828063 -0.000001675538 0.000000001027106
Intervalos de confianza
confint(object = modelo_clase,level = .95)
## 2.5 % 97.5 %
## (Intercept) 1.3998395835 1.7291539588
## X1 0.1219744012 0.3524205485
## X2 -0.0003155438 -0.0001826148
EJERCICIO 2
Cargar los datos
library(readxl)
Ejercicio_2 <- read_excel("Ejercicio_2.xlsx")
head(Ejercicio_2)
## # A tibble: 6 × 3
## Y X1 X2
## <dbl> <dbl> <dbl>
## 1 320 50 7.5
## 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
Obtener otra variable que no este en la data
library(dplyr)
X3 <- mutate(Ejercicio_2, x_3=X1*X2)
Estimar el modelo
library(stargazer)
modelo_lineal_2 <- lm(formula = Y~X1+X2+x_3, data = X3)
stargazer(modelo_lineal_2, title = "Modelo de regresión", type = "text", digits = 6)
##
## Modelo de regresión
## ===============================================
## Dependent variable:
## ---------------------------
## Y
## -----------------------------------------------
## X1 2.328470***
## (0.476584)
##
## X2 -25.067830**
## (11.450310)
##
## x_3 0.286141***
## (0.076628)
##
## Constant 303.686100***
## (71.504320)
##
## -----------------------------------------------
## Observations 20
## R2 0.963435
## Adjusted R2 0.956579
## Residual Std. Error 67.658010 (df = 16)
## F Statistic 140.525700*** (df = 3; 16)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01
matriz A,P,M
mat_x_2<-model.matrix(modelo_lineal_2)
# Matrix X'X
mat_xx_2<-t(mat_x_2)%*%mat_x_2
print(mat_xx_2)
## (Intercept) X1 X2 x_3
## (Intercept) 20.0 3036.0 121.30 18759.2
## X1 3036.0 574618.0 18759.20 3537282.8
## X2 121.3 18759.2 1001.43 152723.2
## x_3 18759.2 3537282.8 152723.18 27686606.9
# Matrix A
mat_A_2<-solve(mat_xx_2)%*%t(mat_x_2)
print(mat_A_2)
## 1 2 3 4
## (Intercept) -0.0356096554 0.21924176776 0.2954481810 0.3161310057
## X1 0.0004498074 -0.00103343874 -0.0014497842 -0.0015540405
## X2 0.0402845728 -0.00677022588 -0.0223101919 -0.0267907244
## x_3 -0.0002420114 0.00003059369 0.0001172122 0.0001410061
## 5 6 7 8
## (Intercept) 0.5229342817 0.3908124303 0.02164584417 0.09419561484
## X1 -0.0026668207 -0.0018314752 0.00008198534 -0.00023838955
## X2 -0.0657936173 -0.0449030381 0.01770369057 0.00359661964
## x_3 0.0003528161 0.0002234023 -0.00009751386 -0.00003179408
## 9 10 11 12
## (Intercept) -0.2631550259 -0.2603304050 0.04488176540 -0.0541571462
## X1 0.0011558430 0.0005707126 0.00020105115 0.0012856655
## X2 0.0660088862 0.0610665025 0.00145713918 0.0121882568
## x_3 -0.0002800182 -0.0001563735 -0.00003650356 -0.0001758376
## 13 14 15 16
## (Intercept) -0.0727262937 -0.01516406912 -0.2237294279 -0.3258582180
## X1 0.0011421885 0.00042224564 0.0024621499 0.0033456933
## X2 0.0103274418 -0.00398293555 0.0314418154 0.0474826342
## x_3 -0.0001207875 0.00002689207 -0.0003099488 -0.0004477805
## 17 18 19 20
## (Intercept) -0.138353677 0.1822093725 0.2979066352 0.0036770193
## X1 0.001537066 -0.0014915076 -0.0025668128 0.0001778607
## X2 0.012296225 -0.0475519444 -0.0692782745 -0.0164728316
## x_3 -0.000127457 0.0004079108 0.0005990749 0.0001271178
# Matrix P
mat_P_2<-mat_x_2%*%mat_A_2
print(mat_P_2)
## 1 2 3 4 5
## 1 0.19826072 0.128265769 0.0995871143 0.090375837 0.028447154
## 2 0.12826577 0.138210836 0.1365101033 0.135248115 0.141411528
## 3 0.09958711 0.136510103 0.1442958033 0.145901071 0.175501505
## 4 0.09037584 0.135248115 0.1459010714 0.148387829 0.185016386
## 5 0.02844715 0.141411528 0.1755015047 0.185016386 0.280894626
## 6 0.04624175 0.125124395 0.1486285407 0.155197592 0.223157052
## 7 0.12195509 0.089921892 0.0763469718 0.071896158 0.042668161
## 8 0.09732800 0.091309788 0.0869859350 0.085392083 0.079710695
## 9 0.18469696 0.059061063 0.0128682989 -0.001702724 -0.118039173
## 10 0.16756392 0.039088764 -0.0090144643 -0.024637124 -0.150563812
## 11 0.05217403 0.053101974 0.0538659219 0.054261906 0.057268046
## 12 0.03559895 0.028614326 0.0298623818 0.031170678 0.034631418
## 13 0.01654363 0.007830786 0.0087418192 0.009831114 0.008875059
## 14 -0.01383928 -0.005829095 0.0002191413 0.002511339 0.010992544
## 15 0.01896090 -0.016661374 -0.0220518963 -0.022145314 -0.039763593
## 16 0.02962851 -0.027410109 -0.0385302441 -0.039916937 -0.071785291
## 17 -0.01707506 -0.028630052 -0.0266047274 -0.024879417 -0.027393741
## 18 -0.09603904 -0.029097155 -0.0042057258 0.003015497 0.052126810
## 19 -0.12536798 -0.029523701 0.0038959856 0.013204858 0.081677600
## 20 -0.06330699 -0.036547852 -0.0228035353 -0.018128946 0.005167027
## 6 7 8 9 10 11
## 1 0.046241751 0.121955092 0.097328003 0.184696960 0.167563924 0.05217403
## 2 0.125124395 0.089921892 0.091309788 0.059061063 0.039088764 0.05310197
## 3 0.148628541 0.076346972 0.086985935 0.012868299 -0.009014464 0.05386592
## 4 0.155197592 0.071896158 0.085392083 -0.001702724 -0.024637124 0.05426191
## 5 0.223157052 0.042668161 0.079710695 -0.118039173 -0.150563812 0.05726805
## 6 0.182146557 0.049725261 0.076824582 -0.073671627 -0.107395447 0.05798842
## 7 0.049725261 0.085510509 0.073277138 0.118478764 0.114744909 0.04963436
## 8 0.076824582 0.073277138 0.071056300 0.067308530 0.054404548 0.05245747
## 9 -0.073671627 0.118478764 0.067308530 0.317660757 0.372651576 0.03265285
## 10 -0.107395447 0.114744909 0.054404548 0.372651576 0.481964523 0.01708991
## 11 0.057988424 0.049634363 0.052457468 0.032652849 0.017089907 0.05454562
## 12 0.046360482 0.036640868 0.044788588 -0.009503208 -0.062019023 0.06633701
## 13 0.021863469 0.029233390 0.033324891 0.012828737 -0.012390724 0.05886949
## 14 0.015548944 0.018004394 0.021988363 0.020181563 0.031741613 0.04843224
## 15 -0.008575898 0.025614139 0.027814886 0.007564146 -0.048814921 0.06883552
## 16 -0.027829177 0.027643199 0.027300617 0.011378157 -0.066870915 0.07560513
## 17 -0.008255798 0.012206610 0.016033174 0.007740738 -0.008615327 0.05741239
## 18 0.028878582 -0.014267431 -0.002143972 -0.005431085 0.078127345 0.02802009
## 19 0.043088890 -0.024370144 -0.008796467 -0.012878045 0.105284939 0.01785780
## 20 0.004953426 -0.004864243 0.003634848 -0.003846276 0.027659708 0.04358983
## 12 13 14 15 16
## 1 0.035598947 0.016543627 -0.0138392778 0.018960898 0.02962851
## 2 0.028614326 0.007830786 -0.0058290953 -0.016661374 -0.02741011
## 3 0.029862382 0.008741819 0.0002191413 -0.022051896 -0.03853024
## 4 0.031170678 0.009831114 0.0025113388 -0.022145314 -0.03991694
## 5 0.034631418 0.008875059 0.0109925440 -0.039763593 -0.07178529
## 6 0.046360482 0.021863469 0.0155489442 -0.008575898 -0.02782918
## 7 0.036640868 0.029233390 0.0180043944 0.025614139 0.02764320
## 8 0.044788588 0.033324891 0.0219883633 0.027814886 0.02730062
## 9 -0.009503208 0.012828737 0.0201815628 0.007564146 0.01137816
## 10 -0.062019023 -0.012390724 0.0317416130 -0.048814921 -0.06687091
## 11 0.066337009 0.058869488 0.0484322383 0.068835516 0.07560513
## 12 0.121597086 0.100558043 0.0638275253 0.150408865 0.18237192
## 13 0.100558043 0.094673424 0.0766512307 0.133369600 0.15661120
## 14 0.063827525 0.076651231 0.0879496240 0.088491296 0.09210567
## 15 0.150408865 0.133369600 0.0884912965 0.213586258 0.26411642
## 16 0.182371919 0.156611203 0.0921056704 0.264116420 0.33314492
## 17 0.108612174 0.111608287 0.0999456236 0.159581907 0.18663791
## 18 -0.011541757 0.037732014 0.1125333727 -0.012595048 -0.05492049
## 19 -0.053139072 0.012217287 0.1173783112 -0.072581899 -0.13932916
## 20 0.054822750 0.081027256 0.1111655784 0.084846013 0.08004867
## 17 18 19 20
## 1 -0.017075060 -0.096039037 -0.125367980 -0.063306992
## 2 -0.028630052 -0.029097155 -0.029523701 -0.036547852
## 3 -0.026604727 -0.004205726 0.003895986 -0.022803535
## 4 -0.024879417 0.003015497 0.013204858 -0.018128946
## 5 -0.027393741 0.052126810 0.081677600 0.005167027
## 6 -0.008255798 0.028878582 0.043088890 0.004953426
## 7 0.012206610 -0.014267431 -0.024370144 -0.004864243
## 8 0.016033174 -0.002143972 -0.008796467 0.003634848
## 9 0.007740738 -0.005431085 -0.012878045 -0.003846276
## 10 -0.008615327 0.078127345 0.105284939 0.027659708
## 11 0.057412388 0.028020086 0.017857804 0.043589832
## 12 0.108612174 -0.011541757 -0.053139072 0.054822750
## 13 0.111608287 0.037732014 0.012217287 0.081027256
## 14 0.099945624 0.112533373 0.117378311 0.111165578
## 15 0.159581907 -0.012595048 -0.072581899 0.084846013
## 16 0.186637914 -0.054920491 -0.139329164 0.080048669
## 17 0.143641852 0.072467900 0.048026048 0.117539508
## 18 0.072467900 0.281984823 0.356404240 0.178951032
## 19 0.048026048 0.356404240 0.465673118 0.201277391
## 20 0.117539508 0.178951032 0.201277391 0.154814807
# Matrix M
mat_M_2<-diag(20)-mat_P_2
print(mat_M_2)
## 1 2 3 4 5
## 1 0.80173928 -0.128265769 -0.0995871143 -0.090375837 -0.028447154
## 2 -0.12826577 0.861789164 -0.1365101033 -0.135248115 -0.141411528
## 3 -0.09958711 -0.136510103 0.8557041967 -0.145901071 -0.175501505
## 4 -0.09037584 -0.135248115 -0.1459010714 0.851612171 -0.185016386
## 5 -0.02844715 -0.141411528 -0.1755015047 -0.185016386 0.719105374
## 6 -0.04624175 -0.125124395 -0.1486285407 -0.155197592 -0.223157052
## 7 -0.12195509 -0.089921892 -0.0763469718 -0.071896158 -0.042668161
## 8 -0.09732800 -0.091309788 -0.0869859350 -0.085392083 -0.079710695
## 9 -0.18469696 -0.059061063 -0.0128682989 0.001702724 0.118039173
## 10 -0.16756392 -0.039088764 0.0090144643 0.024637124 0.150563812
## 11 -0.05217403 -0.053101974 -0.0538659219 -0.054261906 -0.057268046
## 12 -0.03559895 -0.028614326 -0.0298623818 -0.031170678 -0.034631418
## 13 -0.01654363 -0.007830786 -0.0087418192 -0.009831114 -0.008875059
## 14 0.01383928 0.005829095 -0.0002191413 -0.002511339 -0.010992544
## 15 -0.01896090 0.016661374 0.0220518963 0.022145314 0.039763593
## 16 -0.02962851 0.027410109 0.0385302441 0.039916937 0.071785291
## 17 0.01707506 0.028630052 0.0266047274 0.024879417 0.027393741
## 18 0.09603904 0.029097155 0.0042057258 -0.003015497 -0.052126810
## 19 0.12536798 0.029523701 -0.0038959856 -0.013204858 -0.081677600
## 20 0.06330699 0.036547852 0.0228035353 0.018128946 -0.005167027
## 6 7 8 9 10 11
## 1 -0.046241751 -0.121955092 -0.097328003 -0.184696960 -0.167563924 -0.05217403
## 2 -0.125124395 -0.089921892 -0.091309788 -0.059061063 -0.039088764 -0.05310197
## 3 -0.148628541 -0.076346972 -0.086985935 -0.012868299 0.009014464 -0.05386592
## 4 -0.155197592 -0.071896158 -0.085392083 0.001702724 0.024637124 -0.05426191
## 5 -0.223157052 -0.042668161 -0.079710695 0.118039173 0.150563812 -0.05726805
## 6 0.817853443 -0.049725261 -0.076824582 0.073671627 0.107395447 -0.05798842
## 7 -0.049725261 0.914489491 -0.073277138 -0.118478764 -0.114744909 -0.04963436
## 8 -0.076824582 -0.073277138 0.928943700 -0.067308530 -0.054404548 -0.05245747
## 9 0.073671627 -0.118478764 -0.067308530 0.682339243 -0.372651576 -0.03265285
## 10 0.107395447 -0.114744909 -0.054404548 -0.372651576 0.518035477 -0.01708991
## 11 -0.057988424 -0.049634363 -0.052457468 -0.032652849 -0.017089907 0.94545438
## 12 -0.046360482 -0.036640868 -0.044788588 0.009503208 0.062019023 -0.06633701
## 13 -0.021863469 -0.029233390 -0.033324891 -0.012828737 0.012390724 -0.05886949
## 14 -0.015548944 -0.018004394 -0.021988363 -0.020181563 -0.031741613 -0.04843224
## 15 0.008575898 -0.025614139 -0.027814886 -0.007564146 0.048814921 -0.06883552
## 16 0.027829177 -0.027643199 -0.027300617 -0.011378157 0.066870915 -0.07560513
## 17 0.008255798 -0.012206610 -0.016033174 -0.007740738 0.008615327 -0.05741239
## 18 -0.028878582 0.014267431 0.002143972 0.005431085 -0.078127345 -0.02802009
## 19 -0.043088890 0.024370144 0.008796467 0.012878045 -0.105284939 -0.01785780
## 20 -0.004953426 0.004864243 -0.003634848 0.003846276 -0.027659708 -0.04358983
## 12 13 14 15 16
## 1 -0.035598947 -0.016543627 0.0138392778 -0.018960898 -0.02962851
## 2 -0.028614326 -0.007830786 0.0058290953 0.016661374 0.02741011
## 3 -0.029862382 -0.008741819 -0.0002191413 0.022051896 0.03853024
## 4 -0.031170678 -0.009831114 -0.0025113388 0.022145314 0.03991694
## 5 -0.034631418 -0.008875059 -0.0109925440 0.039763593 0.07178529
## 6 -0.046360482 -0.021863469 -0.0155489442 0.008575898 0.02782918
## 7 -0.036640868 -0.029233390 -0.0180043944 -0.025614139 -0.02764320
## 8 -0.044788588 -0.033324891 -0.0219883633 -0.027814886 -0.02730062
## 9 0.009503208 -0.012828737 -0.0201815628 -0.007564146 -0.01137816
## 10 0.062019023 0.012390724 -0.0317416130 0.048814921 0.06687091
## 11 -0.066337009 -0.058869488 -0.0484322383 -0.068835516 -0.07560513
## 12 0.878402914 -0.100558043 -0.0638275253 -0.150408865 -0.18237192
## 13 -0.100558043 0.905326576 -0.0766512307 -0.133369600 -0.15661120
## 14 -0.063827525 -0.076651231 0.9120503760 -0.088491296 -0.09210567
## 15 -0.150408865 -0.133369600 -0.0884912965 0.786413742 -0.26411642
## 16 -0.182371919 -0.156611203 -0.0921056704 -0.264116420 0.66685508
## 17 -0.108612174 -0.111608287 -0.0999456236 -0.159581907 -0.18663791
## 18 0.011541757 -0.037732014 -0.1125333727 0.012595048 0.05492049
## 19 0.053139072 -0.012217287 -0.1173783112 0.072581899 0.13932916
## 20 -0.054822750 -0.081027256 -0.1111655784 -0.084846013 -0.08004867
## 17 18 19 20
## 1 0.017075060 0.096039037 0.125367980 0.063306992
## 2 0.028630052 0.029097155 0.029523701 0.036547852
## 3 0.026604727 0.004205726 -0.003895986 0.022803535
## 4 0.024879417 -0.003015497 -0.013204858 0.018128946
## 5 0.027393741 -0.052126810 -0.081677600 -0.005167027
## 6 0.008255798 -0.028878582 -0.043088890 -0.004953426
## 7 -0.012206610 0.014267431 0.024370144 0.004864243
## 8 -0.016033174 0.002143972 0.008796467 -0.003634848
## 9 -0.007740738 0.005431085 0.012878045 0.003846276
## 10 0.008615327 -0.078127345 -0.105284939 -0.027659708
## 11 -0.057412388 -0.028020086 -0.017857804 -0.043589832
## 12 -0.108612174 0.011541757 0.053139072 -0.054822750
## 13 -0.111608287 -0.037732014 -0.012217287 -0.081027256
## 14 -0.099945624 -0.112533373 -0.117378311 -0.111165578
## 15 -0.159581907 0.012595048 0.072581899 -0.084846013
## 16 -0.186637914 0.054920491 0.139329164 -0.080048669
## 17 0.856358148 -0.072467900 -0.048026048 -0.117539508
## 18 -0.072467900 0.718015177 -0.356404240 -0.178951032
## 19 -0.048026048 -0.356404240 0.534326882 -0.201277391
## 20 -0.117539508 -0.178951032 -0.201277391 0.845185193
Vector de coeficientes estimados
options(scipen = 999999)
modelo_lineal_2$coefficients
## (Intercept) X1 X2 x_3
## 303.6860694 2.3284704 -25.0678343 0.2861407
Obtener la matriz varianza-covarianza del modelo
var_cov_2 <- vcov(modelo_lineal_2)
print(var_cov_2)
## (Intercept) X1 X2 x_3
## (Intercept) 5112.868475 -31.06160236 -720.2279796 4.477105378
## X1 -31.061602 0.22713224 4.5575025 -0.033112632
## X2 -720.227980 4.55750247 131.1095187 -0.817497682
## x_3 4.477105 -0.03311263 -0.8174977 0.005871802
Intervalos de confianza
confint(object = modelo_lineal_2, level = .95)
## 2.5 % 97.5 %
## (Intercept) 152.1036722 455.2684666
## X1 1.3181576 3.3387832
## X2 -49.3413997 -0.7942689
## x_3 0.1236973 0.4485842