A tale of two variables

Introduction to Regression in R

Richie Cotton

Data Evangelist at DataCamp

Swedish motor insurance data

Each row represents one geographic region in Sweden.
There are 63 rows.

n_claims	total_payment_sek
108	392.5
19	46.2
13	15.7
124	422.2
40	119.4
...	...

Descriptive statistics

library(dplyr)
swedish_motor_insurance %>% 
  summarize_all(mean)

# A tibble: 1 x 2
  n_claims total_payment_sek
     <dbl>             <dbl>
1     22.9              98.2

swedish_motor_insurance %>% 
  summarize(
    correlation = cor(n_claims, total_payment_sek)
  )

# A tibble: 1 x 1
  correlation
        <dbl>
1       0.881

What is regression?

Statistical models to explore the relationship a response variable and some explanatory variables.
Given values of explanatory variables, you can predict the values of the response variable.

n_claims	total_payment_sek
108	392.5
19	46.2
13	15.7
124	422.2
40	119.4
200	???

Jargon

Response variable (a.k.a. dependent variable)

The variable that you want to predict.

Explanatory variables (a.k.a. independent variables)

The variables that explain how the response variable will change.

Linear regression and logistic regression

Linear regression

The response variable is numeric.

Logistic regression

The response variable is logical.

Simple linear/logistic regression

There is only one explanatory variable.

Visualizing pairs of variables

library(ggplot2)

ggplot(
  swedish_motor_insurance, 
  aes(n_claims, total_payment_sek)
) +
  geom_point()

A scatter plot of the total payment versus the number of claims. The payment increases as the number of claims increases.

Adding a linear trend line

library(ggplot2)

ggplot(
  swedish_motor_insurance, 
  aes(n_claims, total_payment_sek)
) +
  geom_point() +
  geom_smooth(
    method = "lm", 
    se = FALSE
  )

The same scatter plot seen previously, now with an additional trend line calculated via linear regression. It provides a reasonable fit to the data.

Course flow

Chapter 1

Visualizing and fitting linear regression models.

Chapter 2

Making predictions from linear regression models and understanding model coefficients.

Chapter 3

Assessing the quality of the linear regression model.

Chapter 4

Same again, but with logistic regression models

Let's practice!

Introduction to Regression in R