Example: Correlation coefficient intuition  Mathematics I  High School Math  Khan Academy  Summary and Q&A
TL;DR
Correlation coefficients measure the strength and direction of the relationship between two variables, with values ranging from 1 to 1.
Questions & Answers
Q: What do correlation coefficients measure?
Correlation coefficients measure the strength and direction of the linear relationship between two variables. They provide a numerical value that indicates how well a linear model can describe the relationship.
Q: How is a correlation coefficient of 1 different from a correlation coefficient of 1?
A correlation coefficient of 1 indicates a perfect positive correlation, meaning that as one variable increases, the other also increases. On the other hand, a correlation coefficient of 1 indicates a perfect negative correlation, where as one variable increases, the other decreases.
Q: What does a correlation coefficient of 0 signify?
A correlation coefficient of 0 indicates no linear relationship between the variables. In other words, changes in one variable do not affect the other variable in a predictable manner.
Q: How do scatterplots help in understanding correlation coefficients?
Scatterplots visually represent the relationship between two variables, allowing us to see patterns and trends. By examining the scatterplot, we can gain insights into the correlation coefficient and determine if there is a linear relationship.
Summary & Key Takeaways

Correlation coefficients are used to measure how well a linear model can describe the relationship between two variables.

A correlation coefficient of 1 indicates a perfect positive correlation, where as one variable increases, the other also increases.

A correlation coefficient of 1 indicates a perfect negative correlation, where as one variable increases, the other decreases.

A correlation coefficient of 0 indicates no linear relationship between the variables.