Correlation Coefficient

#Math

Examples

Temperature in Celcius and Fahrenheit: 1.0
Building Height and Number of Stories: 0.951
Age of Driver and Seeing Distance: -0.801
Smoking vs. Lung Cancer: 0.716
MCAT CARS vs SAT Verbal: 0.60
IQ vs. Income: ...
MCAT vs SAT: 0.45
Height and GPA of Students: -0.053

"Correlation Coefficient (r)": [
        # Perfect / near‑perfect
        ("Temperature °C vs °F (exactly linear)", 1.00),
        ("Length in inches vs centimetres (unit conversion)", 1.00),
        ("Age in months vs age in years (same people)", 0.99),
        ("Building height vs number of stories", 0.951),  # Very strong positive (0.8 – 0.99) PSU example
        ("Adult height vs femur length", 0.90),
        ("SAT Math vs SAT Total score", 0.89),
        ("Systolic vs diastolic blood pressure", 0.85),
        ("GDP per capita vs electricity consumption", 0.84),
        ("Study hours vs course grade (intro stats class)", 0.82),  # Strong positive (0.6 – 0.79)
        ("Smoking prevalence vs lung‑cancer mortality (countries)", 0.716),
        ("MCAT CARS vs SAT Verbal subscores", 0.60),
        ("VO₂ max vs 1‑mile run time (negative time removed)", 0.68),
        ("Years education vs log‑income (US)", 0.63),
        ("Height vs weight (adult males)", 0.70),  # Moderate positive (0.3 – 0.59)
        ("IQ vs income (US, log scale)", 0.45),
        ("Quantum efficiency vs solar‑panel output", 0.55),
        ("Coffee consumption vs alertness score", 0.48),
        ("Screen time vs myopia risk (teens)", 0.34),
        ("Daily step count vs resting heart‑rate (inverse sign handled)", 0.38),  # Weak / negligible (|r| < 0.3)
        ("Height vs GPA of college students", -0.053),
        ("Hand span vs piano skill rating", 0.20),
        ("Birth month vs academic performance (large UK sample)", 0.09),
        ("Chocolate consumption vs Nobel laureates (countries)", 0.10),
        ("Age of driver vs distance at which road signs legible", -0.801),
        # Moderate / strong negative (-0.3 → -0.8) PSU example
        ("Daily temperature vs heating‑energy use", -0.75),
        ("Body‑fat % vs vertical‑jump height", -0.64),
        ("Hours of sleep vs daytime sleepiness score", -0.58),
        ("Job stress index vs job satisfaction", -0.52),  # Very strong negative (< –0.8)
        ("Ambient noise level vs speech intelligibility", -0.90),
        ("Elevation vs boiling‑point temperature", -0.97),
        # Practically zero / independence check
        ("Shoe size vs exam score (high‑school sample)", 0.00),
    ],