Correcion de supuestos de un lm
Jorge Méndez González
2022-09-06
IMPORTANTE: en este video explico todo lo de este script
https://www.youtube.com/watch?v=5cDtzvCDzy0
Los datos
setwd("C:/CURSO REG JMG") # Ajuste del directorio de trabajo
data ("airquality") # Conjunto de datos
Datos<-airquality # el objeto
Datos<-Datos %>% drop_na() # Eliminar celdas con NA
attach(Datos) # crucial
str(Datos) # estructura de los datos## 'data.frame': 111 obs. of 6 variables:
## $ Ozone : int 41 36 12 18 23 19 8 16 11 14 ...
## $ Solar.R: int 190 118 149 313 299 99 19 256 290 274 ...
## $ Wind : num 7.4 8 12.6 11.5 8.6 13.8 20.1 9.7 9.2 10.9 ...
## $ Temp : int 67 72 74 62 65 59 61 69 66 68 ...
## $ Month : int 5 5 5 5 5 5 5 5 5 5 ...
## $ Day : int 1 2 3 4 7 8 9 12 13 14 ...El modelo inicial
plot(Temp, Ozone, col="deepskyblue1") # la plot
mod <- lm(Ozone ~ Temp, data=Datos) # el modelo lineal simple
abline(mod, col="red") # la linea de los predichos
summary(mod) # resumen del modelo##
## Call:
## lm(formula = Ozone ~ Temp, data = Datos)
##
## Residuals:
## Min 1Q Median 3Q Max
## -40.922 -17.459 -0.874 10.444 118.078
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -147.6461 18.7553 -7.872 2.76e-12 ***
## Temp 2.4391 0.2393 10.192 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 23.92 on 109 degrees of freedom
## Multiple R-squared: 0.488, Adjusted R-squared: 0.4833
## F-statistic: 103.9 on 1 and 109 DF, p-value: < 2.2e-16library(gvlma) # liberia para evaluar los supuestos
gvlma(mod) # una forma para evaluar los supuestos##
## Call:
## lm(formula = Ozone ~ Temp, data = Datos)
##
## Coefficients:
## (Intercept) Temp
## -147.646 2.439
##
##
## ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
## USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
## Level of Significance = 0.05
##
## Call:
## gvlma(x = mod)
##
## Value p-value Decision
## Global Stat 1.924e+02 0.000e+00 Assumptions NOT satisfied!
## Skewness 4.941e+01 2.076e-12 Assumptions NOT satisfied!
## Kurtosis 1.312e+02 0.000e+00 Assumptions NOT satisfied!
## Link Function 1.185e+01 5.764e-04 Assumptions NOT satisfied!
## Heteroscedasticity 5.076e-03 9.432e-01 Assumptions acceptable.Interpretaciones mas facil
library(performance)## Warning: package 'performance' was built under R version 4.1.3#library(easystats)
library(car)
#library(graphics)
#revisar los supuestos
check_heteroskedasticity (mod) # los errores deben mostrar homogeneidad## Warning: Heteroscedasticity (non-constant error variance) detected (p = 0.019).check_autocorrelation (mod) # residualaes no correlacionados## OK: Residuals appear to be independent and not autocorrelated (p = 0.408).check_collinearity (mod) # variables (x) independienets no correlacioandas## Warning: Not enough model terms in the conditional part of the model to check for
## multicollinearity.## NULLcheck_normality (mod) # normalidad de los residuales (errores)## Warning: Non-normality of residuals detected (p < .001).Corrigiendo la los supuestos de regresion
1. Deteccion de datos atipicos
Los conceptos de atípico e influyente son diferentes y se definen así: Punto atípico (outlier): es una observación que es numéricamente distante del resto de los datos. Punto influyente: punto que tiene impacto en las estimativas del modelo.
library(car)
library(performance)
# Veamos si hay atipicos usando ri, como lo hemos venido haciendo tradicionalmente
Residuales<-cbind(ei=residuals(mod, type='working'), # ordinarios
pi=residuals(mod, type='deviance'),
pe=residuals(mod, type='pearson'),
pa=residuals(mod, type='partial'),
di=rstandard(mod),
ri=rstudent(mod)); Residuales## ei pi pe Temp di ri
## 1 25.22570871 25.22570871 25.22570871 -1.099099 1.065645822 1.06631545
## 2 8.03015918 8.03015918 8.03015918 -6.099099 0.337800946 0.33642397
## 3 -20.84806063 -20.84806063 -20.84806063 -30.099099 -0.876154823 -0.87521386
## 4 14.42125824 14.42125824 14.42125824 -24.099099 0.613399170 0.61163550
## 5 12.10392852 12.10392852 12.10392852 -19.099099 0.512560745 0.51082011
## 6 22.73858795 22.73858795 22.73858795 -23.099099 0.972412941 0.97216807
## 7 6.86036814 6.86036814 6.86036814 -34.099099 0.292295333 0.29106553
## 8 -4.65251110 -4.65251110 -4.65251110 -26.099099 -0.196150433 -0.19528306
## 9 -2.33518138 -2.33518138 -2.33518138 -31.099099 -0.098762481 -0.09831280
## 10 -4.21340120 -4.21340120 -4.21340120 -28.099099 -0.177805796 -0.17701397
## 11 24.17769786 24.17769786 24.17769786 -24.099099 1.036052084 1.03640435
## 12 5.54303843 5.54303843 5.54303843 -28.099099 0.235050192 0.23402881
## 13 20.66481862 20.66481862 20.66481862 -8.099099 0.873982964 0.87302900
## 14 14.61680777 14.61680777 14.61680777 -36.099099 0.627694067 0.62594041
## 15 11.78659880 11.78659880 11.78659880 -12.099099 0.497395212 0.49567117
## 16 7.42125824 7.42125824 7.42125824 -31.099099 0.315658562 0.31435096
## 17 4.73858795 4.73858795 4.73858795 -41.099099 0.202645136 0.20175144
## 18 -19.40895072 -19.40895072 -19.40895072 -31.099099 -0.816029615 -0.81477035
## 19 2.86036814 2.86036814 2.86036814 -38.099099 0.121869882 0.12131782
## 20 30.86036814 30.86036814 30.86036814 -10.099099 1.314848035 1.31930717
## 21 7.22570871 7.22570871 7.22570871 -19.099099 0.305245985 0.30397250
## 22 -4.92182997 -4.92182997 -4.92182997 2.900901 -0.206800594 -0.20589018
## 23 69.95638984 69.95638984 69.95638984 72.900901 2.938047423 3.04770768
## 24 -0.72628044 -0.72628044 -0.72628044 -5.099099 -0.030505230 -0.03036510
## 25 -23.36093987 -23.36093987 -23.36093987 -13.099099 -0.981925053 -0.98176224
## 26 -0.87381912 -0.87381912 -0.87381912 28.900901 -0.036975519 -0.03680575
## 27 -25.55648940 -25.55648940 -25.55648940 -3.099099 -1.077874042 -1.07868242
## 28 -29.36093987 -29.36093987 -29.36093987 -19.099099 -1.234121684 -1.23712108
## 29 -19.16539035 -19.16539035 -19.16539035 -21.099099 -0.804879563 -0.80357048
## 30 9.03015918 9.03015918 9.03015918 -5.099099 0.379867478 0.37837149
## 31 9.10392852 9.10392852 9.10392852 -22.099099 0.385520815 0.38401019
## 32 -18.40895072 -18.40895072 -18.40895072 -30.099099 -0.773985631 -0.77255292
## 33 -24.72628044 -24.72628044 -24.72628044 -29.099099 -1.038553189 -1.03893128
## 34 77.76084032 77.76084032 77.76084032 92.900901 3.271953522 3.42968941
## 35 -10.67826959 -10.67826959 -10.67826959 6.900901 -0.449616912 -0.44796530
## 36 -17.92182997 -17.92182997 -17.92182997 -10.099099 -0.753021762 -0.75151690
## 37 9.19995022 9.19995022 9.19995022 21.900901 0.386883730 0.38536963
## 38 -14.80004978 -14.80004978 -14.80004978 -2.099099 -0.622383636 -0.62062585
## 39 10.00440069 10.00440069 10.00440069 34.900901 0.422364905 0.42076745
## 40 20.24796107 20.24796107 20.24796107 54.900901 0.859119679 0.85807983
## 41 20.24796107 20.24796107 20.24796107 54.900901 0.859119679 0.85807983
## 42 15.56529079 15.56529079 15.56529079 42.900901 0.657853508 0.65613272
## 43 -20.40895072 -20.40895072 -20.40895072 -32.099099 -0.858073599 -0.85702791
## 44 -22.92182997 -22.92182997 -22.92182997 -15.099099 -0.963106827 -0.96278406
## 45 -40.48272006 -40.48272006 -40.48272006 -35.099099 -1.700497555 -1.71558877
## 46 -1.92182997 -1.92182997 -1.92182997 5.900901 -0.080749555 -0.08038069
## 47 -17.36093987 -17.36093987 -17.36093987 -7.099099 -0.729728423 -0.72815415
## 48 3.76084032 3.76084032 3.76084032 18.900901 0.158245393 0.15753592
## 49 14.44351060 14.44351060 14.44351060 36.900901 0.609171506 0.60740554
## 50 3.32173041 3.32173041 3.32173041 20.900901 0.139864063 0.13923350
## 51 -16.84806063 -16.84806063 -16.84806063 -26.099099 -0.708051931 -0.70642294
## 52 17.88262051 17.88262051 17.88262051 37.900901 0.753551710 0.75204856
## 53 48.32173041 48.32173041 48.32173041 65.900901 2.034624338 2.06485974
## 54 -32.36093987 -32.36093987 -32.36093987 -22.099099 -1.360219999 -1.36560579
## 55 -10.11737949 -10.11737949 -10.11737949 9.900901 -0.426333971 -0.42472808
## 56 15.00440069 15.00440069 15.00440069 39.900901 0.633454463 0.63170584
## 57 -12.11737949 -12.11737949 -12.11737949 7.900901 -0.510611520 -0.50887284
## 58 9.19995022 9.19995022 9.19995022 21.900901 0.386883730 0.38536963
## 59 9.07817003 9.07817003 9.07817003 16.900901 0.381437588 0.37993750
## 60 -10.92182997 -10.92182997 -10.92182997 -3.099099 -0.458902671 -0.45723467
## 61 -40.92182997 -40.92182997 -40.92182997 -33.099099 -1.719413060 -1.73520116
## 62 -36.36093987 -36.36093987 -36.36093987 -26.099099 -1.528351086 -1.53789181
## 63 52.56529079 52.56529079 52.56529079 79.900901 2.221626399 2.26324653
## 64 17.12618088 17.12618088 17.12618088 46.900901 0.724691666 0.72310385
## 65 38.12618088 38.12618088 38.12618088 67.900901 1.613303383 1.62540921
## 66 -18.11737949 -18.11737949 -18.11737949 1.900901 -0.763444166 -0.76197401
## 67 -24.36093987 -24.36093987 -24.36093987 -14.099099 -1.023957825 -1.02418777
## 68 17.51727994 17.51727994 17.51727994 22.900901 0.735822387 0.73426520
## 69 -18.16539035 -18.16539035 -18.16539035 -20.099099 -0.762883050 -0.76141097
## 70 13.95638984 13.95638984 13.95638984 16.900901 0.586144244 0.58437100
## 71 -14.72628044 -14.72628044 -14.72628044 -19.099099 -0.618533206 -0.61677273
## 72 -11.60450025 -11.60450025 -11.60450025 -11.099099 -0.487334131 -0.48562284
## 73 1.39549975 1.39549975 1.39549975 1.900901 0.058604390 0.05833586
## 74 -19.16539035 -19.16539035 -19.16539035 -21.099099 -0.804879563 -0.80357048
## 75 -18.96984082 -18.96984082 -18.96984082 -33.099099 -0.797995411 -0.79665696
## 76 -0.04361016 -0.04361016 -0.04361016 2.900901 -0.001831551 -0.00182313
## 77 118.07817003 118.07817003 118.07817003 125.900901 4.961292001 5.61270921
## 78 10.88262051 10.88262051 10.88262051 30.900901 0.458580290 0.45691284
## 79 -12.94758846 -12.94758846 -12.94758846 33.900901 -0.554159269 -0.55239009
## 80 36.36974126 36.36974126 36.36974126 75.900901 1.548028066 1.55813382
## 81 -2.50847855 -2.50847855 -2.50847855 41.900901 -0.107153258 -0.10666622
## 82 3.36974126 3.36974126 3.36974126 42.900901 0.143428407 0.14278244
## 83 21.68707098 21.68707098 21.68707098 53.900901 0.918883233 0.91822178
## 84 1.24796107 1.24796107 1.24796107 35.900901 0.052950908 0.05270813
## 85 -6.19114883 -6.19114883 -6.19114883 30.900901 -0.263089312 -0.26196289
## 86 11.80885117 11.80885117 11.80885117 48.900901 0.501810344 0.50008114
## 87 -17.55648940 -17.55648940 -17.55648940 4.900901 -0.740464932 -0.73892127
## 88 -25.23915968 -25.23915968 -25.23915968 -10.099099 -1.061991577 -1.06262061
## 89 -27.48272006 -27.48272006 -27.48272006 -22.099099 -1.154425844 -1.15620809
## 90 -19.60450025 -19.60450025 -19.60450025 -19.099099 -0.823296298 -0.82207102
## 91 -14.28717053 -14.28717053 -14.28717053 -21.099099 -0.600228781 -0.59845895
## 92 -6.40895072 -6.40895072 -6.40895072 -18.099099 -0.269457822 -0.26830831
## 93 -5.92182997 -5.92182997 -5.92182997 1.900901 -0.248817607 -0.24774398
## 94 -16.72628044 -16.72628044 -16.72628044 -21.099099 -0.702537203 -0.70089578
## 95 -12.16539035 -12.16539035 -12.16539035 -14.099099 -0.510903973 -0.50916499
## 96 -16.53073091 -16.53073091 -16.53073091 -33.099099 -0.695834449 -0.69417870
## 97 -12.53073091 -12.53073091 -12.53073091 -29.099099 -0.527460902 -0.52570713
## 98 3.39549975 3.39549975 3.39549975 3.900901 0.142594932 0.14195256
## 99 2.22570871 2.22570871 2.22570871 -24.099099 0.094023808 0.09359531
## 100 -24.72628044 -24.72628044 -24.72628044 -29.099099 -1.038553189 -1.03893128
## 101 5.78659880 5.78659880 5.78659880 -18.099099 0.244194834 0.24313861
## 102 -36.36093987 -36.36093987 -36.36093987 -26.099099 -1.528351086 -1.53789181
## 103 4.54303843 4.54303843 4.54303843 -29.099099 0.192645616 0.19179254
## 104 -2.53073091 -2.53073091 -2.53073091 -19.099099 -0.106527035 -0.10604277
## 105 -13.92182997 -13.92182997 -13.92182997 -6.099099 -0.584953710 -0.58318033
## 106 -13.65251110 -13.65251110 -13.65251110 -35.099099 -0.575591527 -0.57381784
## 107 7.98214833 7.98214833 7.98214833 -28.099099 0.338978946 0.33759841
## 108 6.90837899 6.90837899 6.90837899 -12.099099 0.291012520 0.28978712
## 109 -21.28717053 -21.28717053 -21.28717053 -28.099099 -0.894310906 -0.89348313
## 110 -19.72628044 -19.72628044 -19.72628044 -24.099099 -0.828543198 -0.82734321
## 111 1.78659880 1.78659880 1.78659880 -22.099099 0.075394582 0.07504990boxplot(Residuales, col=terrain.colors(4)) # todos los residuales
ri=rstudent(mod) # extraer los residuales estudentizados *los importantes*
boxplot(ri) # Graficar los residuales estudentizados
outlierTest(mod, cutoff=Inf, n.max=5) # prueba de bonferroni para detectar outliers## rstudent unadjusted p-value Bonferroni p
## 77 5.612709 1.5566e-07 1.7278e-05
## 34 3.429689 8.5674e-04 9.5098e-02
## 23 3.047708 2.8994e-03 3.2183e-01
## 63 2.263247 2.5620e-02 NA
## 53 2.064860 4.1331e-02 NAstr(Datos)## 'data.frame': 111 obs. of 6 variables:
## $ Ozone : int 41 36 12 18 23 19 8 16 11 14 ...
## $ Solar.R: int 190 118 149 313 299 99 19 256 290 274 ...
## $ Wind : num 7.4 8 12.6 11.5 8.6 13.8 20.1 9.7 9.2 10.9 ...
## $ Temp : int 67 72 74 62 65 59 61 69 66 68 ...
## $ Month : int 5 5 5 5 5 5 5 5 5 5 ...
## $ Day : int 1 2 3 4 7 8 9 12 13 14 ...Eliminar datos atipicos
Datos1<-Datos[-c(23, 34, 77),]
str(Datos1)## 'data.frame': 108 obs. of 6 variables:
## $ Ozone : int 41 36 12 18 23 19 8 16 11 14 ...
## $ Solar.R: int 190 118 149 313 299 99 19 256 290 274 ...
## $ Wind : num 7.4 8 12.6 11.5 8.6 13.8 20.1 9.7 9.2 10.9 ...
## $ Temp : int 67 72 74 62 65 59 61 69 66 68 ...
## $ Month : int 5 5 5 5 5 5 5 5 5 5 ...
## $ Day : int 1 2 3 4 7 8 9 12 13 14 ...ya no hay outliers? corramos el modelo otra vez
mod1 <- lm(Ozone ~ Temp, data=Datos1) # el modelo
outlierTest(mod1, cutoff=Inf, n.max=5) # prueba de bonferroni para detectar outliers## rstudent unadjusted p-value Bonferroni p
## 63 3.177276 0.0019528 0.21090
## 53 2.881109 0.0048053 0.51897
## 65 2.319358 0.0223110 NA
## 80 2.253883 0.0262810 NA
## 61 -2.091863 0.0388630 NAveamos cuantos datos tenemos
Datos_2<-Datos1[-63,]
str(Datos_2)## 'data.frame': 107 obs. of 6 variables:
## $ Ozone : int 41 36 12 18 23 19 8 16 11 14 ...
## $ Solar.R: int 190 118 149 313 299 99 19 256 290 274 ...
## $ Wind : num 7.4 8 12.6 11.5 8.6 13.8 20.1 9.7 9.2 10.9 ...
## $ Temp : int 67 72 74 62 65 59 61 69 66 68 ...
## $ Month : int 5 5 5 5 5 5 5 5 5 5 ...
## $ Day : int 1 2 3 4 7 8 9 12 13 14 ...veamos si ya pasan lo supuestos
plot(Temp, Ozone, col="deepskyblue1") # la plot
mod2 <- lm(Ozone ~ Temp, data=Datos_2); summary(mod2) # el modelo##
## Call:
## lm(formula = Ozone ~ Temp, data = Datos_2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -37.565 -14.557 1.435 12.646 57.128
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -138.7847 14.4150 -9.628 4.2e-16 ***
## Temp 2.2883 0.1844 12.408 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 18.24 on 105 degrees of freedom
## Multiple R-squared: 0.5945, Adjusted R-squared: 0.5907
## F-statistic: 154 on 1 and 105 DF, p-value: < 2.2e-16abline(mod2)
#revisar los supuestos
check_heteroskedasticity (mod2) # los errores deben mostrar homogeneidad## Warning: Heteroscedasticity (non-constant error variance) detected (p = 0.015).check_autocorrelation (mod2) # residualaes no correlacionados## OK: Residuals appear to be independent and not autocorrelated (p = 0.100).check_collinearity (mod2) # variables (x) independienets no correlacioandas## Warning: Not enough model terms in the conditional part of the model to check for
## multicollinearity.## NULLcheck_normality (mod2) # normalidad de los residuales (errores)## OK: residuals appear as normally distributed (p = 0.077).Opcion 2. Regresion ponderada
mod3 <- lm(Ozone ~ Temp, data=Datos_2, weights = 1/(Ozone)) # ponderaciones 1/x, 1/(x)^2, sqrt(x)
summary(mod3) ##
## Call:
## lm(formula = Ozone ~ Temp, data = Datos_2, weights = 1/(Ozone))
##
## Weighted Residuals:
## Min 1Q Median 3Q Max
## -9.633 -1.210 1.314 2.995 6.912
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -84.5220 9.8233 -8.604 8.13e-14 ***
## Temp 1.4626 0.1382 10.583 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.159 on 105 degrees of freedom
## Multiple R-squared: 0.5161, Adjusted R-squared: 0.5115
## F-statistic: 112 on 1 and 105 DF, p-value: < 2.2e-16#revisar los supuestos
check_heteroskedasticity (mod3) # los errores deben mostrar homogeneidad## Warning: Heteroscedasticity (non-constant error variance) detected (p = 0.024).check_autocorrelation (mod3) # residualaes no correlacionados## Warning: Autocorrelated residuals detected (p < .001).check_collinearity (mod3) # variables (x) independienets no correlacioandas## Warning: Not enough model terms in the conditional part of the model to check for
## multicollinearity.## NULLcheck_normality (mod3) # normalidad de los residuales (errores)## Warning: Non-normality of residuals detected (p = 0.005).Opcion 3. Tranformar la variable dependiente (y) a ln
mod5 <- lm(log(Ozone) ~ log(Temp), data=Datos_2) # el modelo
summary(mod5) ##
## Call:
## lm(formula = log(Ozone) ~ log(Temp), data = Datos_2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.05667 -0.31045 0.05166 0.38289 1.24546
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -17.9536 1.8435 -9.739 2.36e-16 ***
## log(Temp) 4.9075 0.4243 11.567 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5552 on 105 degrees of freedom
## Multiple R-squared: 0.5603, Adjusted R-squared: 0.5561
## F-statistic: 133.8 on 1 and 105 DF, p-value: < 2.2e-16#revisar los supuestos
check_heteroskedasticity (mod5) # los errores deben mostrar homogeneidad## Warning: Heteroscedasticity (non-constant error variance) detected (p < .001).check_autocorrelation (mod5) # residualaes no correlacionados## OK: Residuals appear to be independent and not autocorrelated (p = 0.268).check_collinearity (mod5) # variables (x) independienets no correlacioandas## Warning: Not enough model terms in the conditional part of the model to check for
## multicollinearity.## NULLcheck_normality (mod5) # normalidad de los residuales (errores)## Warning: Non-normality of residuals detected (p = 0.005).Opcion 4. Transformación Box Cox de la variable Ozone
# view(Datos_2)
attach(Datos_2)
Lambda<-car::powerTransform(Ozone, family="bcPower") #Buscamos Lambda
# str(Lamba)
Lambda$ start## [1] 0.238367ya se normalizo la variable?
Datos_2$Ozone_Box<-Ozone^Lambda$ start
View(Datos_2)
attach(Datos_2)
shapiro.test(Ozone_Box) # Prueba de normalidad si no es un dataframe##
## Shapiro-Wilk normality test
##
## data: Ozone_Box
## W = 0.98179, p-value = 0.1505hist(Ozone_Box, col = 3)
La regresion con Ozono normalizado
mod4 <- lm(Ozone_Box ~ Temp, data=Datos_2) # el modelo
summary(mod4) ##
## Call:
## lm(formula = Ozone_Box ~ Temp, data = Datos_2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.76478 -0.18871 0.00496 0.20944 0.59107
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.430691 0.213938 -2.013 0.0467 *
## Temp 0.034821 0.002737 12.722 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2708 on 105 degrees of freedom
## Multiple R-squared: 0.6065, Adjusted R-squared: 0.6028
## F-statistic: 161.9 on 1 and 105 DF, p-value: < 2.2e-16#revisar los supuestos
check_heteroskedasticity (mod4) # los errores deben mostrar homogeneidad## OK: Error variance appears to be homoscedastic (p = 0.096).check_autocorrelation (mod4) # residualaes no correlacionados## OK: Residuals appear to be independent and not autocorrelated (p = 0.344).check_collinearity (mod4) # variables (x) independienets no correlacioandas## Warning: Not enough model terms in the conditional part of the model to check for
## multicollinearity.## NULLcheck_normality (mod4) # normalidad de los residuales (errores)## OK: residuals appear as normally distributed (p = 0.254).y como quedo el modelo fina?
plot(Temp, Ozone, col="deepskyblue1") # plot del modelo sin cumplir los supuestos
abline(lm(Ozone ~Temp))
plot(Temp, Ozone_Box, col="deepskyblue1") # plot el modelo supuestos cumplidos
abline(mod4)
# predecir ozono con el el mod final
estimados<-(mod4$ fitted.values); estimados # estimados por el modelo## 1 2 3 4 5 6 7 8
## 1.902285 2.076388 2.146029 1.728182 1.832644 1.623721 1.693362 1.971926
## 9 10 11 12 13 14 15 16
## 1.867464 1.937106 1.588900 1.797823 1.867464 1.554080 1.937106 1.728182
## 17 18 19 20 21 22 24 25
## 1.623721 2.111208 1.693362 1.693362 1.902285 2.389773 2.215670 2.424593
## 26 27 28 29 30 31 32 33
## 2.703157 2.598696 2.424593 2.250490 2.076388 1.832644 2.111208 2.215670
## 35 36 37 38 39 40 41 42
## 2.529055 2.389773 2.459414 2.459414 2.633516 2.772799 2.772799 2.668337
## 43 44 45 46 47 48 49 50
## 2.111208 2.389773 2.354952 2.389773 2.424593 2.494234 2.598696 2.529055
## 51 52 53 54 55 56 57 58
## 2.146029 2.563875 2.529055 2.424593 2.563875 2.633516 2.563875 2.459414
## 59 60 61 62 63 64 66 67
## 2.389773 2.389773 2.389773 2.424593 2.668337 2.703157 2.563875 2.424593
## 68 69 70 71 72 73 74 75
## 2.354952 2.250490 2.320131 2.215670 2.285311 2.285311 2.250490 2.076388
## 76 78 79 80 81 82 83 84
## 2.320131 2.563875 2.946901 2.842440 2.912081 2.842440 2.737978 2.772799
## 85 86 87 88 89 90 91 92
## 2.807619 2.807619 2.598696 2.494234 2.354952 2.285311 2.180849 2.111208
## 93 94 95 96 97 98 99 100
## 2.389773 2.215670 2.250490 2.041567 2.041567 2.285311 1.902285 2.215670
## 101 102 103 104 105 106 107 108
## 1.937106 2.424593 1.797823 2.041567 2.389773 1.971926 1.763003 2.006747
## 109 110 111
## 2.180849 2.215670 1.937106regreso_unidades_originales<-(estimados^(1/Lambda$ start)); regreso_unidades_originales## 1 2 3 4 5 6 7 8
## 14.846358 21.437584 24.619602 9.925177 12.696033 7.640809 9.112833 17.263481
## 9 10 11 12 13 14 15 16
## 13.739178 16.020223 6.976581 11.714330 13.739178 6.357270 16.020223 9.925177
## 17 18 19 20 21 22 24 25
## 7.640809 22.986681 9.112833 9.112833 14.846358 38.662114 28.149231 41.081013
## 26 27 28 29 30 31 32 33
## 64.832286 54.952386 41.081013 30.052249 21.437584 12.696033 22.986681 28.149231
## 35 36 37 38 39 40 41 42
## 49.033707 38.662114 43.613494 43.613494 58.108180 72.133286 72.133286 61.400152
## 43 44 45 46 47 48 49 50
## 22.986681 38.662114 36.353246 38.662114 41.081013 46.263168 54.952386 49.033707
## 51 52 53 54 55 56 57 58
## 24.619602 51.928848 49.033707 41.081013 51.928848 58.108180 51.928848 43.613494
## 59 60 61 62 63 64 66 67
## 38.662114 38.662114 38.662114 41.081013 61.400152 64.832286 51.928848 41.081013
## 68 69 70 71 72 73 74 75
## 36.353246 30.052249 34.150920 28.149231 32.051711 32.051711 30.052249 21.437584
## 76 78 79 80 81 82 83 84
## 34.150920 51.928848 93.129565 80.044305 88.599477 80.044305 68.408628 72.133286
## 85 86 87 88 89 90 91 92
## 76.010433 76.010433 54.952386 46.263168 36.353246 32.051711 26.339410 22.986681
## 93 94 95 96 97 98 99 100
## 38.662114 28.149231 30.052249 19.969305 19.969305 32.051711 14.846358 28.149231
## 101 102 103 104 105 106 107 108
## 16.020223 41.081013 11.714330 19.969305 38.662114 17.263481 10.791537 18.578899
## 109 110 111
## 26.339410 28.149231 16.020223df<-data.frame(estimados, regreso_unidades_originales); df## estimados regreso_unidades_originales
## 1 1.902285 14.846358
## 2 2.076388 21.437584
## 3 2.146029 24.619602
## 4 1.728182 9.925177
## 5 1.832644 12.696033
## 6 1.623721 7.640809
## 7 1.693362 9.112833
## 8 1.971926 17.263481
## 9 1.867464 13.739178
## 10 1.937106 16.020223
## 11 1.588900 6.976581
## 12 1.797823 11.714330
## 13 1.867464 13.739178
## 14 1.554080 6.357270
## 15 1.937106 16.020223
## 16 1.728182 9.925177
## 17 1.623721 7.640809
## 18 2.111208 22.986681
## 19 1.693362 9.112833
## 20 1.693362 9.112833
## 21 1.902285 14.846358
## 22 2.389773 38.662114
## 24 2.215670 28.149231
## 25 2.424593 41.081013
## 26 2.703157 64.832286
## 27 2.598696 54.952386
## 28 2.424593 41.081013
## 29 2.250490 30.052249
## 30 2.076388 21.437584
## 31 1.832644 12.696033
## 32 2.111208 22.986681
## 33 2.215670 28.149231
## 35 2.529055 49.033707
## 36 2.389773 38.662114
## 37 2.459414 43.613494
## 38 2.459414 43.613494
## 39 2.633516 58.108180
## 40 2.772799 72.133286
## 41 2.772799 72.133286
## 42 2.668337 61.400152
## 43 2.111208 22.986681
## 44 2.389773 38.662114
## 45 2.354952 36.353246
## 46 2.389773 38.662114
## 47 2.424593 41.081013
## 48 2.494234 46.263168
## 49 2.598696 54.952386
## 50 2.529055 49.033707
## 51 2.146029 24.619602
## 52 2.563875 51.928848
## 53 2.529055 49.033707
## 54 2.424593 41.081013
## 55 2.563875 51.928848
## 56 2.633516 58.108180
## 57 2.563875 51.928848
## 58 2.459414 43.613494
## 59 2.389773 38.662114
## 60 2.389773 38.662114
## 61 2.389773 38.662114
## 62 2.424593 41.081013
## 63 2.668337 61.400152
## 64 2.703157 64.832286
## 66 2.563875 51.928848
## 67 2.424593 41.081013
## 68 2.354952 36.353246
## 69 2.250490 30.052249
## 70 2.320131 34.150920
## 71 2.215670 28.149231
## 72 2.285311 32.051711
## 73 2.285311 32.051711
## 74 2.250490 30.052249
## 75 2.076388 21.437584
## 76 2.320131 34.150920
## 78 2.563875 51.928848
## 79 2.946901 93.129565
## 80 2.842440 80.044305
## 81 2.912081 88.599477
## 82 2.842440 80.044305
## 83 2.737978 68.408628
## 84 2.772799 72.133286
## 85 2.807619 76.010433
## 86 2.807619 76.010433
## 87 2.598696 54.952386
## 88 2.494234 46.263168
## 89 2.354952 36.353246
## 90 2.285311 32.051711
## 91 2.180849 26.339410
## 92 2.111208 22.986681
## 93 2.389773 38.662114
## 94 2.215670 28.149231
## 95 2.250490 30.052249
## 96 2.041567 19.969305
## 97 2.041567 19.969305
## 98 2.285311 32.051711
## 99 1.902285 14.846358
## 100 2.215670 28.149231
## 101 1.937106 16.020223
## 102 2.424593 41.081013
## 103 1.797823 11.714330
## 104 2.041567 19.969305
## 105 2.389773 38.662114
## 106 1.971926 17.263481
## 107 1.763003 10.791537
## 108 2.006747 18.578899
## 109 2.180849 26.339410
## 110 2.215670 28.149231
## 111 1.937106 16.020223predicion_uno<-(-0.430691+0.034821*80); predicion_uno # prediccion de un solo datos mod final## [1] 2.354989de_regreso<-(predicion_uno^(1/Lambda$ start)); de_regreso## [1] 36.35564Reporte del modelo
library(report)## Warning: package 'report' was built under R version 4.1.3report(mod4)## We fitted a linear model (estimated using OLS) to predict Ozone_Box with Temp
## (formula: Ozone_Box ~ Temp). The model explains a statistically significant and
## substantial proportion of variance (R2 = 0.61, F(1, 105) = 161.86, p < .001,
## adj. R2 = 0.60). The model's intercept, corresponding to Temp = 0, is at -0.43
## (95% CI [-0.85, -6.49e-03], t(105) = -2.01, p = 0.047). Within this model:
##
## - The effect of Temp is statistically significant and positive (beta = 0.03,
## 95% CI [0.03, 0.04], t(105) = 12.72, p < .001; Std. beta = 0.78, 95% CI [0.66,
## 0.90])
##
## Standardized parameters were obtained by fitting the model on a standardized
## version of the dataset. 95% Confidence Intervals (CIs) and p-values were
## computed using a Wald t-distribution approximation.report_model(mod4)## linear model (estimated using OLS) to predict Ozone_Box with Temp (formula: Ozone_Box ~ Temp)report_table(mod4)## Parameter | Coefficient | 95% CI | t(105) | p | Std. Coef. | Std. Coef. 95% CI | Fit
## -----------------------------------------------------------------------------------------------------
## (Intercept) | -0.43 | [-0.85, -0.01] | -2.01 | 0.047 | -3.11e-16 | [-0.12, 0.12] |
## Temp | 0.03 | [ 0.03, 0.04] | 12.72 | < .001 | 0.78 | [ 0.66, 0.90] |
## | | | | | | |
## AIC | | | | | | | 28.03
## BIC | | | | | | | 36.05
## R2 | | | | | | | 0.61
## R2 (adj.) | | | | | | | 0.60
## Sigma | | | | | | | 0.27