Statistics and probability
The correlation coefficient r measures the direction and strength of a linear relationship. Calculating r is pretty complex, so we usually rely on technology for the computations. We focus on understanding what r says about a scatterplot.
What is a correlation coefficient?
The correlation coefficient measures the direction and strength of a linear relationship. Calculating is pretty complex, so we usually rely on technology for the computations. We focus on understanding what says about a scatterplot.
Here are some facts about :
- It always has a value between and .
- Strong positive linear relationships have values of closer to .
- Strong negative linear relationships have values of closer to .
- Weaker relationships have values of closer to .
Let's look at a few examples:
Want to learn more about the correlation coefficient? Check out this video.
Match the correlation coefficients with the scatterplots shown below.
Want to practice more problems like this? Check out this exercise on correlation coefficient intuition.
Want to join the conversation?
- How can we prove that the value of r always lie between 1 and -1 ?(12 votes)
- Weaker relationships have values of r closer to 0. But r = 0 doesn’t mean that there is no relation between the variables, right? I mean, if r = 0 then there is no linear correlation, but we still could have a non linear correlation?(6 votes)
- Calculating the correlation coefficient is complex, but is there a way to visually "estimate" it by looking at a scatter plot? Or do we have to use computors for that?(4 votes)
- Calculating the correlation coefficient is complex, but is there a way to visually(2 votes)
- Yes on a scatterplot if the dots seem close together it indicates the r is high. If points are from one another the r would be low.(1 vote)
- When it is said that to calculate the correlation coefficient is complex, is this simply because there are a lot of data points at play, or is the math difficult to comprehend for the course level?(1 vote)
- How does the slope of r relate to the actual correlation coefficient?
For example, if the points of Scatter Plot A form a perfect line y=0.25x, and the points of Scatter Plot B also form perfect line y=3x, would the correlation coefficient be r=1 for both?(1 vote)
- Yes, the correlation coefficient measures two things, form and direction. If you have two lines that are both positive and perfectly linear, then they would both have the same correlation coefficient. The only way the slope of the regression line relates to the correlation coefficient is the direction(2 votes)