Quiz 2.txt

# Quiz 2 -- More R Coding...

## This quiz covers competencies you should know by the first day of class.
## The first ten questions are intended to be basic.
## The final five questions are more advanced.
## An answer key will be provided by Monday, Aug 12.

## NOTE: Most students find it helpful to code in R using R-Studio.
## This involves installing R, and installing R-Studio, and then 
## running R-Studio. Google it if you run into problems, and 
## if Google can't answer your questions, feel free to email me.

# Load the Matching library, as described at the beginning of the prior quiz
# (Quiz 1). If you've never installed this Matching library before,
# you'll have to begin by doing so -- one way is to use use "install.packages()",
# but there are also 'point-and-click' ways to do it.
# So---the first step is to install the library, and the next step is to load it.

# The "Matching" library comes with a data set called 
# GerberGreenImai which relates to a series of published papers.
# You can see some of those papers if (after loading the library)
# you type:
?GerberGreenImai

# This command opens the help page for the data set. At the bottom of the help page,
# you'll see a list of 4 relevant published papers.

# To load the data set into working memory, type:
data(GerberGreenImai)

# To take a quick look at the data set, type:
head(GerberGreenImai)

# Question 1 (using "dim")
# What are the dimensions of the data set (how many rows and columns)?
dim(GerberGreenImai)  # rows: 10829 columns: 26

# Question 2 (using "names")
# What are the variable names?
names(GerberGreenImai)
# [1] "PERSONS"  "WARD"     "QUESTION" "MAILGRP"  "PHONEGRP" "PERSNGRP" "APPEAL"   "CONTACT"  "MAILINGS" "AGE"     
# [11] "MAJORPTY" "VOTE96.0" "VOTE96.1" "MAILCALL" "VOTED98"  "PHNSCRPT" "DIS.MC"   "DIS.PHN"  "PHN.C"    "PHNTRT1" 
# [21] "PHNTRT2"  "PHN.C1"   "PHN.C2"   "NEW"      "phone"    "AGE2"   

# Question 3 (using "is.na")
# Is there any missing data? If so, how many elements are missing 
# and which rows contain the missing data?
any(is.na(GerberGreenImai))  # False, which means no missing data.
sum(is.na(GerberGreenImai))  # how many elements are missing? Zero.

# Question 4 (using the "mode" function, or "is.factor")
# In this data set, each column is a variable (e.g., "AGE", "WARD", etc.). 
# Which of these variables (if any) is a factor? 
lapply(GerberGreenImai, is.factor)  # WARD is a factor

# Question 5 (using the "class" function)
# Code a for loop that outputs column name and variable type, per the below format:

# column name #1  variable type #1
# column name #2  variable type #2
# column name #3  variable type #3
# etc., etc., etc.,  type of each 
for (colname in names(GerberGreenImai)) {
  cat(colname, ":", class(GerberGreenImai[[colname]]), "\n")
}

# Question 6
# What do you think the variable AGE2 represents? 
# Looks like age squared divided by 100

# Question 7
# Which individuals (and how many) voted in 1998?
which(GerberGreenImai$VOTED98 == 1)  # Individual indices
sum(GerberGreenImai$VOTED98)  # Number of people

# Question 8
# Which individuals (and how many) have age > 35 and did NOT vote in 1998?
which(GerberGreenImai$AGE > 35 & GerberGreenImai$VOTED98 == 0)
sum(GerberGreenImai$AGE > 35 & GerberGreenImai$VOTED98 == 0)

# Question 9
# What line of code eliminates all rows that satisfy the conditions of Question 8?
GerberGreenImai[!(GerberGreenImai$AGE > 35 & GerberGreenImai$VOTED98 == 0), ]
# or
# subset(GerberGreenImai, !(GerberGreenImai$AGE > 35 & GerberGreenImai$VOTED98 == 0))

# Question 10
# Append a column that records a "1" if Question 8's conditions satisfy, 0 if not.
# Congrats, you just created a dummy variable! Google it if you have questions.
GerberGreenImai$myfirstdummy <- as.numeric(GerberGreenImai$AGE > 35 & GerberGreenImai$VOTED98 == 0)

### More advanced questions
# Question 11
# Write a function that performs the algorithm you identified in Question 6.
algo1 <- function(age) {return((age^2)/100)}
# and then try algo1(9) 
# or try algo1(20) or whatever...

# Question 12
# Run a regression w/ AGE2 and AGE as dependent and independent vars (respectively).
# Do you get statistically significant results? Is there something causal going on?
# Does the model make predictions that are not possible in the real world? Explain.
lm.age <- lm(AGE2 ~ AGE, data=GerberGreenImai)
summary(lm.age)
# We get statistically significant results. There's no causation proper here since AGE2
# is calculated directly from AGE. The model does make impossible predictions since the intercept is negative.
# If AGE is zero, AGE2 will be -24.9. 

# Question 13 (hint: see the help page for "formula")
# Consider the following code:
reg1 <- lm(PHN.C1 ~ PERSONS + VOTE96.1 + NEW + MAJORPTY + AGE + 
             WARD + I(PERSONS*VOTE96.1), data=GerberGreenImai[c(1:1000),])
# you can then type something like "summary(reg1)"...

# This regression predicts whether or not a subject received a get-out-the-vote
# phone call based on the first 1000 observations. 

# What is meant by I(PERSONS*VOTE96.1)? Use the resulting regression
# model to make a prediction for individuals in rows 1001 and 1002. Do these 
# predictions make sense? Why or why not?

# It is an interaction term between the number of person in the household and whether 
# they voted in 1996. Namely, the effect of both factors together in influencing the outcome
# prediction that is not explained by the factors in isolation.
testdata <- GerberGreenImai[c(1001:1002),]
predict(reg1, testdata)  
# These predictions make sense if they are interpreted as
# probabilities of having received a phone call.

# Question 14
# Consider the "WARD" variable. Observe the first 20 elements.
# What happens when you perform arithmetic or statistical operations on these
# elements? Why? Provide intuition for the result you obtain.
GerberGreenImai$WARD[1:20]
mean(GerberGreenImai$WARD) # argument is not numeric or logical: returning NA
# R does not interpret the WARD variable as a number since it is coded as a factor.
# hence, it returns errors if we try to perform some operations over this variable.

# Question 15
# Write code that takes the "WARD" variable and creates dummy variables for
# each individual ward. We can call this "dummy-fying" a categorical variable.
for (lvl in levels(GerberGreenImai$WARD)) {
  GerberGreenImai[[lvl]] <- GerberGreenImai$WARD == lvl
}

# Given your answer to Question 14, do you see why you would want to "dummy-fy" 
# this variable prior to performing statistical analysis on it (and
# variables likes this one)?

# We dummify since there is no sensible way to translate difference categories
# of a factor variable into numbers that can be statistically analyzed. When we 
# dummify, we are able to isolate the effect of being part of a certain category or not.