这是一篇来自澳洲的关于现代应用统计代写作业案例分享，以下是作业具体内容：

Note: There is no unique answer for this problem. The report for this problem should be typed. Hand-written report or report including screen-captured R codes or fifigures won’t be marked. An example report written by a student previous year has been posted on LMS.

Data: The dataset comes from the Fiji Fertility Survey and shows data on the number of children ever born to married women of the Indian race classifified by duration since their fifirst marriage(grouped in six categories), type of place of residence (Suva, urban, and rural), and educational level (classifified in four categories: none, lower primary, upper primary, and secondary or higher).

The data can be found in the fifile assignment2 prob1.txt. The dataset has 70 rows representing 70 groups of families. Each row has entries for:

• duration: marriage duration of mothers in each group (years),
• residence: residence of families in each group (Suva, urban, rural),
• education: education of mothers in each group (none, lower primary, upper primary, secondary+),
• nChildren: number of children ever born in each group (e.g. 4), and
• nMother: number of mothers in each group (e.g. 8).

We can summarise data as a table as follows.

> data\$duration <- factor(data\$duration, levels=c(“0-4″,”5-9″,”10-14″,”15-19″,”20-24″,”25-29”)

> , ordered=TRUE)

> data\$residence <- factor(data\$residence, levels=c(“Suva”, “urban”, “rural”))

> data\$education <- factor(data\$education, levels=c(“none”, “lower”, “upper”, “sec+”))

> ftable(xtabs(cbind(nChildren,nMother) ~ duration + residence + education, data))

nChildren nMother

duration residence education

0-4 Suva none 4 8

lower 24 21

upper 38 42

sec+ 37 51

urban none 14 12

lower 23 27

upper 41 39

sec+ 35 51

rural none 60 62

lower 98 102

upper 104 107

sec+ 35 47

5-9 Suva none 31 10

lower 80 30

upper 49 24

sec+ 38 22

urban none 59 13

lower 98 37

upper 118 44

sec+ 48 21

rural none 171 70

lower 317 117

upper 200 81

sec+ 47 21

10-14 Suva none 49 12

lower 99 27

upper 58 20

sec+ 24 12

urban none 75 18

lower 143 43

upper 105 29

sec+ 50 15

rural none 364 88

lower 546 132

upper 197 50

sec+ 30 9

15-19 Suva none 59 14

lower 153 31

upper 41 13

sec+ 11 4

urban none 108 23

lower 225 42

upper 92 20

sec+ 19 5

rural none 577 114

lower 481 86

upper 135 30

sec+ 2 1

20-24 Suva none 118 21

lower 91 18

upper 47 12

sec+ 13 5

urban none 118 22

lower 147 25

upper 65 13

sec+ 16 3

rural none 756 117

lower 431 68

upper 132 23

sec+ 5 2

25-29 Suva none 310 47

lower 182 27

upper 43 8

sec+ 2 1

urban none 300 46

lower 338 45

upper 98 13

sec+ 0 0

rural none 1459 195

lower 461 59

upper 58 10

sec+ 0 0

Problem: We want to determine which factors (duration, residence, education) and two-way interactions are related to the number of children per woman (fertility rate). The observed number of children ever born in each group (nChildren) depends on the number of mothers (nMother) ineach group. We must take account of the difffference in the number of mothers (hint: one of the lab problems shows how to handle this issue). Write a report on the analysis that should summarie the substantive conclusions and include the highlights of your analysis: for example, data visualisation,choice of model (e.g., Poisson, binomial, gamma, etc), model fifitting and model  selection (e.g., using AIC), diagnostic, check for overdispersion if necessary, and summary/interpretation of your fifinal model.

At each step of you analysis, you should write why you do that and your interpretation/conclusion.

For example, “I make an interaction plot to see whether there are interactions between X and Y”,show a plot, and “It seems that there are some interaction between X and Y”.