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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:
Example where r, equals, 1, which is perfect positive correlation
Example where r, equals, 0, point, 5, which is weak positive correlation
Example where r, equals, 0, which is no correlation
Example where r, equals, minus, 0, point, 5, which is weak negative correlation
Example where r, equals, minus, 1, which is perfect negative correlation

### 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
A scatterplot labeled Scatterplot A on an x y coordinate plane. Points rise diagonally in a relatively narrow pattern.
|
A scatterplot labeled Scatterplot B on an x y coordinate plane. Points rise diagonally in a relatively weak pattern.
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
A scatterplot labeled Scatterplot C on an x y coordinate plane. Points fall diagonally in a relatively narrow pattern.
A scatterplot labeled Scatterplot B on an x y coordinate plane. Points fall diagonally in a weak pattern.

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?