# Linear correaltion

**Keywords:** correlation, linear correlation, linearity, pearson product moment correlation

**Description:** How to compute and interpret linear correlation coefficient (Pearson product-moment). Includes equations, sample problems, solutions. Plus free, video lesson.

**Correlation coefficients** measure the strength of association between two variables. The most common correlation coefficient, called the **Pearson product-moment correlation coefficient**. measures the strength of the *linear association* between variables.

In this tutorial, when we speak simply of a correlation coefficient, we are referring to the Pearson product-moment correlation. Generally, the correlation coefficient of a sample is denoted by *r*. and the correlation coefficient of a population is denoted by ρ or *R* .

The sign and the absolute value of a correlation coefficient describe the direction and the magnitude of the relationship between two variables.

- The value of a correlation coefficient ranges between -1 and 1. The greater the absolute value of a correlation coefficient, the stronger the
- A negative correlation means that if one variable gets bigger, the other variable tends to get smaller.

*linear*relationship. The strongest linear relationship is indicated by a correlation coefficient of -1 or 1. The weakest linear relationship is indicated by a correlation coefficient equal to 0. A positive correlation means that if one variable gets bigger, the other variable tends to get bigger.

Keep in mind that the Pearson product-moment correlation coefficient only measures linear relationships. Therefore, a correlation of 0 does not mean zero relationship between two variables; rather, it means zero *linear* relationship. (It is possible for two variables to have zero linear relationship and a strong curvilinear relationship at the same time.)

The scatterplots below show how different patterns of data produce different degrees of correlation.