Handout3Code_RMarkdown_students-1.Rmd

---
title: "Handout3Code_RMarkdown_students"
output: html_document
editor_options: 
  chunk_output_type: console
---

# Example 1: workcrew.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)) 
workData=read_excel('workcrew.xls')
```

View structure and data -*-*-*-* IMPORTANT: Make sure you substitute "???" by the correct code.-*-*-*-*

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

### 1(b-c)

Beta-hat using matrix multiplication

```{r}
(X=matrix(c(rep(1,8), workData$crew, workData$bonus),nrow=8))
(y=workData$productivity)
solve(t(X) %*% X) %*% t(X) %*% y
```

### 1(d)

LS model productivity \~ crew + bonus

\-*-*-*-* IMPORTANT: Make sure you substitute "???" by the correct code.-*-*-*-*

```{r}
fit.work=lm(productivity ~ crew + bonus, data=workData)
summary(workData)
```

### 1(f)

Compute variable means.

\-*-*-*-* IMPORTANT: Make sure you substitute "???" by the correct code.-*-*-*-*

```{r}
mean(???)
mean(???)
```

Prediction at mean values of predictors -*-*-*-* IMPORTANT: Make sure you substitute "???" by the correct code.-*-*-*-*

```{r}
#Write the arithmetic prediction below:
???
#Matrix multiplication prediction:
matrix(c(1,5,2.5),nrow=1) %*% matrix(c(0.375,5.375,9.25),nrow=3)
```

### 1(g)

Predicted values

```{r}
fit.work$fitted.values
```

### 1(h)

Residuals

```{r}
resid(fit.work)
```

### 1(i)

Regression surface

```{r}
#3d scatterplot productivity ~ crew + bonus
library(rgl)
with(workData, plot3d(x=crew, y=bonus, z=productivity, size=10))

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

#plot regression surface
with(workData,{
  x1=seq(min(crew),max(crew),length=100)
  x2=seq(min(bonus),max(bonus),length=100)
  y=outer(x1,x2,work.surface)
  surface3d(x1,x2,y,alpha=0.8,front='lines', back='lines',col='blue')
})
```

Sum residuals

```{r}
round(sum(resid(fit.work)),10)
```

### 1(j)

Compute hat matrix -*-*-*-* IMPORTANT: Make sure you substitute "???" by the correct code.-*-*-*-*

```{r}
H <- X %*% solve(t(X)%*%X) %*% t(X)
H
t(H)
```

### 1(k)

Weight of y_j on (y_i)-hat=h_ij y_j for i=3.\
Reports the hat matrix but only for unit 3.

```{r}
(X %*% solve(t(X) %*% X) %*% t(X))[3,]
```

### 1(l)

Do work by hand!:D

```{r}
0.125*42 + 0.125*39 + 0.375*48 + 0.375*51 -0.125*49 -0.125*53 + 0.125*61 + 0.125*60
```

### 1(m)

Vector of Y values

```{r}
y
```

Vector containing actual contributions of y_j on (y_i)-hat=h_ij y_j for i=3.

```{r}
(X %*% solve(t(X) %*% X) %*% t(X))[3,]*y
```

If you sum the values above, you will get the predicted value for unit 3

```{r}
sum((X %*% solve(t(X) %*% X) %*% t(X))[3,]*y)
```

Predicted value for unit 3

```{r}
fit.work$fitted.values[3]

```