Question

Use the table to answer the question.

−1
−10

0 −8

1 −7

2 −5

3 −3

4 −1

Use the data table to create a scatter plot. Based on the data, which of the following choices would be the best estimated correlation coefficient?

(1 point)
Responses

−1
negative 1

0.98
0.98

−0.98
negative 0.98

−0.90

Answer 1

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:

1. As \( x \) increases from -1 to 4, the value of \( y \) increases from -10 to -1.
2. 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. **−1** (perfect negative correlation)
2. **0.98** (very strong positive correlation)
3. **−0.98** (strong negative correlation)
4. **−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).