In MATHSTATSOU/Intro2R: Introduction to R

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "ws#>",
  fig.align = "center",
  message = FALSE,
  warning = FALSE
)

# directory to Lab
dirdl <- system.file("Lab15",package = "Intro2R")

# create rmd link

library(Intro2R)

Introduction

This lab is a short one. It reviews simple linear regression. There are six questions to answer concerning seed germination.

The main emphasis of the lab is interpretation.

In this introduction I will emphasize the Bayesian methodology. You should understand both paradigms but be most conversant with the classical.

The data

The data comes from that supplied with the 5th edition of the book.

We will use a loess smoother to help understand the nature of the trend within the data. We will also use the plotly package to convert the ggplot to a plotly enhanced graphic so that on hover we can detect unusual points.

data(seed)
library(ggplot2)
library(plotly)
head(seed)
g <- ggplot(seed, aes(x = TEMP, y = CHANGE ))
g <- g + geom_point() + stat_smooth(method = "loess", formula = y ~ x)
ggplotly(g)

Interpretation of plot

The point corresponding to TEMP = 301 is away from the trend and likely an outlier. Otherwise the trend looks straight line and hence a SLR model would be appropriate after the 5th point is removed.

Bayesian analysis

We will use MCMCpack to create a sample from the posterior.

We will examine the histograms of the samples to see if the distributions have likely reached stationarity. Also we will inspect the plots to understand the skewness and modality of the distributions.

library(ggmcmc)
library(MCMCpack)
which(seed$TEMP==301.0)
seedn <- seed[-5,]

postn <-MCMCregress(formula = CHANGE ~ TEMP,data = seedn, burnin = 1000, mcmc = 10000,thin = 1)

s <- ggs(postn)
ggs_histogram(s)
sm <- summary(postn)
sm

The plots are in alphabetical order, and show symmetrical well formed uni-modal distributions for the beta parameters and a typical right skewed distribution for the variance.