Parallel slopes linear regression

Intermediate Regression in R

Richie Cotton

Data Evangelist at DataCamp

The previous course

This course assumes knowledge from Introduction to Regression in R.

From simple regression to multiple regression

Multiple regression is a regression model with more than one explanatory variable.

More explanatory variables can give more insight and better predictions.

The course contents

Chapter 1

"Parallel slopes" regression

Chapter 2

Interactions
Simpson's Paradox

Chapter 3

More explanatory variables
How linear regression works

Chapter 4

Multiple logistic regression
The logistic distribution
How logistic regression works

The fish dataset

mass_g	length_cm	species
242.0	23.2	Bream
5.9	7.5	Perch
200.0	30.0	Pike
40.0	12.9	Roach

Each row represents a fish
mass_g is the response variable
1 numeric, 1 categorical explanatory variable

One explanatory variable at a time

mdl_mass_vs_length <- lm(mass_g ~ length_cm, data = fish)

Call:
lm(formula = mass_g ~ length_cm, data = fish)

Coefficients:
(Intercept)    length_cm  
     -536.2         34.9

1 intercept coefficient
1 slope coefficient

mdl_mass_vs_species <- lm(mass_g ~ species + 0, data = fish)

Call:
lm(formula = mass_g ~ species + 0, data = fish)

Coefficients:
speciesBream  speciesPerch   speciesPike  speciesRoach  
       617.8         382.2         718.7         152.0

1 intercept coefficient for each category

Both variables at same time

mdl_mass_vs_both <- lm(mass_g ~ length_cm + species + 0, data = fish)

Call:
lm(formula = mass_g ~ length_cm + species + 0, data = fish)

Coefficients:
   length_cm  speciesBream  speciesPerch   speciesPike  speciesRoach  
       42.57       -672.24       -713.29      -1089.46       -726.78

1 slope coefficient
1 intercept coefficient for each category

Comparing coefficients

coefficients(mdl_mass_vs_length)

(Intercept)   length_cm 
     -536.2        34.9

coefficients(mdl_mass_vs_species)

speciesBream speciesPerch  speciesPike speciesRoach 
       617.8        382.2        718.7        152.0

coefficients(mdl_mass_vs_both)

length_cm speciesBream speciesPerch  speciesPike speciesRoach 
    42.57      -672.24      -713.29     -1089.46      -726.78

Visualization: 1 numeric explanatory var

library(ggplot2)

ggplot(fish, aes(length_cm, mass_g)) +
  geom_point() +
  geom_smooth(method = "lm", se = FALSE)

Visualization: 1 categorical explanatory var

ggplot(fish, aes(species, mass_g)) +
  geom_boxplot() + 
  stat_summary(fun.y = mean, shape = 15)

Visualization: both explanatory vars

library(moderndive)

ggplot(fish, aes(length_cm, mass_g, color = species)) +
  geom_point() +
  geom_parallel_slopes(se = FALSE)

Let's practice!

Intermediate Regression in R