Handout5Code_RMarkdown_students.Rmd

---
title: "Handout5Code_RMarkdown_students"
output: html_document
editor_options: 
  chunk_output_type: console
---

# Example 1:

ARTIFICIAL POPULATION DATA

```{r}
# generate artifical population of size N=5000 based on characteristics 
# of the real data in "bodyfat.csv" focusing on height vs. weight
# 178.9244=mean(bodyfatData$Weight), 29.38916=sd(bodyfatData$Weight)
# 3.491=s, ,63.270=beta0hat, 0.0384=beta1hat from lm(Height~Weight,data=bodyfatData)
set.seed(11)
Weight=rnorm(5000,178.9244,29.38916)
Error=rnorm(5000,0,3.491)
Height=63.270+0.0384*Weight+Error
set.seed(NULL)

```

Scatterplot of artificial population data

```{r}
par(mfrow=c(1,1))
plot(Weight, Height, cex=0.4)
abline(63.270,0.0384)

```

Draw sample 1 of size 60 from artificial population

```{r}
set.seed(15)
index1=sample(1:5000,60)
weight1=Weight[index1]
height1=Height[index1]

```

### 1(f)

Fit LS line

```{r}
weight=weight1
height=height1

fit=lm(height~weight)

#fitted line plot and model summary for our "real" sample
par(mfrow=c(1,1))
plot(weight,height,col='black',pch=19,cex=1,ylab='Height',xlab='Weight')
abline(fit, col='blue',lwd=2)

#model summary
summary(fit)
```

Compute test statistic "by-hand".

```{r}
(t<-(0.04418-0)/0.01271)

```

### 1(h)

Model summary

```{r}
summary(fit)

```

Confirm calculation (there will be some discrepancies just because of rounding)

```{r}
#RMSE 
summary(fit)$sigma

#MSE
summary(fit)$sigma^2

```

### 1(i)

```{r}
#X=model.matrix( lm(height ~ weight) )
X=model.matrix(fit)
X

```

```{r}
solve(t(X) %*% X)

```

### 1(j)

Check your work:

```{r}
3.024*sqrt(1.766444e-05)

```

### 1(l)

Manual p-value computation

```{r}
(t=(0.04418-0.02)/0.01271)
pt(t,df=60-1-1,lower.tail=FALSE)
#or
pt(1.9, df=58, lower.tail=FALSE)

```

# Example 2: UOPgpa

### 2(b-c)

Import Data from .txt\
Save data file to same location as R script;

```{r}
setwd(dirname(rstudioapi::getActiveDocumentContext()$path))
UOPgpaData = read.table('UOPgpa.txt', header=TRUE, sep="\t")

```

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

```{r}
par(mfrow=c(1,1))
plot(GPA~StudyHours,data=UOPgpaData,pch=19,col='black')
UOPgpa.fit=lm(GPA~StudyHours,data=UOPgpaData)
abline(UOPgpa.fit,col='blue')
summary(UOPgpa.fit)

```

Correlation

```{r}
#Correlation
cor(UOPgpaData$StudyHours, UOPgpaData$GPA)

#Correlation squared
cor(UOPgpaData$StudyHours, UOPgpaData$GPA)^2
#this is the same values of R-squared in the output from the model

```

### 2(d)

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

```{r}
t = (0.08938/0.02771)
t
```

### 2(f-g)

t critical value

```{r}
tstar=qt(p=0.975, df=80-2);tstar

```

CI calculation by hand. -*-*-*-* IMPORTANT: Write the coded needed to answer the question.-*-*-*-*

```{r}
0.08938 + 1.990847*(0.02771)
0.08938 - 1.990847*(0.02771)

```

### 2(h)

Confidence interval for pop. coeff.

```{r}
confint(UOPgpa.fit,level=0.95)

```

# Example 3: Advertising.txt \#

Import Data Save data file to same location as R script; then,

```{r}
#setwd(dirname(rstudioapi::getActiveDocumentContext()$path)) 
AdvData=read.table("Advertising.txt",header=T, sep='\t')
str(AdvData)

```

### 3(a)

\-*-*-*-* IMPORTANT: Write the coded needed to answer the question.-*-*-*-*

Fit a linear model

```{r}
Adv.fit = lm(Sales ~ TV + Radio, data = AdvData)
```

Find the Confidence Intervals for coefficients

```{r}
confint(Adv.fit, level = 0.95)

```

### 3(d-e)

CI's for coefficients w/ Bonferonni Adjustment -*-*-*-* IMPORTANT: Make sure you substitute "???" by the correct code.-*-*-*-*

```{r}
confint(Adv.fit, level = (1 - ((1 - 0.95)/3)))

```

### 3(f)

Model summary: Sales\~TV+Radio\
-*-*-*-* IMPORTANT: Write the coded needed to answer the question.-*-*-*-*\
Tip: Look back to your code from 3a.

```{r}
summary(Adv.fit)

```