---
title: "Student Version to Practice Multiple Regression"
author: "Carolyn J. Anderson"
date: "9/3/2021"
output: 
   html_document:
       toc: yes
---
# Introduction

# Libraries
Library that I used
```{r setup, message=FALSE, warning=FALSE, include=TRUE}
library(ellipse)
library(ggplot2)
library(coda)
library(runjags)
library(rjags)
library(BayesFactor)
library(jagsUI)
library(HDInterval)  # for high density interval
```

# Data

You can find the data on the course web-site.  You need to change the path to where ever you put the data.

```{r}
df <- read.table("C:/Users/cja/Dropbox/edps 590BAY/Lectures/7 Multiple Linear Regression/getting_what_paid_for_data.txt", header=TRUE)
names(df)
head(df)
```


# Plot the Data

..and overlay the normal distribution.  There are a number of ways to do this and what's below keeps things in terms of frequencies.  The first line sets up the histogram and saves it as "h".  The next two lines get data for horizontal and vertical axis.  The third command puts density values of vertical fit values into scale of frequencies and uses information from the historgram.  The "lines" command puts in the normal curve.  

```{r}
h =hist(df$ave_tot, breaks = 10, density = 10,
            col = "darkblue", 
            xlab = "Average Total SAT", 
            ylab = "Frequency",
            main="Normal curve Over histogram")
xfit <- seq(min(df$ave_tot), max(df$ave_tot), length = 50) 
yfit <- dnorm(xfit, mean = mean(df$ave_to), sd = sd(df$ave_tot)) 
yfit <- yfit * diff(h$mids[1:2]) * length(df$ave_tot) 
lines(xfit, yfit, col = "black", lwd = 2)
```

# Sample Statistics

We need the sample size and observed sample mean.  We will pretend that we know what the variance equals and use the sample variance for this.

```{r}
n <- nrow(df)
ybar <- mean(df$ave_tot)
std <- sd(df$ave_tot)
s2 <- var(df$ave_tot)


descriptive <- c(n, ybar, std, s2)
names(descriptive) <- c("N","Ybar","std","s^2")
descriptive
```

```{r}
xs <- data.frame(df$ave_tot, df$exp_pp, df$salary, df$taking, df$ave_pt)
ctab <- cor(xs)
round(ctab,2)     # round correlations to 2 decimals for easier viewing
```

```{r corrPlotColor}
# Figures of correlations in color 
colorfun <- colorRamp(c("#CC0000","white","#3366CC"), space="Lab")
plotcorr(ctab, col=rgb(colorfun((ctab+1)/2), maxColorValue=255),
         mar = c(0.1, 0.1, 0.1, 0.1))
```