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 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.
  • A negative correlation means that if one variable gets bigger, the other variable tends to get smaller.

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.






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