代做STAT 4/6C03、代写R编程、代做Dropbox、代写R语言留学生

日期：2018-10-25 10:01

Midterm exam, STAT 4/6C03

released 17 October 2018, due 24 October 2018

Rules:

You may use any notes or books, but not web resources other than the course web

site. Please do not speak (text, e-mail, etc.) with any one other than me about the

exam. Please feel free to contact me for clarification.

The exam is due in Dropbox by midnight on (i.e., at the end of) Wednesday 24 October.

Please submit your solutions as a single .R, .Rmd, or .Rnw file, with descriptions

and explanations as comments.

Data are available from the course web page.

When in doubt, show how you did something and explain your approach. (e.g., if I

say “do X . . . ”, I want you to include the code that you used.) Your solution should

include working R code (points off for anything that doesn’t work when I try it!) and

an explanation of what you did.

1 Titanic

The classic data set on survivors of the Titanic.

Read in the titanic long binary.csv data set: the variables are

Class: passenger class (1st/2d/3d) or crew

Sex: male or female

Age: age in years

survived: whether a particular individual survived or not.

1. using aggregate from base R or group by + summarise from the dplyr package,

create a new data set that has Class, Sex, Age and two additional columns: prop

(proportion survived) and total (total number in the category). You can compare

your results to the titanic long.csv data set (if you have trouble with this step,

you can use titanic long in the next part of the question).

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2. using ggplot2 and some combination of colour, point shape, facets, and y-axis position,

plot the proportion survived as a function of all three explanatory variables

(class, sex, age), in a single plot (multiple sub-plots/facets are OK).

3. Going back to the original, disaggregated data set for this and following questions: Define

a set of custom contrasts for the Class variable that will define the parameters as

β0=overall average across classes; β1=crew vs passengers (1st, 2nd, 3rd); β2=1st vs

(2nd and 3rd); β3 = 2nd vs 3rd.

4. Fit a logistic regression including all of the two-way interactions, using sum-to-zero

contrasts for all parameters.

5. What does the Age1:Class3 coefficient mean? Why is it NA?

6. What do the Age1:Class1 and Age1:Class2 coefficients mean? Interpret the

magnitude and sign of the coefficients.

7. Run car::Anova on the model with test="LR" and test="Wald". Explain the

meaning of these two kinds of tests. Which p-values differ (e.g. a difference between

p  0.01 and p > 0.05), and why? Which of these two sets of results should you trust

more, and why?

8. Fit a logistic regression with the main effects of the three predictor variables only.

9. Compute the estimated odds ratio for female survival vs. average survival, and its

95% confidence intervals.

10. Compute the estimated probability of survival for a 1st-class passenger, and its 95%

confidence intervals (use Wald intervals on the logit scale, then back-transform to the

probability scale).

11. Based on the reduced (main effects only) model, interpret the meaning of each of

the parameters in summary() (sign and statistical significance only; interpretation

of the magnitude of the parameters is optional).

2 Income

The following question analyzes a data set on adult incomes from the UCI machine learning

repository. Run the following R code to retrieve data on income categories in adults

and simplify it:

## download.file("https://archive.ics.uci.edu/ml/machine-learning-databases/adult/adult.data",dest="adult.csv")

library(dplyr)

adult <- read.csv("adult.csv",header=FALSE,strip.white=TRUE,

stringsAsFactors=FALSE)

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nms <- c("age","workclass","fnlwgt","education","education.num",

"marital.status","occupation","relationship","race","sex",

"capital.gain","capital.loss","hours.per.week","native.country",

"income")

names(adult) <- nms

adult2 <- (adult

## keep a subset of explanatory variables

%>% select(age,education.num,marital.status,race,sex,

native.country,income)

## US only

%>% filter(native.country=="United-States")

## we don't need the native.country variable any more, drop it

%>% select(-native.country)

## select only races with >500 observations

%>% group_by(race)

%>% filter(n()>500)

## select only marital status categories with >500 observations

%>% group_by(marital.status)

%>% filter(n()>1000)

%>% ungroup()

## convert all character variables to factors

%>% mutate_if(is.character,factor)

)

The data contain

age: age in years

education.num: number of years of education

marital status: description of marital status

race: Black or White

sex: Female or Male

income: less than or greater than US$50,000 (this is the response variable)

1. create a variable income.num within the data frame that is 0 for income < $50, 000

and 1 for income ≥ $50, 000

2. for the three categorical predictor variables, use aggregate or dplyr functions to

compute the univariate summaries of the probabilities in each category of having

income ≥ $50, 000.

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3. for the two continuous predictor variables age and education.num, use ggplot to

plot income.num with points along with a smooth function of the predictor

4. Fit a logistic regression including quadratic effects of age (use poly(age,2) so

that the linear and quadratic terms are treated together in the following steps), linear

effects of education, all three categorical predictors, and all of the two-way interactions

among poly(age,2), education.num, and the three categorical predictors

(the resulting model will have 27 total parameters).

5. Use drop1 to run a likelihood ratio test on all of the interaction terms in the model.

Pick one of the statistically significant interactions; for one of the parameters associated

with this interaction (there may be only one), explain what the sign and magnitude

of the parameter mean in terms of the differences in log-odds of having an

income ≥ $50, 000 between particular groups (e.g. “the difference in log-odds between

males and females decreases by (amount) when age increases by 1 year”, or

“the log-odds difference between Blacks and Whites is (amount) greater in males

than for the population as a whole”).

6. Use your model to compute the probability that a 50-year-old, Divorced, White Male

with 12 years of education will have an income > $50, 000.

7. Compute 95% quantile bootstrap confidence intervals for the predicted value from

the previous question. (Reminder: for each bootstrap replicate you’ll need to (1) create

a new data set with observations resampled with replacement from the original

data set; (2) re-fit (update) the original fitted model to use the bootstrapped data; (3)

compute and save the predicted value.) Since this may be a little slow, you can limit

your computation to 100 bootstrap replicates.