Concept 4

Compare models and select a better fit based on given evidence/data.

Compare residuals across the same data points to decide which model fits better.

Core Idea

A better model is the one that stays closer to the data. Compare the size of the errors, not just the look of the equation.

Understanding

Rule: Smaller residuals mean a better fit.

  • Use the same observed values for both models.
  • Compare absolute residuals, not just one nice-looking point.
  • Choose the model with the smaller overall error.

Step by Step

  1. Use each model to predict the output for the same input values.
  2. Compare each prediction with the actual data value.
  3. Compute or estimate the absolute residuals.
  4. Choose the model with the smaller overall error or the stronger overall fit.

Misconceptions

  • Choosing the model with the larger slope just because it changes faster.
  • Comparing raw predictions without checking which one is actually closer to the observed data.
  • Assuming two models fit equally well because both are linear.
Question

Worked Example

A student's study hours and quiz scores are shown below.

Hours studied Actual quiz score
2 68
4 79
6 90

Model A: 𝑠 =5ℎ +58

Model B: 𝑠 =6ℎ +55

Based on the data, which statement is best supported?

Select an answer to see the explanation