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### 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 $-1$ and $1$.
• Strong positive linear relationships have values of $r$ closer to $1$.
• Strong negative linear relationships have values of $r$ closer to $-1$.
• 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.
$\text{Scatterplot A}$$\text{Scatterplot B}$
|
$\text{Scatterplot C}$$\text{Scatterplot D}$

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?
• 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)
• lots of data points. definition is easy to understand.