APFIVE Regarding the coefficient of determination $$$$r^2$$$$ in a regression analysis, rank the following statements in order of logical interpretation from most central to more descriptive details. That is, start with the primary definition and progress to additional properties:
- Represents the percentage of variability in the response variable explained by the linear model.
- Equals 1 minus the proportion of unexplained variation.
- Indicates the association strength without implying causation.
- Is the square of the correlation coefficient.
TITLE: Coefficient of Determination Interpretation: #000000
| Property | Description |
|---|---|
| 1 | Represents the percentage of variability in $$y$$ explained by the model. |
| 2 | Equals 1 minus the proportion of unexplained variation. |
| 3 | Is the square of the correlation coefficient (thus non-negative). |
| 4 | Indicates association strength without implying causation. |
Indicates association strength (without causation), Square of the correlation coefficient, Percentage of variability explained, 1 minus unexplained variability (this order begins with a secondary property rather than the primary definition)
Square of the correlation coefficient, Percentage of variability explained, 1 minus unexplained variability, Indicates association strength (without causation)
Percentage of variability explained, 1 minus unexplained variability, Indicates association strength (without causation), Square of the correlation coefficient
1 minus unexplained variability, Percentage of variability explained, Square of the correlation coefficient, Indicates association strength (without causation)
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