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 Prior_Distribution Prior_Location Prior_Scale
(Intercept) 0.0047118 0.95 -0.1832279 0.1820132 0.51900 1.0000771 3300.694 normal 0 2.5
hp -0.1720874 0.95 -0.5041621 0.1767126 0.83475 1.0000367 2899.518 normal 0 2.5
cyl -0.3703854 0.95 -0.8421462 0.1282401 0.93225 0.9997860 2144.550 normal 0 2.5
disp -0.3829240 0.95 -0.8228923 0.0476500 0.96125 0.9998687 2447.111 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