The scores of 9 females and 10 males in some professional exam before and after a refresher training are given below where the first 9 entries in each case correspond to the female exam scores. before=c(51,54,61,54,49,54,46,47,43,86,28,45,59,49,56,69,51,74,42) after=c(58,65,86,77,74,59,46,50,37,82,37,51,56,53,90,80,71,88,43) (a) Define change-after-before. Assume a normal GLM for the response variable 'change'. Give an approximate 95% confidence interval for the mean change in score, assuming that it is not affected by sex or the 'before' score. [6] On the next 2 pages, the R output of various normal GLMs with the response variable 'change' and various combinations of the covariates 'sex' and 'before score' are given. Answer the following questions based on the output. (b) Write down the GLM corresponding to ModelD in the R output. Also provide interpretations of the parameters in the model, such as change in the average response for change in the covariates and so on. [14] (c) What is the design matrix for ModelD? [4] (d) Which of the other models are nested in ModelD? For those that are nested, identify the parameter constraints that they impose on ModelD. [8] (e) What do we mean by the null deviance? What is its numerical value for this GLM? [6] (f) Is there evidence of a difference between men and women in the 'before' hostility scores? Use one of the R outputs to answer. [6] (g) Start with ModelD and use the backward selection to investigate whether any interaction term is needed. Also provide the interpretation of the parameters as in Part (b) to describe the effects of the parameters
