---
title: Massey University --- School of Mathematical and Computational Sciences
subtitle: 161.251 Regression Modelling
author: "Staff member responsible for this workshop: Jonathan Marshall j.c.marshall@massey.ac.nz"
date: "last updated `r format(lubridate::today(), '%d %B %Y')`"
output:
  html_document:
    code_download: true
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(comment="", dev="png")
library(tidyverse)
library(broom)
library(nlme)
library(tsibble)
library(fable)
library(feasts)
```

# Computer Laboratory Exercise 12A

## Modelling Motel Use in Victoria

In this exercise you will:

  - gain more experience in fitting linear models with autocorrelated errors;

  - Investigate whether room occupancy (as measured by `RoomNights`, your
response variable) depends on `AvePrice`, having adjusted for seasonality
and long term temporal trend, while  taking care to account for possible autocorrelation 
in your model.


1. The data we need for this exercise can be read in and assigned to the data frame
`motel_raw`, with one of the following commands.

```{r}
motel_raw <- read_csv("https://www.massey.ac.nz/~jcmarsha/161251/data/motel.csv")
motel_raw
```

2. Take a look at the data frame and make all the variables we need.

    - We'll need a `Time` variable for the modelling which is an integer increase in months (Why?)
    - We'll need a `Month` variable as an unordered factor (Why?)

```{r}
```

3. Re-fit the models used in lectures (excluding the quadratic), including the model that accounts for autocorrelation in the residuals.

```{r}
```

4. Add the potential predictor variable `AvePrice` to these models. What do we see?

```{r}
```

5. Produce a plot of **standard** residuals against Time, and an ACF plot for the residuals for all the regression models (`lm` and `gls`). The standard residuals can be obtained just using `residuals()` or `resid()`

```{r}
```

6. For the `gls` models only, produce a plot of **normalized** residuals against Time and an ACF plot for those residuals. The normalized residuals can be obtained using `type="normalized"` in `residuals()`. These should be uncorrelated in the `gls` models.

```{r}
```

7. Do you think that there is evidence of autocorrelation in the error terms for the standard linear model, and is this resolved in the GLS model?

8. Look at the model summaries for the models that you have fitted. Are
their parameter estimates and/or standard errors markedly different?

```{r}
```

9. Looking at the summary for the `gls` models, what is the
estimated lag one correlation for the residuals?

```{r}
```

10. To get an idea of the uncertainty in our estimate, you can generate confidence intervals for estimated model parameters by using the `intervals()` command.

```{r}
```