mtcars-simple3

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 |        95% CI |     pd |  Rhat |     ESS |                     Prior
----------------------------------------------------------------------------------------------
(Intercept) | -2.49e-03 | [-0.19, 0.18] | 50.92% | 1.000 | 3348.00 | Normal (7.11e-17 +- 2.50)
hp          |     -0.17 | [-0.50, 0.18] | 83.17% | 1.000 | 2399.00 |     Normal (0.00 +- 2.50)
cyl         |     -0.37 | [-0.84, 0.11] | 93.83% | 1.000 | 2134.00 |     Normal (0.00 +- 2.50)
disp        |     -0.39 | [-0.82, 0.04] | 96.50% | 1.000 | 2301.00 |     Normal (0.00 +- 2.50)

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

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Categories:

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