Kutner14.11

library(ggplot2)

lines <- 
    "deposit sold returned
    2.0  500.0   72.0
    5.0  500.0  103.0
   10.0  500.0  170.0
   20.0  500.0  296.0
   25.0  500.0  406.0
   30.0  500.0  449.0"
con <- textConnection(lines)
bottles <- read.csv(con, sep="")

fit <- glm(formula = cbind(returned, sold - returned) ~ deposit, family = binomial, 
    data = bottles)
summary(fit)

## 
## Call:
## glm(formula = cbind(returned, sold - returned) ~ deposit, family = binomial, 
##     data = bottles)
## 
## Deviance Residuals: 
##       1        2        3        4        5        6  
##  0.1754   0.4330   0.5784  -2.9193   1.2710   1.2209  
## 
## Coefficients:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -2.076565   0.084839  -24.48   <2e-16 ***
## deposit      0.135851   0.004772   28.47   <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: 1108.171  on 5  degrees of freedom
## Residual deviance:   12.181  on 4  degrees of freedom
## AIC: 53.419
## 
## Number of Fisher Scoring iterations: 3

exp(confint(fit))

## Waiting for profiling to be done...

##                 2.5 %    97.5 %
## (Intercept) 0.1059309 0.1477395
## deposit     1.1349710 1.1564067

logit <- function(x){log(x/(1-x))}
qplot(deposit, returned/sold, data=bottles)

qplot(deposit, logit(returned/sold), data=bottles)

bottles$linear.predictors <- fit$linear.predictors
qplot(deposit, linear.predictors, data=bottles)

ggplot(bottles, aes(deposit)) + 
  geom_point(aes(y=returned/sold)) +
  geom_line(aes(y=plogis(linear.predictors), colour="Prediction"))