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Question

p299

Fit some of the non-linear models investigated in this chapter to the Auto data set. Is there evidence for non-linear relationships in this data set? Create some informative plots to justify your answer.

glimpse(Auto)
## Rows: 392
## Columns: 9
## $ mpg          <dbl> 18, 15, 18, 16, 17, 15, 14, 14, 14, 15, 15, 14, 15, 14, …
## $ cylinders    <dbl> 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 6, 6, 6, 4,…
## $ displacement <dbl> 307, 350, 318, 304, 302, 429, 454, 440, 455, 390, 383, 3…
## $ horsepower   <dbl> 130, 165, 150, 150, 140, 198, 220, 215, 225, 190, 170, 1…
## $ weight       <dbl> 3504, 3693, 3436, 3433, 3449, 4341, 4354, 4312, 4425, 38…
## $ acceleration <dbl> 12.0, 11.5, 11.0, 12.0, 10.5, 10.0, 9.0, 8.5, 10.0, 8.5,…
## $ year         <dbl> 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, …
## $ origin       <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3,…
## $ name         <fct> chevrolet chevelle malibu, buick skylark 320, plymouth s…
library(skimr)
skim(Auto)
Data summary
Name Auto
Number of rows 392
Number of columns 9
_______________________
Column type frequency:
factor 1
numeric 8
________________________
Group variables None

Variable type: factor

skim_variable n_missing complete_rate ordered n_unique top_counts
name 0 1 FALSE 301 amc: 5, for: 5, toy: 5, amc: 4

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
mpg 0 1 23.45 7.81 9 17.00 22.75 29.00 46.6 ▆▇▆▃▁
cylinders 0 1 5.47 1.71 3 4.00 4.00 8.00 8.0 ▇▁▃▁▅
displacement 0 1 194.41 104.64 68 105.00 151.00 275.75 455.0 ▇▂▂▃▁
horsepower 0 1 104.47 38.49 46 75.00 93.50 126.00 230.0 ▆▇▃▁▁
weight 0 1 2977.58 849.40 1613 2225.25 2803.50 3614.75 5140.0 ▇▇▅▅▂
acceleration 0 1 15.54 2.76 8 13.78 15.50 17.02 24.8 ▁▆▇▂▁
year 0 1 75.98 3.68 70 73.00 76.00 79.00 82.0 ▇▆▇▆▇
origin 0 1 1.58 0.81 1 1.00 1.00 2.00 3.0 ▇▁▂▁▂ 
## The following object is masked from package:ggplot2:
## 
##     mpg