mtcars-simple3

regression

en

bayes

frequentist

qm1

stats-nutshell

qm2

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.

Which of the predictors in the above model has the weakest causal impact on the output variable?

Notes:

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

Answerlist

cyl
hp
disp
All are equally strong
none of the above

Solution

library(rstanarm)
library(easystats)
library(tidyverse)

In order to gauge the relative importance of the predictors, we need to make sure they are on the same scale:

mtcars2 <-
  standardise(mtcars)

Compute Model:

lm1_freq <- lm(mpg ~ hp + cyl + disp, data = mtcars2)
lm1_bayes <- stan_glm(mpg ~ hp + cyl + disp, data = mtcars2, refresh = 0)

Get parameters:

parameters(lm1_bayes)

Parameter	Median	CI	CI_low	CI_high	pd	Rhat	ESS_tail	Prior_Distribution	Prior_Location	Prior_Scale
(Intercept)	0.0032447	0.95	-0.1763947	0.1817065	0.51475	1.000001	2227	normal	0	2.5
hp	-0.1724119	0.95	-0.5093495	0.1732813	0.84250	1.001527	2157	normal	0	2.5
cyl	-0.3496643	0.95	-0.8058727	0.1336430	0.92575	1.000285	2065	normal	0	2.5
disp	-0.3998787	0.95	-0.8494027	0.0372232	0.96225	0.999581	2011	normal	0	2.5

Note that the absolute value of the coefficient’s estimate is what we are after.

The predictors with the strongest impact is disp, and cyl. The weakest influence has hp.

Answerlist

wrong
correct
wrong
wrong
wrong

Categories:

regression
en
bayes
frequentist
qm1
stats-nutshell

---
exname: mtcars-simple3
extype: num
exsolution: 512
exshuffle: yes
extol: 0.1
expoints: 1
categories:
- regression
- en
- bayes
- frequentist
- qm1
- stats-nutshell
- qm2
- mtcars
date: '2022-09-04'
slug: mtcars-simple3
title: mtcars-simple3

---




```{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.

*Which of the predictors in the above model has the weakest causal impact on the output variable?*


Notes:

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


Answerlist
----------
* `cyl`
* `hp`
* `disp`
* All are equally strong
* none of the above






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</br>
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</br>
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</br>
</br>

# Solution

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


In order to gauge the relative importance of the predictors,
we need to make sure they are on the same scale:


```{r}
mtcars2 <-
  standardise(mtcars)
```


Compute Model:

```{r}
lm1_freq <- lm(mpg ~ hp + cyl + disp, data = mtcars2)
lm1_bayes <- stan_glm(mpg ~ hp + cyl + disp, data = mtcars2, refresh = 0)
```


Get parameters:


```{r}
parameters(lm1_bayes)
```

Note that the absolute value of the coefficient's estimate is what we are after.

The predictors with the strongest impact is `disp`, and `cyl`. 
The weakest influence has `hp`.



Answerlist
----------


* wrong
* correct
* wrong
* wrong
* wrong





---

Categories: 

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