APFIVE Coefficient of Determination and Slope
When interpreting regression analysis output, which of the following is true about the relationship between the coefficient of determination $$ R^2 $$ and the slope estimate?
| Regression Summary Statistics |
|---|
| Coefficient of Determination (R^2): $$0.75$$ |
(This value represents the proportion of variance explained by the predictor.)
A
The $$ R^2 $$ value and the slope estimate are redundant measures of the same relationship.
B
A lower $$ R^2 $$ means the slope must be nearly zero.
C
A higher $$ R^2 $$ indicates a larger proportion of variability in the response explained by the predictor, but does not necessarily imply a steeper slope.
D
A higher $$ R^2 $$ always implies that the slope is large and statistically significant.
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