lab 1 · vectors (R) — source
A. Stamm 
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# ============================================================
# Lab 1: Vectors, subsetting & lists
# The R Statistical Language · Session 1
#
# Work through the exercises. Comment your thought process
# as you go: a reproducible script is one a stranger can read.
# ============================================================
## Part A: building vectors ---------------------------------
# A1. Build the numeric vector 1 4 7 10 13 ... up to 28 in three ways:
# (i) using c() literally,
# (ii) using seq(from, to, by),
# (iii) using 3 * (1:10) - 2 (a formula).
# Confirm all three are identical with == and all().
# (Hint: all(... == ...))
# A2. Build the character vector c("red","green","blue") and
# a logical vector of length 5 that alternates TRUE/FALSE.
# Use rep() for the logical one.
## Part B: vectorized arithmetic ---------------------------------
# B1. Heights (cm) and weights (kg) for 10 people:
height <- c(168, 177, 177, 177, 178, 172, 165, 171, 178, 170)
weight <- c(88, 72, 85, 52, 71, 69, 61, 61, 51, 75)
# Compute BMI = weight / (height/100)^2, element-wise.
# What is the mean and standard deviation of BMI?
# B2. Convert a Celsius vector c(0, 10, 20, 30) to Fahrenheit:
# F = C * 9/5 + 32 (vectorized).
## Part C: subsetting ---------------------------------
# C1. For x <- 1:100:
x <- 1:100
# - keep only the odd numbers;
# - keep only numbers divisible by 3;
# - keep numbers divisible by 3 OR 5;
# - keep numbers divisible by 3 or 5, but NOT both.
# (first use the modulo operator %%, then try filtering
# with setdiff() between the "or" and "and" results.)
# C2. For x <- c(10, 3, NA, 5, 8, 1, NA):
# - all non-missing values;
# - all even (non-missing) values. (Careful: %% on NA -> NA)
# C3. Named vector x <- c(abc = 1, def = 2, xyz = 5).
# Subset it with a character vector to get elements "xyz" and "def".
## Part D: distributions ---------------------------------
# D1. Sample 100 values from a Weibull distribution with
# shape 2 and scale 1. (?Weibull)
# Compute sum, mean, variance, sd, median, 25th & 75th
# percentiles, min, max.
# (Find the quantile function with help.search("quantile").)
# D2. Sample 5000 values from N(3, 2^2) using rnorm().
# Estimate P(X <= 0) two ways:
# (i) as the fraction of the sample <= 0 (mean of a logical),
# (ii) exactly with pnorm(0, 3, 2).
# How close are they? (Law of large numbers.)
## Part E: STRETCH (go further, only if the above felt easy) ----------
# E1. Recycling: what does c(1,2,3,4) + c(10,20) give? Explain in a
# comment. What warning does c(1,2,3) == c(1,2) produce, and why?
# E2. Write a one-liner that returns the products of the even numbers
# from 1 to 100 using modulo + logical subsetting (no loop).
# E3. A "Central Limit Theorem" appetiser: N <- 30; R <- 1000
# Start with m <- numeric(R), then for (i in 1:R) set
# m[i] <- mean(rexp(N)). Look at a histogram of m (hist(m)).
# Why does it look bell-shaped though the data are exponential?
# (We'll formalise this in Session 2.)
## Part F: lists ---------------------------------
# F1. Build a list of three vectors of lengths 10, 20 and 30, then
# compute the mean of each with lapply(), then again with sapply()
# and vapply(). What differs in the three returned values?
# F2. Make a list of two length-5 vectors. Use lapply() to double each
# element; store and inspect the result.
# F3. Subsetting: for x <- list(a = 1, b = "a", c = TRUE):
# - x["a"] vs x[["a"]] (what classes do you get?)
# - x$b vs x[["b"]]
# - x[[5]] vs x[["nope"]] (predict, then read each error)
# F4. Extend a list: x$d <- 1:3 and x[["e"]] <- "new".
# What happened to the list? Compare adding via $ vs [[.
# F5. Nested lists: l <- list(a = list(1, "x"), b = 2).
# Predict l$a[1], l$a[[1]], l[[1]][2], then check with the console.
# (This is exactly the pepper shaker metaphor from the slides.)