Chapter 5 · Data Analysis: A Concise Overview of Statistical Techniques · Slide 212/274
Linear Correlation Coefficient
Worked Example
5.2.3 · Relationship between Two VariablesWorked Example
Linear Correlation Coefficient
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 |
| 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 |
QUESTIONSTAR · Dr. Paul Marx212 / 274