```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
library(rjags)
library(coda)
library(lattice)
library(caret)
```

## Introduction

In this report, bayesian logistic regression is fitted on the bank-note authentication dataset. This data set has 1372 samples of bank notes each having 4 features and 1 dependent variable (deciding if note is authentic or not).

This data were extracted from images that were taken from genuine and forged banknote-like specimens [1]. For digitization, an industrial camera usually used for print inspection was used. The final images have 400x 400 pixels. Due to the object lens and distance to the investigated object gray-scale pictures with a resolution of about 660 dpi were gained. Wavelet Transform tool were used to extract features from images.

The feature set is:

1. variance of Wavelet Transformed image (continuous)
2. skewness of Wavelet Transformed image (continuous)
3. curtosis of Wavelet Transformed image (continuous)
4. entropy of image (continuous)
5. class (integer)

## Data Preparation

```{r}
dat <- read.csv("data_banknote_authentication.txt", header = FALSE)
names(dat) <- c("Variance", "Skewness", "Curtosis", "Entropy", "Class")
sum(is.na(dat))
dat$Variance <- (dat$Variance - mean(dat$Variance))/sd(dat$Variance)
dat$Skewness <- (dat$Skewness - mean(dat$Skewness))/sd(dat$Skewness)
dat$Curtosis <- (dat$Curtosis - mean(dat$Curtosis))/sd(dat$Curtosis)
dat$Entropy <- (dat$Entropy - mean(dat$Entropy))/sd(dat$Entropy)
```

Data doesn't have any missing data. Each numeric predictor is
normalized to zero mean and unit variance.

```{r}
pairs(dat)
```

Skewness and Curtosis are negatively correlated. Variance and Entropy looks
positive correlated. Coorelated features may be capturing the same information and may not be the best feature for predictive model.

1. What is the null hypothesis when using ANOVA a. All the varianc...