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## Statistics and probability

### Course: Statistics and probability>Unit 5

Lesson 2: Correlation coefficients

# Correlation coefficient review

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 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.
Here are some facts about r:
• It always has a value between minus, 1 and 1.
• Strong positive linear relationships have values of r closer to 1.
• Strong negative linear relationships have values of r closer to minus, 1.
• Weaker relationships have values of r closer to 0.
Let's look at a few examples:

### Practice problem

Match the correlation coefficients with the scatterplots shown below.
start color #1fab54, start text, S, c, a, t, t, e, r, p, l, o, t, space, A, end text, end color #1fab54start color #ca337c, start text, S, c, a, t, t, e, r, p, l, o, t, space, B, end text, end color #ca337c
|
start color #e07d10, start text, S, c, a, t, t, e, r, p, l, o, t, space, C, end text, end color #e07d10start color #11accd, start text, S, c, a, t, t, e, r, p, l, o, t, space, D, end text, end color #11accd

Want to practice more problems like this? Check out this exercise on correlation coefficient intuition.

## Want to join the conversation?

• i dont know what im still doing here
• How can we prove that the value of r always lie between 1 and -1 ?
• 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?
• Theoretically, yes. The r-value you are referring to is specific to the linear correlation.
• I am taking Algebra 1 not whatever this is but I still chose to do this
• 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?
• Calculating the correlation coefficient is complex, but is there a way to visually
• 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)
• Is the correlation coefficient a measure of the association between two random variables?