make_forbes_check_data: Forbes Dataset (1857)¶
The make_forbes_check_data function retrieves Forbes' historic dataset on boiling points measured in the Alps. This dataset is a standard benchmark in robust statistics, often used to demonstrate the impact of outliers on regression models.
Overview¶
Collected by James D. Forbes in the 19th century, this dataset contains 17 observations of the boiling point of water and barometric pressure at various altitudes in the Alps.
- Features (\(X\)): Boiling Point in degrees Fahrenheit (\(^\circ\)F).
- Target (\(y\)): Barometric Pressure in inches of mercury (inHg).
- Significance: It is classically used to demonstrate robust regression because Observation 12 is widely considered an outlier (likely due to a transcription or measurement error) that skews standard least-squares regression.
- Typical Usage: Modeling the relationship: \(100 \times \log_{10}(\text{Pressure}) \sim \text{BoilingPoint}\).
Returns¶
| Return | Type | Description |
|---|---|---|
X |
numpy.ndarray | Boiling Point (\(^\circ\)F). Shape (17, 1). |
y |
numpy.ndarray | Pressure (inHg). Shape (17,). |
Example Usage¶
from machinegnostics.datasets import make_forbes_check_data
import numpy as np
# Load the dataset
X, y = make_forbes_check_data()
print(f"Dataset shape: X={X.shape}, y={y.shape}")
# Output: Dataset shape: X=(17, 1), y=(17,)
# Inspect the known outlier (Index 11, Observation 12)
print(f"Observation 12: Boiling Point={X[11,0]}, Pressure={y[11]}")
Source: Forbes, J. D. (1857). "Further experiments on the boiling point of water". Transactions of the Royal Society of Edinburgh. 21 (2): 235–243.
Author: Nirmal Parmar