Assessing model performance

Intermediate Regression in R

Richie Cotton

Data Evangelist at DataCamp

Model performance metrics

Coefficient of determination (R-squared): how well the linear regression line fits the observed values.
- Larger is better.
Residual standard error (RSE): the typical size of the residuals.
- Smaller is better.

library(dplyr)
library(broom)

mdl_mass_vs_length %>% 
  glance() %>% 
  pull(r.squared)

0.8226

mdl_mass_vs_species %>% 
  glance() %>% 
  pull(r.squared)

0.7163

mdl_mass_vs_both %>% 
  glance() %>% 
  pull(r.squared)

0.9694

More explanatory variables increases $R^2$.
Too many explanatory variables causes overfitting.
Adjusted coefficient of determination penalizes more explanatory variables.
$\bar{R ^ 2} = 1 - (1 - R ^ 2) \frac{n_{obs} - 1}{n_{obs} - n_{var} - 1}$
Penalty is noticeable when $R^2$ is small, or $n_{var}$ is large fraction of $n_{obs}$.
In glance(), it's the adj.r.squared element.

library(dplyr)
library(broom)

mdl_mass_vs_length %>% 
  glance() %>% 
  select(r.squared, adj.r.squared)

  r.squared adj.r.squared
      <dbl>         <dbl>
1    0.8226        0.8212

mdl_mass_vs_species %>% 
  glance() %>% 
  select(r.squared, adj.r.squared)

  r.squared adj.r.squared
      <dbl>         <dbl>
1    0.7163        0.7072

mdl_mass_vs_both %>% 
  glance() %>% 
  select(r.squared, adj.r.squared)

  r.squared adj.r.squared
      <dbl>         <dbl>
1    0.9694        0.9682

library(dplyr)
library(broom)

mdl_mass_vs_length %>% 
  glance() %>% 
  pull(sigma)

152.1

mdl_mass_vs_species %>% 
  glance() %>% 
  pull(sigma)

313.6

mdl_mass_vs_both %>% 
  glance() %>% 
  pull(sigma)

103.4

Intermediate Regression in R