NCEA Level 3 Statistics: Model Purpose & Reliability

Model Purpose & Reliability

Lesson 2: US Crime vs. Poverty Dataset (NCEA Level 3 Statistics)

1. Why do we build models?

Once we establish a relationship exists, we calculate a Line of Best Fit. This is our mathematical model. Its entire purpose is to make predictions. By inputting an explanatory value (x), the equation estimates the response (y). Use the Prediction Tool below to see how the model calculates expected crime rates based on poverty levels.

Eq: y = 63.0x + 159.0
r = 0.85

Evaluate the Reliability of this Model:

A random scenario has been generated. Use the vocabulary tree below to evaluate how reliable this mathematical model is for making predictions.

Model Evaluation Framework
- Baseline Trend
  Equation (y=mx+c) Gradient Correlation (r-value)
  Impact: Establishes the expected response and overall predictive strength.
- Outliers (X & Y Axes)
  Leverage Influential Point "Pulling the gradient"
  Impact: Tilts or shifts the line, making predictions for normal data points inaccurate.
- Variation
  Heteroscedasticity Fan Effect Non-constant Scatter
  Impact: Expanding scatter means predictions at high x-values become highly unreliable.