Untitled

Ejercicio 13.3

Se está estudiando la resistencia a la compresión de un sujetador de aleación utilizado en la construcción de aviones.Se seleccionaron diez cargas en el rango de 2500 a 4300 psi y Se probaron varios sujetadores en esas cargas. Se registró el número de sujetadores que fallaron en cada carga. Se muestran los datos completos de la prueba abajo.

Tabla de datos

Ajuste un modelo de regresión logística a los datos. Utilice un modelo de regresión lineal simple como estructura para el predictor lineal.

b.¿La desviación del modelo indica que el modelo de regresión logística de la parte a es adecuado?

c.Expanda el predictor lineal para incluir un término cuadrático. ¿Hay alguna evidencia de que este término cuadrático sea requerido en el modelo?

d.Para el modelo cuadrático de la parte c, encuentre estadísticas de Wald para cada parámetro de modelo individual.

e.Encuentre intervalos de confianza aproximados del 95% en los parámetros del modelo para el modelo cuadrático de la parte c.

Solución:

Load<-c(2500,2700,2900,3100,3300,3500,3700,3900,4100,4300)
sample<-c(50,70,100,60,40,85,90,50,80,65)
failling<-c(10,17,30,21,18,43,54,33,60,51)

library(GLMsData);

####

Load<-c(2500,2700,2900,3100,3300,3500,3700,3900,4100,4300)
sample<-c(50,70,100,60,40,85,90,50,80,65)
failling<-c(10,17,30,21,18,43,54,33,60,51)

lista<-cbind(Load,sample,failling)
datos<-as.data.frame(lista)
datos

##    Load sample failling
## 1  2500     50       10
## 2  2700     70       17
## 3  2900    100       30
## 4  3100     60       21
## 5  3300     40       18
## 6  3500     85       43
## 7  3700     90       54
## 8  3900     50       33
## 9  4100     80       60
## 10 4300     65       51

attach(datos)

## The following objects are masked _by_ .GlobalEnv:
## 
##     failling, Load, sample

#pag 335

forma1 <- glm( failling/sample ~ Load, family=binomial(link = "logit"),
               weights=sample, data=datos)
summary(forma1)

## 
## Call:
## glm(formula = failling/sample ~ Load, family = binomial(link = "logit"), 
##     data = datos, weights = sample)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -0.29475  -0.11129   0.04162   0.08847   0.35016  
## 
## Coefficients:
##               Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -5.3397115  0.5456932  -9.785   <2e-16 ***
## Load         0.0015484  0.0001575   9.829   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 112.83207  on 9  degrees of freedom
## Residual deviance:   0.37192  on 8  degrees of freedom
## AIC: 49.088
## 
## Number of Fisher Scoring iterations: 3

forma2 <- glm( failling/sample ~ Load, family=binomial(link = "cloglog"),
               weights=sample, data=datos)

forma3 <- glm( failling/sample ~ Load, family=binomial(link = "probit"),
               weights=sample, data=datos,control=list(trace=TRUE) )

## Deviance = 0.43738 Iterations - 1
## Deviance = 0.4373459 Iterations - 2
## Deviance = 0.4373459 Iterations - 3

forma5<- glm( cbind(failling, sample-failling) ~ Load,
                        family=binomial, data=datos,control=list(trace=TRUE) )

## Deviance = 0.3720094 Iterations - 1
## Deviance = 0.3719169 Iterations - 2
## Deviance = 0.3719169 Iterations - 3

coef(forma1)

##  (Intercept)         Load 
## -5.339711512  0.001548434

coef(forma5)

##  (Intercept)         Load 
## -5.339711512  0.001548434

coef(forma2)

##  (Intercept)         Load 
## -4.191745285  0.001094139

coef(forma3)

##   (Intercept)          Load 
## -3.2712087961  0.0009488532

##
summary(forma1)

## 
## Call:
## glm(formula = failling/sample ~ Load, family = binomial(link = "logit"), 
##     data = datos, weights = sample)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -0.29475  -0.11129   0.04162   0.08847   0.35016  
## 
## Coefficients:
##               Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -5.3397115  0.5456932  -9.785   <2e-16 ***
## Load         0.0015484  0.0001575   9.829   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 112.83207  on 9  degrees of freedom
## Residual deviance:   0.37192  on 8  degrees of freedom
## AIC: 49.088
## 
## Number of Fisher Scoring iterations: 3

summary(forma5)

## 
## Call:
## glm(formula = cbind(failling, sample - failling) ~ Load, family = binomial, 
##     data = datos, control = list(trace = TRUE))
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -0.29475  -0.11129   0.04162   0.08847   0.35016  
## 
## Coefficients:
##               Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -5.3397115  0.5456932  -9.785   <2e-16 ***
## Load         0.0015484  0.0001575   9.829   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 112.83207  on 9  degrees of freedom
## Residual deviance:   0.37192  on 8  degrees of freedom
## AIC: 49.088
## 
## Number of Fisher Scoring iterations: 3

coefficients(forma5)

##  (Intercept)         Load 
## -5.339711512  0.001548434

confint(forma5)

## Waiting for profiling to be done...

## Deviance = 0.6190478 Iterations - 1
## Deviance = 0.6190477 Iterations - 2
## Deviance = 0.6190477 Iterations - 3
## Deviance = 1.350781 Iterations - 1
## Deviance = 1.350781 Iterations - 2
## Deviance = 1.350781 Iterations - 3
## Deviance = 2.552616 Iterations - 1
## Deviance = 2.552616 Iterations - 2
## Deviance = 2.552616 Iterations - 3
## Deviance = 4.210077 Iterations - 1
## Deviance = 4.210077 Iterations - 2
## Deviance = 4.210077 Iterations - 3
## Deviance = 6.308761 Iterations - 1
## Deviance = 6.30876 Iterations - 2
## Deviance = 6.30876 Iterations - 3
## Deviance = 8.834382 Iterations - 1
## Deviance = 8.834382 Iterations - 2
## Deviance = 8.834382 Iterations - 3
## Deviance = 0.6238617 Iterations - 1
## Deviance = 0.6238616 Iterations - 2
## Deviance = 0.6238616 Iterations - 3
## Deviance = 1.389269 Iterations - 1
## Deviance = 1.389269 Iterations - 2
## Deviance = 1.389269 Iterations - 3
## Deviance = 2.682377 Iterations - 1
## Deviance = 2.682377 Iterations - 2
## Deviance = 2.682377 Iterations - 3
## Deviance = 4.517212 Iterations - 1
## Deviance = 4.517212 Iterations - 2
## Deviance = 4.517212 Iterations - 3
## Deviance = 6.907517 Iterations - 1
## Deviance = 6.907517 Iterations - 2
## Deviance = 0.6238197 Iterations - 1
## Deviance = 0.6238196 Iterations - 2
## Deviance = 0.6238196 Iterations - 3
## Deviance = 1.388933 Iterations - 1
## Deviance = 1.388933 Iterations - 2
## Deviance = 1.388933 Iterations - 3
## Deviance = 2.681244 Iterations - 1
## Deviance = 2.681244 Iterations - 2
## Deviance = 2.681244 Iterations - 3
## Deviance = 4.514532 Iterations - 1
## Deviance = 4.514531 Iterations - 2
## Deviance = 4.514531 Iterations - 3
## Deviance = 6.902297 Iterations - 1
## Deviance = 6.902296 Iterations - 2
## Deviance = 0.6190895 Iterations - 1
## Deviance = 0.6190895 Iterations - 2
## Deviance = 0.6190895 Iterations - 3
## Deviance = 1.351115 Iterations - 1
## Deviance = 1.351114 Iterations - 2
## Deviance = 1.351114 Iterations - 3
## Deviance = 2.553737 Iterations - 1
## Deviance = 2.553737 Iterations - 2
## Deviance = 2.553737 Iterations - 3
## Deviance = 4.212721 Iterations - 1
## Deviance = 4.212721 Iterations - 2
## Deviance = 4.212721 Iterations - 3
## Deviance = 6.313897 Iterations - 1
## Deviance = 6.313897 Iterations - 2
## Deviance = 8.843204 Iterations - 1
## Deviance = 8.843204 Iterations - 2

##                    2.5 %       97.5 %
## (Intercept) -6.430606344 -4.289373629
## Load         0.001245115  0.001863257

vcov(forma5)

##               (Intercept)          Load
## (Intercept)  2.977811e-01 -8.497023e-05
## Load        -8.497023e-05  2.481820e-08

#
library(ResourceSelection)

## ResourceSelection 0.3-5   2019-07-22

hoslem.test(forma5$y, forma5$fitted)

## 
##  Hosmer and Lemeshow goodness of fit (GOF) test
## 
## data:  forma5$y, forma5$fitted
## X-squared = 0.0055883, df = 8, p-value = 1

###3

forma1 <- glm( failling/sample ~ log(Load) + (log(Load))^2, family=binomial(link = "logit"),
               weights=sample, data=datos , control = list(trace=TRUE))

## Deviance = 1.363322 Iterations - 1
## Deviance = 1.361951 Iterations - 2
## Deviance = 1.361951 Iterations - 3

vcov(forma1)

##             (Intercept)  log(Load)
## (Intercept)   18.568840 -2.2832959
## log(Load)     -2.283296  0.2808665

summary(forma1)

## 
## Call:
## glm(formula = failling/sample ~ log(Load) + (log(Load))^2, family = binomial(link = "logit"), 
##     data = datos, weights = sample, control = list(trace = TRUE))
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -0.52946  -0.11592  -0.07591   0.28265   0.60107  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  -42.111      4.309  -9.772   <2e-16 ***
## log(Load)      5.177      0.530   9.769   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 112.832  on 9  degrees of freedom
## Residual deviance:   1.362  on 8  degrees of freedom
## AIC: 50.078
## 
## Number of Fisher Scoring iterations: 3

coefficients(forma1)

## (Intercept)   log(Load) 
##  -42.110558    5.177246

Untitled

David ortega

2023-01-30

Ejercicio 13.3