Assignment 11.Rmd

---
title: "Assignment 11"
author: "Your Name"
date: "Due: Thursday, April 22, midnight"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```
 
For the exercises in this assignment we'll use the `survey` data set from the `MASS` package. 

1. The `survey` data set has a variable `Exer`, a factor with $k=3$ levels describing the amount of physical exercise time each student gets: none, some, or frequent. Obtain a count of the number of students in each category (I recommend using your tidyverse skills) and produce side-by-side boxplots of student height split by exercise. 

2. Assuming independence of the observations and normality, fit a linear regression model with height as the response variable and exercise as teh explanatory variable. What's the default referenc elevel of the predictor? Produce a model summary. 

3. Draw a conclusion based on your fitted model: does it appear that exercise frequency has any impact on mean height? What is the nature of the estimated effect? 

4. Predict the mean heights of one individual in each of the three exercise categories, accompanied by 95 percent prediction intervals. 

5. Conduct a one-way ANOVA on the same variables: `Height ~ Exer`. Compare the F-statistic and P-value from your ANOVA and the bottom line output from your summary of the `lm` object. What do you observe?