The Correlation Coefficient
Aligned to S-ID.C.8 — Common Core State Standards for Mathematics.
What this lesson teaches
The correlation coefficient r measures how closely points follow a straight line, ranging from −1 to 1. Values near 1 or −1 show a strong linear relationship; values near 0 show a weak one.
Worked examples
Example 1
A data set has r = 0.95. Since 0.95 is close to 1, the points lie close to a rising line, showing a strong positive linear relationship between the two variables.
Example 2
r = −0.9 is just as strong as r = 0.9. The sign gives direction and the magnitude gives strength.
Example 3
r only measures LINEAR fit. A perfect parabola can have r near 0 while the relationship is exact.
Practice questions
- Does r = −0.9 show a strong or weak relationship? Rising or falling?
- Which is stronger: r = 0.3 or r = −0.8?
- What does r near 0 tell you about a linear fit?
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
El Coeficiente de Correlación
El coeficiente de correlación r mide qué tan de cerca siguen los puntos una línea recta, y va de −1 a 1. Los valores cercanos a 1 o −1 muestran una relación lineal fuerte; los cercanos a 0 muestran una débil.
Ejemplo 1: Un conjunto de datos tiene r = 0.95. Como 0.95 está cerca de 1, los puntos quedan cerca de una recta ascendente, lo que muestra una relación lineal positiva fuerte entre las dos variables.
Ejemplo 2: r = −0.9 es igual de fuerte que r = 0.9. El signo da la dirección y la magnitud da la fuerza.
Ejemplo 3: r solo mide el ajuste LINEAL. Una parábola perfecta puede tener r cerca de 0 aunque la relación sea exacta.
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