---
title: "Regression and Other Stories: Ch 1.4 - 1.6"
output: pdf_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
library(tidyverse) 
library(rstanarm)
set.seed(08252020)
```


### Building, interpreting, and checking regression models

The authors present four cycles for an iterative data analysis process:

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1. Model Building: 

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2. Model Fitting: 

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3. Understanding model fits: 

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4. Criticism: 

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## Classical and Bayesian Inference

Model fitting can be done in different ways... With any approach there are three considerations:

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#### Information

Information pertains to what 

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#### Assumptions

The authors discuss three basic assumptions that underlay a regression model


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#### Interpretation

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__Classical (or frequentist) Inference:__ This approach summarize the data 

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The results and interpretation are based long-run expectations of the methods that are correct on average (unbiased) and confidence intervals that contain the true parameter the appropriate percent of the time (coverage). 

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Classical methods do tend to be conservative, in that strong statements are not make with _weak_ data. 

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__Bayesian Inference:__ This approach summarize the data 


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Results and interpretations are probabilistic 


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Bayesian inference uses additional information which can potentially give more reasonable results (using the prior to regularize the model), 


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### Computing

Classical methods tend to use least-squares estimation (or maximum likelihood). 

```{r}
beer <- read_csv('http://math.montana.edu/ahoegh/Data/Brazil_cerveja.csv')
lm_beer <- lm(consumed ~ max_tmp, data = beer)
summary(lm_beer)
```

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The textbook authors (and your instructor), recommend using Bayesian inference for regression. 

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Furthermore, using Bayesian methods with _weakly informative_ prior information enables stable estimates and simulation based inference, *but also can result (or approximately result) in frequentist solutions.*

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```{r}
stan_glm(consumed ~ max_tmp, data = beer, refresh = 0) %>% print()
```