mtcars-simple2

regression

en

bayes

frequentist

qm1

stats-nutshell

mtcars

Published

September 4, 2022

Exercise

We will use the dataset mtcars in this exercise.

Assume your causal model of your research dictates that fuel economy is a linear function of horse power, cylinder count and displacement of the engine.

Compute the explained variance (point estimate) for the above model!

Notes:

Use can either use frequentist or bayesian modeling.
Use R for all computations.
There are multiple ways to find a solution.

Solution

Compute Model:

lm1_freq <- lm(mpg ~ hp + cyl + disp, data = mtcars)

library(rstanarm)
lm1_bayes <- stan_glm(mpg ~ hp + cyl + disp, data = mtcars, refresh = 0)

Get R2:

library(easystats)

r2(lm1_freq)

# R2 for Linear Regression
       R2: 0.768
  adj. R2: 0.743

r2(lm1_bayes)

# Bayesian R2 with Compatibility Interval

  Conditional R2: 0.746 (95% CI [0.610, 0.856])

The coefficient is estimated as about 0.77.

Categories:

regression
en
bayes
frequentist
qm1
stats-nutshell

---
exname: mtcars-simple2
extype: num
exsolution: r round(r2(lm1_freq)[["R2"]], 2)
exshuffle: no
extol: 0.1
expoints: 1
categories:
- regression
- en
- bayes
- frequentist
- qm1
- stats-nutshell
- mtcars
date: '2022-09-04'
slug: mtcars-simple2
title: mtcars-simple2

---




```{r libs, include = FALSE}
library(tidyverse)
#library(glue)
options(mc.cores = parallel::detectCores())

```


```{r global-knitr-options, include=FALSE}
knitr::opts_chunk$set(fig.pos = 'H',
                      fig.asp = 0.618,
                      fig.width = 4,
                      fig.cap = "", 
                      fig.path = "",
                      echo = TRUE,
                      message = FALSE,
                      fig.show = "hold")
```






# Exercise

We will use the dataset `mtcars` in this exercise.

Assume your causal model of your research dictates that fuel economy is a linear function of horse power, cylinder count and displacement of the engine.

*Compute the explained variance (point estimate) for the above model!*


Notes:

- Use can either use frequentist or bayesian modeling.
- Use R for all computations.
- There are multiple ways to find a solution.



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# Solution

Compute Model:

```{r}
lm1_freq <- lm(mpg ~ hp + cyl + disp, data = mtcars)

library(rstanarm)
lm1_bayes <- stan_glm(mpg ~ hp + cyl + disp, data = mtcars, refresh = 0)
```


Get R2:

```{r message=FALSE}
library(easystats)
```


```{r}
r2(lm1_freq)
```

```{r}
r2(lm1_bayes)
```


The coefficient is estimated as about `r round(r2(lm1_freq)[["R2"]], 2)`.



---

Categories: 

- regression
- en
- bayes
- frequentist
- qm1
- stats-nutshell