---
url: "https://questionstar.com/principles-of-survey-research/chapter-5/slide-212.html"
title: "Linear Correlation Coefficient"
type: "lehrbuch-slide"
chapter: 5
chapterTitle: "Data Analysis: A Concise Overview of Statistical Techniques"
slide: 212
---

# Linear Correlation Coefficient

*Worked Example*

Strength of the Relationship between Variables

| r-value | Interpretation |
|------|------|
| 0 to 0.3 | Very weak |
| 0.3 to 0.5 | Weak |
| 0.5 to 0.7 | Moderate |
| 0.7 to 0.9 | High |
| 0.9 to 1 | Very high |

![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)

| x | y | (xᵢ−x̄) | (yᵢ−ȳ) | (xᵢ−x̄)(yᵢ−ȳ) | (xᵢ−x̄)² | (yᵢ−ȳ)² |
|------|------|------|------|------|------|------|
| 86 | 98 | 12.5 | 13.5 | 168.75 | 156.25 | 182.25 |
| 62 | 70 | −11.5 | −14.5 | 166.75 | 132.25 | 210.25 |
| 52 | 56 | −21.5 | −28.5 | 612.75 | 462.25 | 812.25 |
| 90 | 110 | 16.5 | 25.5 | 420.75 | 272.25 | 650.25 |
| 66 | 76 | −7.5 | −8.5 | 63.75 | 56.25 | 72.25 |
| 80 | 96 | 6.5 | 11.5 | 74.75 | 42.25 | 132.25 |
| 78 | 86 | 4.5 | 1.5 | 6.75 | 20.25 | 2.25 |
| 74 | 84 | 0.5 | −0.5 | −0.25 | 0.25 | 0.25 |
| Mean | 73.5 | 84.5 |  |  |  |  |
| Sum |  |  |  | 1514 | 1142 | 2062 |

![r = 1514 divided by (Sqrt 1142 times Sqrt 2062) ≈ 0.987](/principles-of-survey-research/media/formel_r_bsp.png)

*[Diagramm: Linear Correlation Coefficient]*

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*Slide 212 of 274 · Chapter 5: Data Analysis: A Concise Overview of Statistical Techniques · Principles of Survey Research · Dr. Paul Marx*