代做STAT 4/6C03作业、代写R编程作业、代做Dropbox作业、代写R语言留学生作业
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.
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