> #######
> # Blood Pressure and Heart Disease
> #######
> 
> y1 <- c(3,17,12,16,12,8,16,8)
> y2 <- c(153,235,272,255,127,77,83,35)
> 
> y <- cbind(y1,y2)
> x <- c(111.5,121.5,131.5,141.5,151.5,161.5,176.5,191.5)
> 
> g1 <- glm(y~x,fam=binomial)
> summary(g)

Call:
glm(formula = y ~ x, family = binomial)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-1.0617  -0.5977  -0.2245   0.2140   1.8501  

Coefficients:
             Estimate Std. Error z value Pr(>|z|)    
(Intercept) -6.082031   0.724091  -8.400   <2e-16 ***
x            0.024338   0.004842   5.026    5e-07 ***
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 30.0226  on 7  degrees of freedom
Residual deviance:  5.9092  on 6  degrees of freedom
AIC: 42.61

Number of Fisher Scoring iterations: 3

> 1-pchisq(5.9092,6)
[1] 0.4334381

########
#  I fit a logistic model with x (blood pressure) as the redictor variable.
#  The fitted mode is 
#  log(p/(1-p))=-6.082+0.0243 x
#  The residual deviance is 5.909 based on 6 degrees of freedom which indicates
#  the fit is good. 
#  The independent model is not good since the null deviance is 30.02 based on 7 degrees of freedom.
#  The goodness of the fit can be read from the last p-value reported. If the p-value is less than 0.05
#  then, the fit is not good.
#########
# Next I compute the Pearson chisq goodness of fit and its p-value.
#########

> ######
> # Goodness of Fit
> ######
> # Pearson chi-square: 
> ######
> 
> y.total <- apply(y,1,sum)
> y.pred <- cbind(g1$fit*y.total,(1-g1$fit)*y.total)
> 
> pearson.chisq <- sum((y-y.pred)^2/y.pred)
> pearson.chisq
[1] 6.289936
> 1-pchisq(6.2899,6)
[1] 0.3915111

#########
# It also indicates the fit is good.
#########

> #####
> # loglikelihood ratio Chi-square
> #####
> 
> loglikelihood.chisq <- 2*sum(y*log(y/y.pred))
> loglikelihood.chisq
[1] 5.909158

######
# It is exactly the residuce deviance.
######

> #######
> # O-rings 
> #######
> 
> orings <- read.table("u:\\stat526\\dataset\\ascdata\\orings.txt",h=T)
> g2 <- glm(cbind(damage,6-damage)~temp,fam=binomial,data=orings)
> summary(g2)

Call:
glm(formula = cbind(damage, 6 - damage) ~ temp, family = binomial, 
    data = orings)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-0.9529  -0.7345  -0.4393  -0.2079   1.9565  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept) 11.66299    3.29575   3.539 0.000402 ***
temp        -0.21623    0.05317  -4.067 4.76e-05 ***
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 38.898  on 22  degrees of freedom
Residual deviance: 16.912  on 21  degrees of freedom
AIC: 33.675

Number of Fisher Scoring iterations: 5

> 1-pchisq(16.912,21)
[1] 0.7164267

##############
# The fit is also good.
#############