Handout2Code_RMarkdown_students-1.Rmd

---
title: "Handout2Code_RMarkdown_students"
output: html_document
editor_options: 
  chunk_output_type: console
  markdown: 
    wrap: 72
---

# Example 3: HeightFoot.xls

Import Data Into R from Excel file (1) Run command:
install.packages("readxl") if have never done so (2) Save data file to
same location as R script; then, (3) Run the following three commands

```{r}
library(readxl)
setwd(dirname(rstudioapi::getActiveDocumentContext()$path)) 
HHFData=read_excel("HandHeightFoot.xls")

```

View initial rows of data frame & view data frame structure

```{r}
head(HHFData)
str(HHFData)
```

### 3(b)

Scatterplot Height v. Footsize

```{r}
plot(Height~Footsize,data=HHFData,pch=19)
```

Compute correlation r

```{r}
cor(HHFData$Height,HHFData$Footsize)
```

### 3(f)

SAE(ybar)

```{r}
sum( abs( HHFData$Height - 69.97 ) )

```

SSE(ybar)

```{r}
sum( ( HHFData$Height - 69.97 )^2 )

```

### 3(g)

LAD fit & summary

```{r}
#install.packages("L1pack")
library(L1pack)
fitLAD=lad(Height~Footsize,data=HHFData)
summary(fitLAD)
```

SAE(LAD)

```{r}
sum( abs( HHFData$Height - fitted(fitLAD) ) )
```

SSE(LAD)

```{r}
sum( ( HHFData$Height - fitted(fitLAD) )^2 )

```

LS fit & summary

```{r}
fitLS=lm(Height~Footsize,data=HHFData)
summary(fitLS)
```

SAE(LS)

```{r}
sum( abs( HHFData$Height - fitted(fitLS) ) )
```

SSE(LS)

```{r}
sum( ( HHFData$Height - fitted(fitLS) )^2 )

```

Scatterplot Height v. Footsize

```{r}
plot(Height~Footsize,data=HHFData,pch=19)

```

Colors for fitted lines

```{r}
plot(Height~Footsize,data=HHFData,pch=19)

#install.packages(RColorBrewer)
library(RColorBrewer)
cols <- brewer.pal(3, "Set1")

#Superimpose mean line
abline(h=mean(HHFData$Height),col=cols[1],lty=2)

#Superimpose LAD line
abline(fitLAD,col=cols[2],lty=3)

# superimpose LS line
abline(fitLS,col=cols[3],lty=1)

#add plot legend
legend('topleft',lty=c(2,3,1),legend=c('mean','LAD','LS'),col=cols)
```

### 3(i)

Prediction w/ footsize=28

```{r}
40.41+1.12*28

```

### 3(j)

Prediction w/ footsize=40

```{r}
40.41+1.12*85.21

```

# Example 4: paper.xls

Import Data Into R from Excel file (1) Run command:
install.packages("readxl") if have never done so (2) Save data file to
same location as R script; then, (3) Run the following three commands

```{r}
library(readxl)
setwd(dirname(rstudioapi::getActiveDocumentContext()$path)) 
PaperData = read_excel('paper.xlsx', col_names=TRUE)
```

View structure

```{r}
head(PaperData)
str(PaperData)
```

LS fit

```{r}
paper.fit=lm(Strength ~CookingTime+Pressure, data=PaperData)
summary(paper.fit)
```

3d sccatterplot Strength \~ CookingTime+Pressure

```{r}
library(rgl)
with(PaperData, plot3d(CookingTime, Pressure, Strength, size=8,xlab='Time'))
```

3d sccatterplot Strength with regression surface

```{r}
with(PaperData, plot3d(CookingTime, Pressure, Strength, size=8,xlab='Time'))

#regression surface function
paper.surface<-function(x1,x2){
  paper.fit$coeff[1]+paper.fit$coeff[2]*x1+paper.fit$coeff[3]*x2
}

#plot regression surface
with(PaperData,{
  x1=seq(min(CookingTime),max(CookingTime),length=100)
  x2=seq(min(Pressure),max(Pressure),length=100)
  y=outer(x1,x2,paper.surface)
  surface3d(x1,x2,y,alpha=0.8,front='lines', back='lines',col='red')
})
```

### 4(b)

Prediction w/ CookingTime=2 & Pressure=600

```{r}
189.5 + 1.5*3 + 0.0064*600
```

### 4(b)

Prediction w/ CookingTime=3 & Pressure=600

```{r}
189.5 + 1.5*4 + 0.0064*600
```

## MEAN PLANE

Compute mean strength

```{r}
mean(PaperData$Strength)
```

3d scatterplot Strength \~ CookingTime+Pressure

```{r}
with(PaperData, plot3d(x=CookingTime, y=Pressure, z=Strength, size=8,xlab='Time'))
```

3d scatterplot Strength with MEAN PLANE

```{r}
with(PaperData, plot3d(x=CookingTime, y=Pressure, z=Strength, size=8,xlab='Time'))

#Regression surface function (mean plane)
paper.surface2<-function(x1,x2){
  mean(PaperData$Strength)+0*x1+0*x2
}

#Plot mean plane
with(PaperData,{
  x1=seq(min(CookingTime),max(CookingTime),length=100)
  x2=seq(min(Pressure),max(Pressure),length=100)
  y=outer(x1,x2,paper.surface2)
  #print(y)
  surface3d(x1,x2,y,alpha=0.8,front='lines', back='lines',col='green')
})
```

LS plane SSE

```{r}
sum( ( PaperData$Strength - fitted(paper.fit) )^2 )
```

Mean plane SSE

```{r}
sum( ( PaperData$Strength - mean(PaperData$Strength) )^2 )
```

### 4(g)

R\^2 by hand calculation

```{r}
((30.49-66.31)/30.49)*100
((66.31-30.49)/66.31)*100
```

### 4(i)

R\^2 from r by hand calculation

```{r}

(0.802)^2
```