penguins-lm

1 Exercise

Consider the dataset penguins. Compute a linear model with body mass as output variable (DV) and flipper length as input (IV).

1. Report the coefficients and interpret them.
2. Plot the model and the coefficients.
3. Report the model fit (R squared).
4. BONUS: predict() the weight of an average flipper-sized animal. Check out the internet for examples of how to do so in case you need support.

2 Solution

2.1 Setup

library(tidyverse)
library(easystats)
library(ggpubr)

# import data:
penguins <- read.csv("https://vincentarelbundock.github.io/Rdatasets/csv/palmerpenguins/penguins.csv")

2.2 Let’s go

lm1 <- lm(body_mass_g ~ flipper_length_mm, data = penguins)

Plot the model:

plot(estimate_relation(lm1))

Alternative plotting method:

ggscatter(penguins,
          x = "flipper_length_mm",
          y = "body_mass_g",
          add ="reg.line")

Coefficients (parameters):

parameters(lm1)

Parameter	Coefficient	SE	CI	CI_low	CI_high	t	df_error	p
(Intercept)	-5781	305.8	0.95	-6382	-5179	-19	340	0
flipper_length_mm	50	1.5	0.95	47	53	33	340	0

Plot the coefficients:

plot(parameters(lm1))

Model fit (explained variance by model):

r2(lm1)

# R2 for Linear Regression
       R2: 0.759
  adj. R2: 0.758

Predict weight of average animal:

penguins |> 
  summarise(flipper_length_mm_avg = 
              mean(flipper_length_mm, na.rm = TRUE))

flipper_length_mm_avg
201

2.3 For average flipper length, what’s the expected weight?

predict(lm1, newdata = data.frame(flipper_length_mm = 200))

   1 
4156 

Around 4 kgs.

2.4 Centering the data

Center the data:

penguins_c <-
  penguins |> 
  mutate(flipper_length_mm_c = center(flipper_length_mm))

Now the mean value is (nearly) zero:

mean(penguins_c$flipper_length_mm_c, na.rm = TRUE)

[1] -1.2e-14

Run the model again:

lm2 <- lm(body_mass_g ~ flipper_length_mm_c, data = penguins_c)

parameters(lm2)

Parameter	Coefficient	SE	CI	CI_low	CI_high	t	df_error	p
(Intercept)	4202	21.3	0.95	4160	4244	197	340	0
flipper_length_mm_c	50	1.5	0.95	47	53	33	340	0