Questions: The correlation between percentage voting Democrat in 1980 and percentage voting Democrat in 1984 is r=0.704. The correlation between percentage of high school seniors taking the SAT and average SAT Mathematics score in the states is r=-0.86 Which of these two correlations indicates a stronger straight-line relationship? Explain your answer. The correlation r=-0.86 is stronger because -0.86 is smaller than 0.704. The correlation r=0.704 is stronger because 0.704 is larger than -0.86. The correlation r=-0.86 is stronger because the absolute value of -0.86 is closer to 1 than is the absolute value of 0.704. The correlation r=0.704 is stronger because the absolute value of 0.704 is closer to 0 than the absolute value of -0.86.

The correlation between percentage voting Democrat in 1980 and percentage voting Democrat in 1984 is r=0.704. The correlation between percentage of high school seniors taking the SAT and average SAT Mathematics score in the states is r=-0.86

Which of these two correlations indicates a stronger straight-line relationship? Explain your answer. The correlation r=-0.86 is stronger because -0.86 is smaller than 0.704. The correlation r=0.704 is stronger because 0.704 is larger than -0.86. The correlation r=-0.86 is stronger because the absolute value of -0.86 is closer to 1 than is the absolute value of 0.704. The correlation r=0.704 is stronger because the absolute value of 0.704 is closer to 0 than the absolute value of -0.86.

Transcript text: of The correlation between percentage voting Democrat in 1980 and percentage voting Democrat in 1984 is $r=0.704$. The correlation between percentage of high school seniors taking the SAT and average SAT Mathematics score in the states is $r=-0.86$ Which of these two correlations indicates a stronger straight-line relationship? Explain your answer. The correlation $r=-0.86$ is stronger because -0.86 is smaller than 0.704 . The correlation $r=0.704$ is stronger because 0.704 is larger than -0.86 . The correlation $r=-0.86$ is stronger because the absolute value of -0.86 is closer to 1 than is the absolute value of 0.704 . The correlation $r=0.704$ is stronger because the absolute value of 0.704 is closer to 0 than the absolute value of -0.86 .

Solution

Solution Steps

Step 1: Calculate Absolute Values of Correlations

The correlation between the percentage voting Democrat in 1980 and 1984 is given as $ r = 0.704 $. The absolute value of this correlation is:

\[ |r_{1980, 1984}| = 0.704 \]

The correlation between the percentage of high school seniors taking the SAT and the average SAT Mathematics score is given as $ r = -0.86 $. The absolute value of this correlation is:

\[ |r_{SAT}| = 0.86 \]

Step 2: Compare Absolute Values

Next, we compare the absolute values of the two correlations:

\[ |r_{1980, 1984}| = 0.704 \quad \text{and} \quad |r_{SAT}| = 0.86 \]

Since $ 0.86 > 0.704 $, we conclude that the correlation $ r = -0.86 $ indicates a stronger straight-line relationship.

Step 3: Conclusion

The correlation $ r = -0.86 $ is stronger because the absolute value of $ -0.86 $ is closer to $ 1 $ than the absolute value of $ 0.704 $.