# Class: Foundations of Statistics Using R
# Title: in-class exercises
# Session: 1
# Topic: Getting Started with R
# Last updated: 4/14/2015
### 1. ####
# (123 − 45)/4 + 4 × (72/2.34 − 3)
(123-45)/4 + 4 * (72/2.34 - 3)
## [1] 130.5769
# [1] 130.5769
### 2. ####
# abs(-88)
abs(-88)
## [1] 88
# [1] 88
### 3. ####
# log10(72)
log10(72)
## [1] 1.857332
# [1] 1.857332
#check the log function
10^1.857332 # ~ 72
## [1] 71.99992
# 4.
# e^1.45 − 2.612
#compute the exponetial function (the term exponential function is almost exclusively used as a shortcut for the natural exponential function ex, where e is Euler's number, a number (approximately 2.718281828) such that the function ex is its own derivative)
exp(1.45) - 2.612
## [1] 1.651115
# [1] 1.651115
# we could write our own:
# ~ (2.718281828 ^ 1.45 )- 2.612
(2.718281828 ^ 1.45 )- 2.612
## [1] 1.651115
# 5.
year_born = 1984
year_current = 2014
age = year_current - year_born
age
## [1] 30
# [1] 34
age >= 18
## [1] TRUE
# [1] TRUE
# 6.
# Area = pi * r^2
Area = 100
r = sqrt(Area/pi)
r
## [1] 5.641896
# [1] 5.641896
# 7.
# went to lunch and bill was $45.90
# compute following to two decimal places
# a) compute subtotal: add NYC tax of 8.875%
# b) compute 15% tip on subtotal
# c) compute 20% tip on subtotal
bill = 45.90
taxrate = 8.875
subtot = bill*(1+taxrate/100)
subtot
## [1] 49.97363
round(subtot,2)
## [1] 49.97
# 7a
# [1] 49.97
tip15 = subtot* 1.15
round(tip15, 2)
## [1] 57.47
# 7b
# [1] 57.47
tip20= subtot* 1.20
round(tip20, 2)
## [1] 59.97
# 7c
# [1] 59.97