2 · Linear regression (exercises) — source
A. Stamm 
This page shows the source file of the exercise below. Use the button to download it as a plain file and run it in your own workspace.
---
title: "Linear Regression with R"
---
```thlbnuupr
#| include: false
library(tidyverse)
knitr::opts_chunk$set(comment = NA)
html_table <- function(x, page_length = nrow(x)) {
DT::datatable(
data = x,
rownames = FALSE,
options = list(
dom = 'tip',
scrollX = TRUE,
pageLength = page_length
)
)
}
dt_glance <- function(x) {
x |>
broom::glance() |>
html_table() |>
DT::formatSignif(columns = c(1:5, 7:10), digits = 3)
}
dt_tidy <- function(x) {
x |>
broom::tidy() |>
html_table() |>
DT::formatSignif(columns = 2:5, digits = 3)
}
```
## Expectations
In the following exercises, you will be asked to study the relationship of a
continuous response variable and one or more predictors. In doing so, remember
to:
- perform model diagnosis
- including visualization tools
- including multicollinearity assessment
- perform informed model selection
- comment each result of an analysis you run with R
## Exercise 1
Analysis of the `production` data set which is composed of the following
variables:
Variable name | Description
------------- | -------------
x | Number of produced pieces
y | Production cost
Study the relationship between `x` and `y`.
## Exercise 2
Analysis of the `brain` data set which is composed of the following variables:
Variable name | Description
------------- | -------------
body_weight | Body weight in kg
brain_weight | Brain weight in kg
Study the relationship between body and brain weights, to establish how the variable `brain_weight` changes with the variable `body_weight`.
## Exercise 3
Analysis of the `anscombe` data set which is composed of the following variables:
Variable name | Description
------------- | -------------
x1 | Predictor to be used for explaining `y1`
x2 | Predictor to be used for explaining `y2`
x3 | Predictor to be used for explaining `y3`
x4 | Predictor to be used for explaining `y4`
y1 | Response to be explained by `x1`
y2 | Response to be explained by `x2`
y3 | Response to be explained by `x3`
y4 | Response to be explained by `x4`
Study the relationship between each $y_i$ and the corresponding $x_i$.
```ujieezcptjhi
```
## Exercise 4
Analysis of the `cement` data set, which contains the following variables:
Variable name | Description
----------------- | ----------------
aluminium | Percentage of $\mathrm{Ca}_3 \mathrm{Al}_2 \mathrm{O}_6$
silicate | Percentage of $\mathrm{C}_2 \mathrm{S}$
aluminium_ferrite | Percentage of $4 \mathrm{CaO} \mathrm{Al}_2 \mathrm{O}_3 \mathrm{Fe}_2 \mathrm{O}_3$
silicate_bic | Percentage of $\mathrm{C}_3 \mathrm{S}$
hardness | Hardness of the cement obtained by mixing the above four components
Study, using a multiple linear regression model, how the variable `hardness` depends on the four predictors.
## Exercise 5
Analysis of the `job` data set, which contains the following variables:
Variable name | Description
------------- | ----------------
average_score | Average score obtained by the employee in the test
years_service | Number of years of service
sex | Male or female
We want to see if it is possible to use the sex of the person in addition to the years of service to predict, with a linear model, the average score obtained in the test. Estimate a linear regression of `average_score` vs. `years_service`, considering the categorical variable `sex`.
## Exercise 6
Analysis of the `cars` data set, which contains the following variables:
Variable name | Description
------------- | ----------------
speed | Speed of the car before starting braking
dist | Distance travelled by the car during the braking period until it completely stops
Verify if the distance travelled during the braking depends on the starting velocity of the car:
1. Choose the best model to explain the distance as function of the speed,
2. Predict the braking distance for a starting velocity of 25 km/h, using a point estimate and a prediction interval.
```eznxfrws
```
## Exercise 7
Analysis of the `mussels` data set, which contains the following variables:
Variable name | Description
------------- | ----------------
length | Length of a mussel (mm)
width | Width of a mussel (mm)
height | Height of a mussel (mm)
size | Mass of a mussel (g)
weight | Weight of eatable part of a mussel (g)
We want to study how the eatable part of a mussel varies as a function of the other four variables using a multiple linear regression.
```vgtdurchzsp
```