R Markdown Tutorial

Step One: Load libraries and transformation functions

#ANOVA Workflow
library(ggplot2)
library(plyr)

#data transformation section
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)}

Step Two: Import the data

data("faithful")
head(faithful)
##   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
summary(faithful) #mean, median, min
##    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
str(faithful)
## '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 ...

Step Three: Inspect the data distributions

hist(faithful$eruptions)
Figure: Histogram of eruption time form the faithful dataset.

Figure: Histogram of eruption time form the faithful dataset. 

qqnorm(faithful$eruptions)
qqline(faithful$eruptions)
Figure: QQ_Norm plot of eruptions from the faithful dataset.

Figure: QQ_Norm plot of eruptions from the faithful dataset. 

plot(faithful$waiting ~ faithful$eruptions)
Figure: Dotplot of length of eruptions vs. length of waiting time between eruptions from the faithful dataset.

Figure: Dotplot of length of eruptions vs. length of waiting time between eruptions from the faithful dataset.

Step Four: Transformation needed?

faithful$eruptionstran <- -1/(faithful$eruptions)^3

qqnorm(faithful$eruptionstran)
qqline(faithful$eruptionstran)
Figure: Inverse Cubed Transformation QQ-Norm Plot of Eruptions from Faithful Dataset.

Figure: Inverse Cubed Transformation QQ-Norm Plot of Eruptions from Faithful Dataset.

Step Five: Run the ANOVA model

LM1 <- lm(eruptions ~ waiting, data = faithful)
plot(LM1)
Figure: Diagnostic plots for untransformed data for Eruptions vs. Time Waiting

Figure: Diagnostic plots for untransformed data for Eruptions vs. Time Waiting

Figure: Diagnostic plots for untransformed data for Eruptions vs. Time Waiting

Figure: Diagnostic plots for untransformed data for Eruptions vs. Time Waiting

Figure: Diagnostic plots for untransformed data for Eruptions vs. Time Waiting

Figure: Diagnostic plots for untransformed data for Eruptions vs. Time Waiting

Figure: Diagnostic plots for untransformed data for Eruptions vs. Time Waiting

Figure: Diagnostic plots for untransformed data for Eruptions vs. Time Waiting 

summary(LM1)
## 
## Call:
## lm(formula = eruptions ~ waiting, data = faithful)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.29917 -0.37689  0.03508  0.34909  1.19329 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -1.874016   0.160143  -11.70   <2e-16 ***
## waiting      0.075628   0.002219   34.09   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4965 on 270 degrees of freedom
## Multiple R-squared:  0.8115, Adjusted R-squared:  0.8108 
## F-statistic:  1162 on 1 and 270 DF,  p-value: < 2.2e-16

Step Six: Plot the results

plott <- ggplot(faithful, aes(x=eruptions, y=waiting))

plott + geom_point(size=0.8, colour="palevioletred2") + ylab("time waiting for eruptions (min)") + xlab("length of eruption (min)") + ggtitle("Time Between Eruptions and the Duration of Old Faithful Eruptions") + theme(panel.background = element_rect(fill = 'slategray1', colour = 'black'))
Figure: Length of eruption and time before an eruption from Old Faithful Geyser

Figure: Length of eruption and time before an eruption from Old Faithful Geyser