Key to assignment 11 

1.(a) glue <- factor(glue)
      coplot(strength<-thick|glue)

 
  (b) options(contrast="contr.treatment")

      reg101.sep<-lm(strength~glue/thick-1)
      reg101.samesl<-lm(strength~glue+thick)
      anova(reg101.samesl, reg101.sep)

      Conclusion: separate slopes NOT necessary.


  (c) summary(reg101.samesl)
      Different levels of glue do not have significant effect.

      Also, you can do following:

      reg101.same<-lm(strength~thick)
      anova(reg101.same, reg101.samesl)
      
      Therefore, separate intercepts are NOT necessary. This means

        strength ~ a + b*thick

      Both intercept and slope are significant.   
      
      
2.(a) glm2<-glm(disease ~ socio*age, family=binomial)
      summary(glm2)

      p-values are large. Try  

      glm3<-glm(disease ~ socio + age, family=binomial)  
      summary(glm3)  

      Fitted model:  
     
      log(p/(1-p)) = 2.63 - 1.56 sociomiddle - 2.84 socioupper - 0.10 age
 
      where p is probab of disease; sociomiddle is 1 if middle class, 
      0 otherwise; and socioupper is 1 if upperclass, 0 otherwise.

      p-value for coefficient of sociomiddle is 0.06. Should we drop it?

  (b) Try to expand the model. For example, quadratic term in age.
      Then use `anova' of the fit. Residual deviance does not change much 
      for the quadratice term.

      Try model reduction. Drop one variable and use `anova' to compare 
      smaller model with the bigger one.

      Final model is as in 2(a).
      
      As age increases, odds of getting disease decreases.
      
      For `socio', reference class is `lower'.
      odds for upper class is (significantly) less than lower class.