To determine the best estimated correlation coefficient based on the given data, let's first examine the values in the table you provided:
- When \( x = -1 \), \( y = -10 \)
- When \( x = 0 \), \( y = -8 \)
- When \( x = 1 \), \( y = -7 \)
- When \( x = 2 \), \( y = -5 \)
- When \( x = 3 \), \( y = -3 \)
- When \( x = 4 \), \( y = -1 \)
Now, let's identify the trend of the data:
- As \( x \) increases from -1 to 4, the value of \( y \) increases from -10 to -1.
- This indicates a positive correlation between \( x \) and \( y \).
However, if you were to consider the \( y \) values being negative, the overall relationship would be interpreted in the context of the values of \( y \)—increasing from -10 (a relatively more negative value) to -1 (less negative).
To evaluate the correlation coefficient (denoted as \( r \)):
- If the points form a strong linear pattern, \( r \) will be close to 1 (in this case, positive).
- If the points form a strong linear pattern but negatively correlated, \( r \) would be close to -1.
Given your options:
- −1 (perfect negative correlation)
- 0.98 (very strong positive correlation)
- −0.98 (strong negative correlation)
- −0.90 (strong negative correlation)
The data trend shows a linear increase in \( y \) with increasing \( x \). Therefore, the best estimate choice for the correlation coefficient based on the scatter plot you would create from the table is:
0.98 (very strong positive correlation).