R Markdown Basics and Old Faithful

Step 1: Loading the data set and preparing transformation functions

Loading Faithful data

data("faithful") #registers data for the Old Faithful dataset
str(faithful) #describes structure of OF data

## 'data.frame':    272 obs. of  2 variables:
##  $ eruptions: num  3.6 1.8 3.33 2.28 4.53 ...
##  $ waiting  : num  79 54 74 62 85 55 88 85 51 85 ...

summary(faithful) #summarizes data

##    eruptions        waiting    
##  Min.   :1.600   Min.   :43.0  
##  1st Qu.:2.163   1st Qu.:58.0  
##  Median :4.000   Median :76.0  
##  Mean   :3.488   Mean   :70.9  
##  3rd Qu.:4.454   3rd Qu.:82.0  
##  Max.   :5.100   Max.   :96.0

head(faithful) #gives first few data points of OF. Should have two columns

##   eruptions waiting
## 1     3.600      79
## 2     1.800      54
## 3     3.333      74
## 4     2.283      62
## 5     4.533      85
## 6     2.883      55

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Transformation function object assignments

#Loading necessary packages
library(ggplot2)
library(plyr)

#Potential transformation functions
Cube.Tns <- function (x) { x ^ 3 }
Square.Tns <- function (x) { x ^ 2 }
Raw.Tns <- function (x) { x }
Sqrt.Tns <- function (x) { sqrt(x) }
Log.Tns <- function (x) { log10(x + 0.00001) }
RecipRoot.Tns <- function (x) { -1 / sqrt(x) }
Recip.Tns <- function (x) { -1 / (x) }
InvSquare.Tns <- function (x) { -1 / (x ^ 2) }

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Step 2: Transforming and analyzing data

Inspecting Data Distributions

hist(faithful$waiting) 

Figure 1: Histogram of waiting time from the Faithful data set.

hist(faithful$eruptions)

Figure 2: Histogram of eruption length from the Faithful data set.

qqnorm(faithful$waiting)
qqline(faithful$waiting)

Figure 3: Q-Q Plot for waiting length

qqnorm(faithful$eruptions)
qqline(faithful$eruptions)

Figure 4: Q-Q Plot for eruption time

This data does not look very statistically sound, so I am going to run a log transformation to see if that makes it look any better. Woo!

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Transforming the data

faithful$waitingLOG <- Log.Tns(faithful$waiting)
qqnorm(faithful$waitingLOG)
qqline(faithful$waitingLOG)

Figure 5: Q-Q plot of logarithmic transformation of waiting time

faithful$eruptionsLOG <- Log.Tns(faithful$eruptions)
qqnorm(faithful$eruptionsLOG)
qqline(faithful$eruptionsLOG)

Figure 6: Q-Q plot of logarithmic transformation of eruption time

Better? Debatable!

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Linear Model

LinMod <- lm(waitingLOG~eruptionsLOG, data = faithful)
plot(LinMod)

Diagnostic plots for linear model of waiting time by eruptions

Diagnostic plots for linear model of waiting time by eruptions

Diagnostic plots for linear model of waiting time by eruptions

Diagnostic plots for linear model of waiting time by eruptions

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Step 3: Graphing the data in a scatter plot

FinalGraph <- ggplot(faithful, aes(x=waitingLOG, y=eruptionsLOG))
FinalGraph + geom_point(shape=1) +    # Use hollow circles
    geom_smooth(method=lm) +   #linear regression line, shading 95% confidence level
    theme_classic() +
  labs(title = "Eruption duration by waiting time" ,
       x = "Logarithmic transformation of waiting time (minutes)" ,
       y = "Logarithmic transformation of euption time (minutes)") #labels axes and gives title 

Figure 11: final scatter plot with transformed data and a best-fit line