The question asks for the correct interpretation comparing two correlation coefficients, $r_1 = 0.6$ and $r_2 = 0.3$. While direct comparison suggests $r_1$ is twice $r_2$, a common statistical interpretation compares the proportion of variance explained, represented by the square of the correlation coefficient ($r^2$).

Interpreting Correlation Strength via Variance Explained

The coefficient of determination, $r^2$, indicates the proportion of the variance in the dependent variable that is predictable from the independent variable(s). Comparing correlation coefficients is often done by comparing their $r^2$ values.

Calculating Squared Coefficients

1. Calculate $r_1^2$: $r_1^2 = (0.6)^2 = 0.36$
2. Calculate $r_2^2$: $r_2^2 = (0.3)^2 = 0.09$

Comparing Variance Explained

Now, compare the squared values to see how many times greater $r_1^2$ is compared to $r_2^2$:

Ratio = $\frac{r_1^2}{r_2^2} = \frac{0.36}{0.09} = 4$

This calculation shows that the variance explained by the relationship associated with $r_1$ is 4 times the variance explained by the relationship associated with $r_2$. Therefore, in terms of the proportion of variance explained, $r_1$ is considered four times as high as $r_2$.

Conclusion

Based on the comparison of the coefficients of determination ($r^2$), $r_1$ explains four times the variance explained by $r_2$. This interpretation aligns with Option D.

Given values:

• $r_1 = 0.6$
• $r_2 = 0.3$

Analysis of Options:

• Option 1: $|r_1 - r_2| = |0.6 - 0.3| = 0.3$. (True statement, but not the intended comparison).
• Option 2: $r_1 = 2 \times r_2 \implies 0.6 = 2 \times 0.3$. (True statement, but not the intended comparison).
• Option 3: $r_1 = 3 \times r_2 \implies 0.6 = 3 \times 0.3 = 0.9$. (False).
• Option 4: Interpreting "as high as" via $r^2$: $\frac{r_1^2}{r_2^2} = \frac{(0.6)^2}{(0.3)^2} = \frac{0.36}{0.09} = 4$. Thus, $r_1^2$ is 4 times $r_2^2$. This matches the structure "r$_1$ is four times as high as r$_2$". (True under $r^2$ interpretation).

Final Answer Determination: The interpretation comparing the variance explained ($r^2$) leads to the conclusion that $r_1$ is four times as high as $r_2$.