---
title: "Regression and Other Stories: Ch 2"
output: pdf_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
library(tidyverse) 
library(gridExtra)
library(rstanarm)
set.seed(08312020)
```


## Data and measurement

This linear models course focuses on:

- fitting lines (functional relationships),
- making comparisons and predictions, and
- assessing uncertainties in inferences.

A major component of these steps requires understanding and assessing assumptions. However, before talking about that and more, it is necessary to understand the data. There is a common adage, 



### Validity and Reliability

As you start working with datasets, I'd encourage you to think about where the data came from 

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#### Measurement

Consider the data collection process for vegetation cover class data.

![Cover class data, source: Upper Columbia Basin Network
Sagebrush Steppe Vegetation Monitoring Protocol by Yeo, Rodhouse, Dicus, Irvine, Garrett](ord_sample.png)

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When designing studies and collecting data, precision of the measurements is an important consideration 

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Measurement can be challenging in many situations, a few include:



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Taking multiple measurements can be advantageous.



#### Validity

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The __validity __ of measurement is the degree to which it represents what you are trying to measure. 

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ROS defines validity as 

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#### Reliability 
The __reliability__ of a measurement is the degree to which it is 

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#### Sample Selection

A fundamental goal in statistics is to extend inferences from a sample to a study population. 

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This extension requires understanding how the data was selected. In particular, 

### Data Visualiztion

ROS suggests that all graphs are comparisons.

```{r}
beer <- read_csv('http://math.montana.edu/ahoegh/Data/Brazil_cerveja.csv')
```

_Q:_ What kind of graph is this and what is the comparison?

```{r, echo = F}
beer %>% ggplot(aes(y = consumed, x = max_tmp)) + 
  geom_point() + theme_bw() + ylab('Beer Consumed') +
  xlab('Max Temperature (C)')
```

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Graphical displays of data enable viewing several pieces of data. Specifically, a different variable can be associated with all of the following elements.

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```{r, fig.cap = 'Exploration of beer consumption by temperature and weekend / weekday. The figures suggest higher temperatures and weekends are associated with predicted increases in beer consumption. '}
fig1 <- beer %>% mutate(weekend_fact = factor(weekend, labels = c('weekday','weekend')))  %>% 
  ggplot(aes(y = consumed, x = max_tmp, color = weekend_fact, shape = weekend_fact)) + 
  geom_point() + theme_bw() + ylab('Beer Consumed (l)') +
  xlab('Max Temperature (C)') + labs(color = 'Day of Week') + 
  geom_smooth(method = 'loess', formula = 'y~x') +  guides(shape = FALSE) +     
  ggtitle('Sample of Beer Consumption in Sao Paolo, Brazil')

fig2 <- beer %>% mutate(weekend_fact = factor(weekend, labels = c('weekday','weekend'))) %>% 
  ggplot(aes(y = consumed, x = weekend_fact, color = weekend_fact, shape = weekend_fact)) +
  geom_violin() + geom_jitter()  + ylab('Beer Consumed (l)') +
  ylim(0,NA) + theme_bw() + theme(legend.position = 'none') + xlab('Day of Week') + 
  labs(caption = 'source:https://www.kaggle.com/dongeorge/beer-consumption-sao-paulo')

grid.arrange(fig1, fig2)
```

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There are three main types of graphics:

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1. Exploratory Data Analysis: 

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2. Graphs of fitted models and inferences: 

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3. Graphs of Final Results:

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