---
title: "Topic 1. Introduction to Analytics"
author: "EW (Jed) Frees"
date: "16 November 2024"
output: html_document
---
  
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

#  Example 2.3.1. Under- and Over-Fitting. From Loss Data Analytics

```{r eval = FALSE}

# Generate the Data
rmse <- Metrics::rmse
n <- 100
set.seed(1234)
u <- sample(6, n, replace = TRUE)
x1 <- as.factor((u == 4) + (u == 5))
x2 <- as.factor(u)
y <- 1 * (x1 == 1) + rnorm(n, sd = 1)
xyData <- data.frame(x1, x2, y)

n <- nrow(xyData)
set.seed(123)

# Number of folds
k <- 5
splt <- split(sample(n), 1:k)
Rmse.mat <- matrix(0, nrow = k, ncol = 3) -> AIC.mat
for (i in 1:k) {
    test.id <- splt[[i]]
    test <- xyData[test.id, ]
    train <- xyData[-test.id, ]
    model0 <- lm(y ~ 1, data = train)
    model1 <- lm(y ~ x1, data = train)
    model2 <- lm(y ~ x2, data = train)

    Rmse.mat[i, 1] <- rmse(test$y, predict(model0, test))
    Rmse.mat[i, 2] <- rmse(test$y, predict(model1, test))
    Rmse.mat[i, 3] <- rmse(test$y, predict(model2, test))
    AIC.mat[i, 1] <- AIC(model0)
    AIC.mat[i, 2] <- AIC(model1)
    AIC.mat[i, 3] <- AIC(model2)
}
OutMat <- rbind(round(Rmse.mat, digits = 3), round(colMeans(Rmse.mat), digits = 3),
    round(colMeans(AIC.mat), digits = 3))
colnames(OutMat) <- c("Community Rating", "Two Levels", "Six Levels")
row.names(OutMat) <- c("Rmse - Fold 1", "Rmse - Fold 2", "Rmse - Fold 3", "Rmse - Fold 4",
    "Rmse - Fold 5", "Rmse - Average", "AIC - Average")
TableGen1(TableData = OutMat, TextTitle = "Under- and Over-Fitting of Models", Align = "c",
    Digits = 3, ColumnSpec = 1:3, ColWidth = ColWidth5)
```


#  From Chapter 3 of  Regression Modeling with Actuarial and Financial Applications


```{r eval = FALSE}
#Term <- read.csv("CSVData/TermLife.csv", header=TRUE)
Term <- read.csv(file = "https://instruction.bus.wisc.edu/jfrees/jfreesbooks/Regression%20Modeling/BookWebDec2010/CSVData/TermLife.csv", header = TRUE)

#  SELECCIONAR EL SUBCONJUNTO DE DATOS CORRESPONDIENTE A LA COMPRA DE SEGURO
Term2  <-subset(Term, FACE > 0)
#  TABLA 3.1 ESTADÍSTICAS DESCRIPTIVAS 
BookSummStats <- function(Xymat){
meanSummary <- sapply(Xymat, mean,  na.rm=TRUE) 
sdSummary   <- sapply(Xymat, sd,    na.rm=TRUE) 
minSummary  <- sapply(Xymat, min,   na.rm=TRUE) 
maxSummary  <- sapply(Xymat, max,   na.rm=TRUE) 
medSummary  <- sapply(Xymat, median,na.rm=TRUE) 
tableMat  <- cbind(meanSummary, medSummary, sdSummary, minSummary, maxSummary)
return(tableMat)
}

LNFACE <- log(Term2$FACE)
LNINCOME <- log(Term2$INCOME)

Xymat <- data.frame(cbind(Term2$FACE,
Term2$INCOME,Term2$EDUCATION, Term2$NUMHH,LNFACE, LNINCOME) ) 
tableMat  <- BookSummStats(Xymat)

colnames(tableMat)  <- c("Media" , "Mediana" , "Desviaci n Est ndar" , 
                         "M nimo" , "M ximo")
rownames(tableMat)  <- c("FACE", "INCOME", "EDUCATION", "NUMHH",
                         "LNFACE", "LNINCOME")
tableMat1 <- tableMat
tableMat1[3:6,]  <- round(tableMat1[3:6,], digits = 3)
tableMat1[1:2,] <- format(round(tableMat[1:2,], digits=0), big.mark = ',')

TableGen1(TableData=tableMat1, 
         TextTitle='Estad sticas Descriptivas del Seguro de Vida Temporal', 
         Align='r', Digits=3, ColumnSpec=1:5,
         ColWidth = ColWidth5) 
```


```{r eval = FALSE}

#  Change the read.csv to point to your local data folder
#Term <- read.csv("CSVData/TermLife.csv", header=TRUE)
#  SELECCIONAR EL SUBCONJUNTO DE DATOS CORRESPONDIENTE A LA COMPRA DE SEGURO
Term2  <-subset(Term, FACE > 0)
Term2$LNFACE <- log(Term2$FACE)
Term2$LNINCOME <- log(Term2$INCOME)
#  FIGURA 3.1
par(mfrow=c(1, 2), cex=1.1, mar=c(4.1,4,1.5,1))
plot(Term2$INCOME, Term2$FACE, ylab="", las=1, yaxt="n", xaxt="n", xlab="INCOME (en Millones)")
mtext("FACE (en Millones)", side=2, at=15200000, las=1, cex=1.1, adj=.4)
axis(2,at=seq(0,14000000,2000000), labels=c("0", "2", 
    "4", "6", "8","10","12","14"), las=1)
axis(1,at=seq(0,11000000,1000000), labels=c("0","1", "2","3

", 
    "4","5", "6","7","8","9","10","11"))
plot(Term2$LNINCOME, Term2$LNFACE, ylab="", xlab = "LNINCOME", las=1)
mtext("LNFACE", side=2, at=16.8, las=1, cex=1.1, adj=1.1)
```

#  From Chapter 3 Multiple Linear Regression of the Online Tutorial


```{r eval = FALSE}

#  Note the different case of the variables, e.g; income vs INCOME, ...
#Term <- read.csv("CSVData\\term_life.csv", header = TRUE)
Term <- read.csv("https://assets.datacamp.com/production/repositories/2610/datasets/efc64bc2d78cf6b48ad2c3f5e31800cb773de261/term_life.csv", header = TRUE)
#  PICK THE SUBSET OF THE DATA CORRESPONDING TO TERM PURCHASE
Term1 <- subset(Term, subset = face > 0)
str(Term1)
head(Term1)

library(psych)
Term2 <- Term1[, c("education", "face", "income", "logface", "logincome", "numhh")]
#options(scipen = 100, digits = 4)
head(Term2)
describe(Term2)#[,c(3,4,8,5,9,2)]
```