---
url: "https://questionstar.com/principles-of-survey-research/chapter-5/slide-211.html"
title: "Linear Correlation Coefficient"
type: "lehrbuch-slide"
chapter: 5
chapterTitle: "Data Analysis: A Concise Overview of Statistical Techniques"
slide: 211
---

# Linear Correlation Coefficient

*The (Pearson) linear correlation coefficient measures the strength of the linear relationship between two variables.*

Properties:

- Values of the linear correlation coefficient always lie between **−1 and 1** .
- When r = +1 there is a perfect **positive** linear relationship between the variables.
- When r = −1 there is a perfect **negative** linear relationship between the variables.
- The closer r is to +1 or −1, the stronger the respective relationship.
- If r is close to **0** , there is little evidence of a linear relationship — but this does not mean there is no relationship at all, just no *linear* .

### Linear Correlation Coefficient

The **(Pearson) linear correlation coefficient** measures the strength of the linear relationship between two variables.

![r = Sum (x_i − x̄)(y_i − ȳ) divided by Sqrt(Sum (x_i − x̄)²) times Sqrt(Sum (y_i − ȳ)²)](/principles-of-survey-research/media/formel_r_pearson.png)

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*Slide 211 of 274 · Chapter 5: Data Analysis: A Concise Overview of Statistical Techniques · Principles of Survey Research · Dr. Paul Marx*